Year 5: Rounding and estimating

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10 that 74 is between. Rounding to the nearest 10 means choosing the closest multiple of 10.
   70  <  74  <  80
2. Look at the ones digit (the digit just to the right of the tens digit). This digit tells us if we are past halfway.
   The ones digit is 4.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   4 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the tens column become zeros.
   74 ≈ 70 (to the nearest 10)

Check. Distances: 74 − 70 = 4 and 80 − 74 = 6. 70 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10 that 365 is between. Rounding to the nearest 10 means choosing the closest multiple of 10.
   360  <  365  <  370
2. Look at the ones digit (the digit just to the right of the tens digit). This digit tells us if we are past halfway.
   The ones digit is 5.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the tens column become zeros.
   365 ≈ 370 (to the nearest 10)

Check. Distances: 365 − 360 = 5 and 370 − 365 = 5. 370 is the one we choose when exactly halfway (halfway rounds up). ✓

Watch out. Only look at the digit just to the right. Do not round twice. Halfway always rounds up.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10 that 2,384 is between. Rounding to the nearest 10 means choosing the closest multiple of 10.
   2,380  <  2,384  <  2,390
2. Look at the ones digit (the digit just to the right of the tens digit). This digit tells us if we are past halfway.
   The ones digit is 4.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   4 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the tens column become zeros.
   2,384 ≈ 2,380 (to the nearest 10)

Check. Distances: 2,384 − 2,380 = 4 and 2,390 − 2,384 = 6. 2,380 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10 that 15,495 is between. Rounding to the nearest 10 means choosing the closest multiple of 10.
   15,490  <  15,495  <  15,500
2. Look at the ones digit (the digit just to the right of the tens digit). This digit tells us if we are past halfway.
   The ones digit is 5.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the tens column become zeros.
   15,495 ≈ 15,500 (to the nearest 10)

Check. Distances: 15,495 − 15,490 = 5 and 15,500 − 15,495 = 5. 15,500 is the one we choose when exactly halfway (halfway rounds up). ✓

Watch out. Only look at the digit just to the right. Do not round twice. Halfway always rounds up.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10 that 70,001 is between. Rounding to the nearest 10 means choosing the closest multiple of 10.
   70,000  <  70,001  <  70,010
2. Look at the ones digit (the digit just to the right of the tens digit). This digit tells us if we are past halfway.
   The ones digit is 1.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   1 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the tens column become zeros.
   70,001 ≈ 70,000 (to the nearest 10)

Check. Distances: 70,001 − 70,000 = 1 and 70,010 − 70,001 = 9. 70,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10 that 428,555 is between. Rounding to the nearest 10 means choosing the closest multiple of 10.
   428,550  <  428,555  <  428,560
2. Look at the ones digit (the digit just to the right of the tens digit). This digit tells us if we are past halfway.
   The ones digit is 5.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the tens column become zeros.
   428,555 ≈ 428,560 (to the nearest 10)

Check. Distances: 428,555 − 428,550 = 5 and 428,560 − 428,555 = 5. 428,560 is the one we choose when exactly halfway (halfway rounds up). ✓

Watch out. Only look at the digit just to the right. Do not round twice. Halfway always rounds up.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100 that 347 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.
   300  <  347  <  400
2. Look at the tens digit (the digit just to the right of the hundreds digit). This digit tells us if we are past halfway.
   The tens digit is 4.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   4 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the hundreds column become zeros.
   347 ≈ 300 (to the nearest 100)

Check. Distances: 347 − 300 = 47 and 400 − 347 = 53. 300 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100 that 3,650 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.
   3,600  <  3,650  <  3,700
2. Look at the tens digit (the digit just to the right of the hundreds digit). This digit tells us if we are past halfway.
   The tens digit is 5.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the hundreds column become zeros.
   3,650 ≈ 3,700 (to the nearest 100)

Check. Distances: 3,650 − 3,600 = 50 and 3,700 − 3,650 = 50. 3,700 is the one we choose when exactly halfway (halfway rounds up). ✓

Watch out. Only look at the digit just to the right. Do not round twice. Halfway always rounds up.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100 that 62,238 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.
   62,200  <  62,238  <  62,300
2. Look at the tens digit (the digit just to the right of the hundreds digit). This digit tells us if we are past halfway.
   The tens digit is 3.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   3 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the hundreds column become zeros.
   62,238 ≈ 62,200 (to the nearest 100)

