Year 4: Rounding to the nearest 10, 100 or 1000
Part of the Year 4 place value chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Rounding to the nearest 10, 100 or 1000
Sometimes we do not need an exact number. A newspaper might say “about 3,500 people came to the match” when the real number was 3,467. Changing a number to a nearby, simpler number is called rounding. We round to the nearest 10, 100 or 1000.
Look at 3,467 on this number line. It is between 3,460 and 3,470. The halfway point is 3,465. 3,467 is past halfway, so it is nearer to 3,470.
Here is the rule. Look at the digit to the right of the place you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down. The digits after the rounding place become zeros.
For 3,467 to the nearest 100: look at the tens digit, 6. It is 5 or more, so round up to 3,500. For 3,467 to the nearest 1000: look at the hundreds digit, 4. It is 4 or less, so round down to 3,000. When a number is exactly halfway, such as 6,500, we always round up.
Rounding helps us estimate. To estimate 4,968 + 3,012, round to the nearest 1000: 5,000 + 3,000 = 8,000. The real answer is close to 8,000.
Key words. To round is to change a number to a nearby, simpler one. An estimate is a sensible guess that is close to the exact answer. ≈ means “is about equal to”.
Key ideas
- Look at the digit to the right of the place you are rounding to.
- 5 or more: round up. 4 or less: round down.
- Digits to the right of the rounding place become zeros.
- Halfway always rounds up: 6,500 to the nearest 1000 is 7,000.
- A 9 can carry: 9,960 to the nearest 100 is 10,000.
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.
- Find the two multiples of 10 that 3,467 is between. Rounding to the nearest 10 means choosing the closest multiple of 10.3,460 < 3,467 < 3,470
- Picture it on a number line. The halfway point between 3,460 and 3,470 is 3,465.
- 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 7.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.7 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the tens column become zeros.3,467 ≈ 3,470 (to the nearest 10)
Check. Distances: 3,467 − 3,460 = 7 and 3,470 − 3,467 = 3. 3,470 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.
- Find the two multiples of 100 that 5,382 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.5,300 < 5,382 < 5,400
- 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 8.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.8 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the hundreds column become zeros.5,382 ≈ 5,400 (to the nearest 100)
Check. Distances: 5,382 − 5,300 = 82 and 5,400 − 5,382 = 18. 5,400 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.
- Find the two multiples of 1,000 that 6,500 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.6,000 < 6,500 < 7,000
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.5 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the thousands column become zeros.6,500 ≈ 7,000 (to the nearest 1,000)
Check. Distances: 6,500 − 6,000 = 500 and 7,000 − 6,500 = 500. 7,000 is the one we choose when exactly halfway. ✓
Watch out. Only look at the digit just to the right. Do not round twice. Halfway (like 6,500 to the nearest 1,000) 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.
- Find the two multiples of 100 that 7,962 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.7,900 < 7,962 < 8,000
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.6 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the hundreds column become zeros.7,962 ≈ 8,000 (to the nearest 100)
Check. Distances: 7,962 − 7,900 = 62 and 8,000 − 7,962 = 38. 8,000 is the nearer one. ✓
Watch out. Only the digit just to the right decides. Do not look at digits further along.
Watch out
Only look at the digit just to the right. To round 3,459 to the nearest 10, the ones digit 9 tells us to round up to 3,460. Do not round the 9 up to make the 5 into a 6 and then round again. Also remember: 5 rounds up, so 3,465 to the nearest 10 is 3,470.Exercise 1D Rounding and estimating
Non-calculatorKey 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.
- Find the two multiples of 10 that 63 is between. Rounding to the nearest 10 means choosing the closest multiple of 10.60 < 63 < 70
- 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 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.
- Write the rounded number. Digits to the right of the tens column become zeros.63 ≈ 60 (to the nearest 10)
Check. Distances: 63 − 60 = 3 and 70 − 63 = 7. 60 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.
- Find the two multiples of 10 that 78 is between. Rounding to the nearest 10 means choosing the closest multiple of 10.70 < 78 < 80
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.8 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the tens column become zeros.78 ≈ 80 (to the nearest 10)
Check. Distances: 78 − 70 = 8 and 80 − 78 = 2. 80 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.
- Find the two multiples of 10 that 145 is between. Rounding to the nearest 10 means choosing the closest multiple of 10.140 < 145 < 150
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.5 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the tens column become zeros.145 ≈ 150 (to the nearest 10)
Check. Distances: 145 − 140 = 5 and 150 − 145 = 5. 150 is the one we choose when exactly halfway. ✓
Watch out. Only look at the digit just to the right. Do not round twice. Halfway (like 6,500 to the nearest 1,000) 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.
- 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
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.4 is 4 or less, so round down.
- Write the rounded number. 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.
- Find the two multiples of 10 that 5,495 is between. Rounding to the nearest 10 means choosing the closest multiple of 10.5,490 < 5,495 < 5,500
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.5 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the tens column become zeros.5,495 ≈ 5,500 (to the nearest 10)
Check. Distances: 5,495 − 5,490 = 5 and 5,500 − 5,495 = 5. 5,500 is the one we choose when exactly halfway. ✓
Watch out. Only look at the digit just to the right. Do not round twice. Halfway (like 6,500 to the nearest 1,000) 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.