Check. Distances: 62,238 − 62,200 = 38 and 62,300 − 62,238 = 62. 62,200 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100 that 49,950 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.
   49,900  <  49,950  <  50,000
2. Look at the tens digit (the digit just to the right of the hundreds digit). This digit tells us if we are past halfway.
   The tens digit is 5.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the hundreds column become zeros.
   49,950 ≈ 50,000 (to the nearest 100)

Check. Distances: 49,950 − 49,900 = 50 and 50,000 − 49,950 = 50. 50,000 is the one we choose when exactly halfway (halfway rounds up). ✓

Watch out. Only look at the digit just to the right. Do not round twice. Halfway always rounds up.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100 that 128,449 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.
   128,400  <  128,449  <  128,500
2. Look at the tens digit (the digit just to the right of the hundreds digit). This digit tells us if we are past halfway.
   The tens digit is 4.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   4 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the hundreds column become zeros.
   128,449 ≈ 128,400 (to the nearest 100)

Check. Distances: 128,449 − 128,400 = 49 and 128,500 − 128,449 = 51. 128,400 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100 that 999,960 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.
   999,900  <  999,960  <  1,000,000
2. Look at the tens digit (the digit just to the right of the hundreds digit). This digit tells us if we are past halfway.
   The tens digit is 6.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   6 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the hundreds column become zeros.
   999,960 ≈ 1,000,000 (to the nearest 100)

Check. Distances: 999,960 − 999,900 = 60 and 1,000,000 − 999,960 = 40. 1,000,000 is the nearer one. ✓

Watch out. A 9 can carry: when you round up a 9 it becomes 10, so the next digit goes up too.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 1,000 that 4,280 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.
   4,000  <  4,280  <  5,000
2. Look at the hundreds digit (the digit just to the right of the thousands digit). This digit tells us if we are past halfway.
   The hundreds digit is 2.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   2 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the thousands column become zeros.
   4,280 ≈ 4,000 (to the nearest 1,000)

Check. Distances: 4,280 − 4,000 = 280 and 5,000 − 4,280 = 720. 4,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 1,000 that 36,500 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.
   36,000  <  36,500  <  37,000
2. Look at the hundreds digit (the digit just to the right of the thousands digit). This digit tells us if we are past halfway.
   The hundreds digit is 5.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the thousands column become zeros.
   36,500 ≈ 37,000 (to the nearest 1,000)

Check. Distances: 36,500 − 36,000 = 500 and 37,000 − 36,500 = 500. 37,000 is the one we choose when exactly halfway (halfway rounds up). ✓

Watch out. Only look at the digit just to the right. Do not round twice. Halfway always rounds up.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 1,000 that 79,999 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.
   79,000  <  79,999  <  80,000
2. Look at the hundreds digit (the digit just to the right of the thousands digit). This digit tells us if we are past halfway.
   The hundreds digit is 9.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   9 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the thousands column become zeros.
   79,999 ≈ 80,000 (to the nearest 1,000)

Check. Distances: 79,999 − 79,000 = 999 and 80,000 − 79,999 = 1. 80,000 is the nearer one. ✓

Watch out. A 9 can carry: when you round up a 9 it becomes 10, so the next digit goes up too.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 1,000 that 252,499 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.
   252,000  <  252,499  <  253,000
2. Look at the hundreds digit (the digit just to the right of the thousands digit). This digit tells us if we are past halfway.
   The hundreds digit is 4.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   4 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the thousands column become zeros.
   252,499 ≈ 252,000 (to the nearest 1,000)

Check. Distances: 252,499 − 252,000 = 499 and 253,000 − 252,499 = 501. 252,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 1,000 that 499,501 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.
   499,000  <  499,501  <  500,000
2. Look at the hundreds digit (the digit just to the right of the thousands digit). This digit tells us if we are past halfway.
   The hundreds digit is 5.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the thousands column become zeros.
   499,501 ≈ 500,000 (to the nearest 1,000)

Check. Distances: 499,501 − 499,000 = 501 and 500,000 − 499,501 = 499. 500,000 is the nearer one. ✓

Watch out. A 9 can carry: when you round up a 9 it becomes 10, so the next digit goes up too.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 1,000 that 910,350 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.
   910,000  <  910,350  <  911,000
2. Look at the hundreds digit (the digit just to the right of the thousands digit). This digit tells us if we are past halfway.
   The hundreds digit is 3.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   3 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the thousands column become zeros.
   910,350 ≈ 910,000 (to the nearest 1,000)

Check. Distances: 910,350 − 910,000 = 350 and 911,000 − 910,350 = 650. 910,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10,000 that 38,200 is between. Rounding to the nearest 10,000 means choosing the closest multiple of 10,000.
   30,000  <  38,200  <  40,000
2. Look at the thousands digit (the digit just to the right of the ten thousands digit). This digit tells us if we are past halfway.
   The thousands digit is 8.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   8 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the ten thousands column become zeros.
   38,200 ≈ 40,000 (to the nearest 10,000)

Check. Distances: 38,200 − 30,000 = 8,200 and 40,000 − 38,200 = 1,800. 40,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10,000 that 65,000 is between. Rounding to the nearest 10,000 means choosing the closest multiple of 10,000.
   60,000  <  65,000  <  70,000
2. Look at the thousands digit (the digit just to the right of the ten thousands digit). This digit tells us if we are past halfway.
   The thousands digit is 5.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the ten thousands column become zeros.
   65,000 ≈ 70,000 (to the nearest 10,000)

Check. Distances: 65,000 − 60,000 = 5,000 and 70,000 − 65,000 = 5,000. 70,000 is the one we choose when exactly halfway (halfway rounds up). ✓

Watch out. Only look at the digit just to the right. Do not round twice. Halfway always rounds up.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10,000 that 124,999 is between. Rounding to the nearest 10,000 means choosing the closest multiple of 10,000.
   120,000  <  124,999  <  130,000
2. Look at the thousands digit (the digit just to the right of the ten thousands digit). This digit tells us if we are past halfway.
   The thousands digit is 4.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   4 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the ten thousands column become zeros.
   124,999 ≈ 120,000 (to the nearest 10,000)

Check. Distances: 124,999 − 120,000 = 4,999 and 130,000 − 124,999 = 5,001. 120,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10,000 that 449,500 is between. Rounding to the nearest 10,000 means choosing the closest multiple of 10,000.
   440,000  <  449,500  <  450,000
2. Look at the thousands digit (the digit just to the right of the ten thousands digit). This digit tells us if we are past halfway.
   The thousands digit is 9.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   9 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the ten thousands column become zeros.
   449,500 ≈ 450,000 (to the nearest 10,000)

Check. Distances: 449,500 − 440,000 = 9,500 and 450,000 − 449,500 = 500. 450,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10,000 that 895,001 is between. Rounding to the nearest 10,000 means choosing the closest multiple of 10,000.
   890,000  <  895,001  <  900,000
2. Look at the thousands digit (the digit just to the right of the ten thousands digit). This digit tells us if we are past halfway.
   The thousands digit is 5.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the ten thousands column become zeros.
   895,001 ≈ 900,000 (to the nearest 10,000)

Check. Distances: 895,001 − 890,000 = 5,001 and 900,000 − 895,001 = 4,999. 900,000 is the nearer one. ✓

Watch out. A 9 can carry: when you round up a 9 it becomes 10, so the next digit goes up too.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10,000 that 7,300 is between. Rounding to the nearest 10,000 means choosing the closest multiple of 10,000.
   0  <  7,300  <  10,000
2. Look at the thousands digit (the digit just to the right of the ten thousands digit). This digit tells us if we are past halfway.
   The thousands digit is 7.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   7 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the ten thousands column become zeros.
   7,300 ≈ 10,000 (to the nearest 10,000)

Check. Distances: 7,300 − 0 = 7,300 and 10,000 − 7,300 = 2,700. 10,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100,000 that 340,000 is between. Rounding to the nearest 100,000 means choosing the closest multiple of 100,000.
   300,000  <  340,000  <  400,000
2. Look at the ten thousands digit (the digit just to the right of the hundred thousands digit). This digit tells us if we are past halfway.
   The ten thousands digit is 4.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   4 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the hundred thousands column become zeros.
   340,000 ≈ 300,000 (to the nearest 100,000)

Check. Distances: 340,000 − 300,000 = 40,000 and 400,000 − 340,000 = 60,000. 300,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100,000 that 450,000 is between. Rounding to the nearest 100,000 means choosing the closest multiple of 100,000.
   400,000  <  450,000  <  500,000
2. Look at the ten thousands digit (the digit just to the right of the hundred thousands digit). This digit tells us if we are past halfway.
   The ten thousands digit is 5.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the hundred thousands column become zeros.
   450,000 ≈ 500,000 (to the nearest 100,000)

Check. Distances: 450,000 − 400,000 = 50,000 and 500,000 − 450,000 = 50,000. 500,000 is the one we choose when exactly halfway (halfway rounds up). ✓

Watch out. Only look at the digit just to the right. Do not round twice. Halfway always rounds up.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100,000 that 249,999 is between. Rounding to the nearest 100,000 means choosing the closest multiple of 100,000.
   200,000  <  249,999  <  300,000
2. Look at the ten thousands digit (the digit just to the right of the hundred thousands digit). This digit tells us if we are past halfway.
   The ten thousands digit is 4.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   4 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the hundred thousands column become zeros.
   249,999 ≈ 200,000 (to the nearest 100,000)

Check. Distances: 249,999 − 200,000 = 49,999 and 300,000 − 249,999 = 50,001. 200,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100,000 that 650,100 is between. Rounding to the nearest 100,000 means choosing the closest multiple of 100,000.
   600,000  <  650,100  <  700,000
2. Look at the ten thousands digit (the digit just to the right of the hundred thousands digit). This digit tells us if we are past halfway.
   The ten thousands digit is 5.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the hundred thousands column become zeros.
   650,100 ≈ 700,000 (to the nearest 100,000)

Check. Distances: 650,100 − 600,000 = 50,100 and 700,000 − 650,100 = 49,900. 700,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100,000 that 85,000 is between. Rounding to the nearest 100,000 means choosing the closest multiple of 100,000.
   0  <  85,000  <  100,000
2. Look at the ten thousands digit (the digit just to the right of the hundred thousands digit). This digit tells us if we are past halfway.
   The ten thousands digit is 8.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   8 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the hundred thousands column become zeros.
   85,000 ≈ 100,000 (to the nearest 100,000)

Check. Distances: 85,000 − 0 = 85,000 and 100,000 − 85,000 = 15,000. 100,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100,000 that 960,500 is between. Rounding to the nearest 100,000 means choosing the closest multiple of 100,000.
   900,000  <  960,500  <  1,000,000
2. Look at the ten thousands digit (the digit just to the right of the hundred thousands digit). This digit tells us if we are past halfway.
   The ten thousands digit is 6.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   6 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the hundred thousands column become zeros.
   960,500 ≈ 1,000,000 (to the nearest 100,000)

Check. Distances: 960,500 − 900,000 = 60,500 and 1,000,000 − 960,500 = 39,500. 1,000,000 is the nearer one. ✓

Watch out. A 9 can carry: when you round up a 9 it becomes 10, so the next digit goes up too.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10 that 354,628 is between. Rounding to the nearest 10 means choosing the closest multiple of 10.
   354,620  <  354,628  <  354,630
2. Look at the ones digit (the digit just to the right of the tens digit). This digit tells us if we are past halfway.
   The ones digit is 8.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   8 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the tens column become zeros.
   354,628 ≈ 354,630 (to the nearest 10)

Check. Distances: 354,628 − 354,620 = 8 and 354,630 − 354,628 = 2. 354,630 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100 that 354,628 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.
   354,600  <  354,628  <  354,700
2. Look at the tens digit (the digit just to the right of the hundreds digit). This digit tells us if we are past halfway.
   The tens digit is 2.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   2 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the hundreds column become zeros.
   354,628 ≈ 354,600 (to the nearest 100)

Check. Distances: 354,628 − 354,600 = 28 and 354,700 − 354,628 = 72. 354,600 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 1,000 that 354,628 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.
   354,000  <  354,628  <  355,000
2. Look at the hundreds digit (the digit just to the right of the thousands digit). This digit tells us if we are past halfway.
   The hundreds digit is 6.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   6 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the thousands column become zeros.
   354,628 ≈ 355,000 (to the nearest 1,000)

Check. Distances: 354,628 − 354,000 = 628 and 355,000 − 354,628 = 372. 355,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10,000 that 354,628 is between. Rounding to the nearest 10,000 means choosing the closest multiple of 10,000.
   350,000  <  354,628  <  360,000
2. Look at the thousands digit (the digit just to the right of the ten thousands digit). This digit tells us if we are past halfway.
   The thousands digit is 4.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   4 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the ten thousands column become zeros.
   354,628 ≈ 350,000 (to the nearest 10,000)

Check. Distances: 354,628 − 350,000 = 4,628 and 360,000 − 354,628 = 5,372. 350,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100,000 that 354,628 is between. Rounding to the nearest 100,000 means choosing the closest multiple of 100,000.
   300,000  <  354,628  <  400,000
2. Look at the ten thousands digit (the digit just to the right of the hundred thousands digit). This digit tells us if we are past halfway.
   The ten thousands digit is 5.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the hundred thousands column become zeros.
   354,628 ≈ 400,000 (to the nearest 100,000)

Check. Distances: 354,628 − 300,000 = 54,628 and 400,000 − 354,628 = 45,372. 400,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10,000 that 43,816 is between. Rounding to the nearest 10,000 means choosing the closest multiple of 10,000.
   40,000  <  43,816  <  50,000
2. Look at the thousands digit (the digit just to the right of the ten thousands digit). This digit tells us if we are past halfway.
   The thousands digit is 3.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   3 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the ten thousands column become zeros.
   43,816 ≈ 40,000 (to the nearest 10,000)

Check. Distances: 43,816 − 40,000 = 3,816 and 50,000 − 43,816 = 6,184. 40,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10,000 that 128,450 is between. Rounding to the nearest 10,000 means choosing the closest multiple of 10,000.
   120,000  <  128,450  <  130,000
2. Look at the thousands digit (the digit just to the right of the ten thousands digit). This digit tells us if we are past halfway.
   The thousands digit is 8.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   8 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the ten thousands column become zeros.
   128,450 ≈ 130,000 (to the nearest 10,000)

Check. Distances: 128,450 − 120,000 = 8,450 and 130,000 − 128,450 = 1,550. 130,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10,000 that 96,500 is between. Rounding to the nearest 10,000 means choosing the closest multiple of 10,000.
   90,000  <  96,500  <  100,000
2. Look at the thousands digit (the digit just to the right of the ten thousands digit). This digit tells us if we are past halfway.
   The thousands digit is 6.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   6 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the ten thousands column become zeros.
   96,500 ≈ 100,000 (to the nearest 10,000)

Check. Distances: 96,500 − 90,000 = 6,500 and 100,000 − 96,500 = 3,500. 100,000 is the nearer one. ✓

Watch out. A 9 can carry: when you round up a 9 it becomes 10, so the next digit goes up too.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10,000 that 252,049 is between. Rounding to the nearest 10,000 means choosing the closest multiple of 10,000.
   250,000  <  252,049  <  260,000
2. Look at the thousands digit (the digit just to the right of the ten thousands digit). This digit tells us if we are past halfway.
   The thousands digit is 2.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   2 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the ten thousands column become zeros.
   252,049 ≈ 250,000 (to the nearest 10,000)

Check. Distances: 252,049 − 250,000 = 2,049 and 260,000 − 252,049 = 7,951. 250,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. The numbers that round to 250 are all the numbers that are closer to 250 than to any other multiple of 10, and also the halfway number below it. Find the halfway points on each side.

1. Find the multiples of 10 on each side. The numbers either side are one step away.
   240, 250, 260
2. Find the halfway point below. Halfway is half of 10 = 5 below 250. Halfway rounds up, so this number does round to 250.
   250 − 5 = 245 (smallest)
3. Find the halfway point above. The halfway number above is 255, but halfway rounds up, so it goes to 260. So the largest is 1 less.
   255 − 1 = 254 (largest)
4. Show it on a number line. The shaded part is every number that rounds to 250. The solid dot is included; the open dot is not.

Check. 245 rounds up to 250 ✓. 244 rounds down to 240. 254 rounds down to 250 ✓. 255 rounds up to 260.

Watch out. The halfway number at the bottom is included but the halfway number at the top is not, because halfway rounds up.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. The numbers that round to 7,000 are all the numbers that are closer to 7,000 than to any other multiple of 1,000, and also the halfway number below it. Find the halfway points on each side.

1. Find the multiples of 1,000 on each side. The numbers either side are one step away.
   6,000, 7,000, 8,000
2. Find the halfway point below. Halfway is half of 1,000 = 500 below 7,000. Halfway rounds up, so this number does round to 7,000.
   7,000 − 500 = 6,500 (smallest)
3. Find the halfway point above. The halfway number above is 7,500, but halfway rounds up, so it goes to 8,000. So the largest is 1 less.
   7,500 − 1 = 7,499 (largest)
4. Show it on a number line. The shaded part is every number that rounds to 7,000. The solid dot is included; the open dot is not.

Check. 6,500 rounds up to 7,000 ✓. 6,499 rounds down to 6,000. 7,499 rounds down to 7,000 ✓. 7,500 rounds up to 8,000.

Watch out. The halfway number at the bottom is included but the halfway number at the top is not, because halfway rounds up.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. The numbers that round to 300,000 are all the numbers that are closer to 300,000 than to any other multiple of 100,000, and also the halfway number below it. Find the halfway points on each side.

1. Find the multiples of 100,000 on each side. The numbers either side are one step away.
   200,000, 300,000, 400,000
2. Find the halfway point below. Halfway is half of 100,000 = 50,000 below 300,000. Halfway rounds up, so this number does round to 300,000.
   300,000 − 50,000 = 250,000 (smallest)
3. Find the halfway point above. The halfway number above is 350,000, but halfway rounds up, so it goes to 400,000. So the largest is 1 less.
   350,000 − 1 = 349,999 (largest)
4. Show it on a number line. The shaded part is every number that rounds to 300,000. The solid dot is included; the open dot is not.

Check. 250,000 rounds up to 300,000 ✓. 249,999 rounds down to 200,000. 349,999 rounds down to 300,000 ✓. 350,000 rounds up to 400,000.

Watch out. The halfway number at the bottom is included but the halfway number at the top is not, because halfway rounds up.

Key words. An estimate is a sensible answer that is close to the exact one. We find it by rounding first.

Method. Round both numbers to the nearest 1,000, then do the easy calculation.

1. Round the first number. Look at the digit just to the right of the thousands column.
   6,214 ≈ 6,000
2. Round the second number. Do the same.
   2,788 ≈ 3,000
3. Do the easy calculation. Rounded numbers are quick to add and take away.
   6,000 + 3,000 = 9,000

Check. The exact answer is 9,002, which is close to 9,000. ✓

Watch out. An estimate is not exact. It tells you roughly how big the answer should be.

Key words. An estimate is a sensible answer that is close to the exact one. We find it by rounding first.

Method. Round both numbers to the nearest 10,000, then do the easy calculation.

1. Round the first number. Look at the digit just to the right of the ten thousands column.
   48,920 ≈ 50,000
2. Round the second number. Do the same.
   21,350 ≈ 20,000
3. Do the easy calculation. Rounded numbers are quick to add and take away.
   50,000 − 20,000 = 30,000

Check. The exact answer is 27,570, which is close to 30,000. ✓

Watch out. An estimate is not exact. It tells you roughly how big the answer should be.

Key words. An estimate is a sensible answer that is close to the exact one. We find it by rounding first.

Method. Round both numbers to the nearest 100,000, then do the easy calculation.

1. Round the first number. Look at the digit just to the right of the hundred thousands column.
   418,200 ≈ 400,000
2. Round the second number. Do the same.
   189,700 ≈ 200,000
3. Do the easy calculation. Rounded numbers are quick to add and take away.
   400,000 + 200,000 = 600,000

Check. The exact answer is 607,900, which is close to 600,000. ✓

Watch out. An estimate is not exact. It tells you roughly how big the answer should be.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 1,000 that 14,950 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.
   14,000  <  14,950  <  15,000
2. Look at the hundreds digit (the digit just to the right of the thousands digit). This digit tells us if we are past halfway.
   The hundreds digit is 9.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   9 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the thousands column become zeros.
   14,950 ≈ 15,000 (to the nearest 1,000)

Check. Distances: 14,950 − 14,000 = 950 and 15,000 − 14,950 = 50. 15,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100 that 14,950 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.
   14,900  <  14,950  <  15,000
2. Look at the tens digit (the digit just to the right of the hundreds digit). This digit tells us if we are past halfway.
   The tens digit is 5.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the hundreds column become zeros.
   14,950 ≈ 15,000 (to the nearest 100)

Check. Distances: 14,950 − 14,900 = 50 and 15,000 − 14,950 = 50. 15,000 is the one we choose when exactly halfway (halfway rounds up). ✓

Watch out. Only look at the digit just to the right. Do not round twice. Halfway always rounds up.

Key words. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10,000 that 14,950 is between. Rounding to the nearest 10,000 means choosing the closest multiple of 10,000.
   10,000  <  14,950  <  20,000
2. Look at the thousands digit (the digit just to the right of the ten thousands digit). This digit tells us if we are past halfway.
   The thousands digit is 4.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   4 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the ten thousands column become zeros.
   14,950 ≈ 10,000 (to the nearest 10,000)

Check. Distances: 14,950 − 10,000 = 4,950 and 20,000 − 14,950 = 5,050. 10,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.