- Find the two multiples of 10 that 7,001 is between. Rounding to the nearest 10 means choosing the closest multiple of 10.7,000 < 7,001 < 7,010
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.1 is 4 or less, so round down.
- Write the rounded number. Digits to the right of the tens column become zeros.7,001 ≈ 7,000 (to the nearest 10)
Check. Distances: 7,001 − 7,000 = 1 and 7,010 − 7,001 = 9. 7,000 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.
- Find the two multiples of 100 that 340 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.300 < 340 < 400
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.4 is 4 or less, so round down.
- Write the rounded number. Digits to the right of the hundreds column become zeros.340 ≈ 300 (to the nearest 100)
Check. Distances: 340 − 300 = 40 and 400 − 340 = 60. 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.
- 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
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.5 is 5 or more, so round up.
- Write the rounded number. 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. ✓
Watch out. Only look at the digit just to the right. Do not round twice. Halfway (like 6,500 to the nearest 1,000) 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.
- Find the two multiples of 100 that 6,238 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.6,200 < 6,238 < 6,300
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.3 is 4 or less, so round down.
- Write the rounded number. Digits to the right of the hundreds column become zeros.6,238 ≈ 6,200 (to the nearest 100)
Check. Distances: 6,238 − 6,200 = 38 and 6,300 − 6,238 = 62. 6,200 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.
- Find the two multiples of 100 that 4,950 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.4,900 < 4,950 < 5,000
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.5 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the hundreds column become zeros.4,950 ≈ 5,000 (to the nearest 100)
Check. Distances: 4,950 − 4,900 = 50 and 5,000 − 4,950 = 50. 5,000 is the one we choose when exactly halfway. ✓
Watch out. Only look at the digit just to the right. Do not round twice. Halfway (like 6,500 to the nearest 1,000) 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.
- Find the two multiples of 100 that 8,449 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.8,400 < 8,449 < 8,500
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.4 is 4 or less, so round down.
- Write the rounded number. Digits to the right of the hundreds column become zeros.8,449 ≈ 8,400 (to the nearest 100)
Check. Distances: 8,449 − 8,400 = 49 and 8,500 − 8,449 = 51. 8,400 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.
- Find the two multiples of 100 that 9,960 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.9,900 < 9,960 < 10,000
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.6 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the hundreds column become zeros.9,960 ≈ 10,000 (to the nearest 100)
Check. Distances: 9,960 − 9,900 = 60 and 10,000 − 9,960 = 40. 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.
- 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
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.2 is 4 or less, so round down.
- Write the rounded number. 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.
- Find the two multiples of 1,000 that 6,500 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.6,000 < 6,500 < 7,000
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.5 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the thousands column become zeros.6,500 ≈ 7,000 (to the nearest 1,000)
Check. Distances: 6,500 − 6,000 = 500 and 7,000 − 6,500 = 500. 7,000 is the one we choose when exactly halfway. ✓
Watch out. Only look at the digit just to the right. Do not round twice. Halfway (like 6,500 to the nearest 1,000) 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.
- Find the two multiples of 1,000 that 7,999 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.7,000 < 7,999 < 8,000
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.9 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the thousands column become zeros.7,999 ≈ 8,000 (to the nearest 1,000)
Check. Distances: 7,999 − 7,000 = 999 and 8,000 − 7,999 = 1. 8,000 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.
- Find the two multiples of 1,000 that 2,499 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.2,000 < 2,499 < 3,000
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.4 is 4 or less, so round down.
- Write the rounded number. Digits to the right of the thousands column become zeros.2,499 ≈ 2,000 (to the nearest 1,000)
Check. Distances: 2,499 − 2,000 = 499 and 3,000 − 2,499 = 501. 2,000 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.
- Find the two multiples of 1,000 that 9,501 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.9,000 < 9,501 < 10,000
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.5 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the thousands column become zeros.9,501 ≈ 10,000 (to the nearest 1,000)
Check. Distances: 9,501 − 9,000 = 501 and 10,000 − 9,501 = 499. 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.
- Find the two multiples of 1,000 that 1,350 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.1,000 < 1,350 < 2,000
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.3 is 4 or less, so round down.
- Write the rounded number. Digits to the right of the thousands column become zeros.1,350 ≈ 1,000 (to the nearest 1,000)
Check. Distances: 1,350 − 1,000 = 350 and 2,000 − 1,350 = 650. 1,000 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.
- Find the two multiples of 100 that 4,372 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.4,300 < 4,372 < 4,400
- 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 7.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.7 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the hundreds column become zeros.4,372 ≈ 4,400 (to the nearest 100)
Check. Distances: 4,372 − 4,300 = 72 and 4,400 − 4,372 = 28. 4,400 is the nearer one. ✓
Watch out. Only the digit just to the right decides. Do not look at digits further along.
Method. First read the number the arrow points to. Then round it to the nearest 1000.
- Work out what each small mark is worth. The line goes from 6,000 to 7,000 in 10 equal steps.7,000 − 6,000 = 1,000 and 1,000 ÷ 10 = 100
- Read the arrow. It is 3 marks after 6,000.6,000 + 3 × 100 = 6,300
- Round to the nearest 1000. Look at the hundreds digit: 3 is 4 or less, so round down.6,300 ≈ 6,000
Check. 6,300 is 300 from 6,000 but 700 from 7,000, so 6,000 is nearer. ✓
Watch out. Read the arrow first, then round. Do not just pick the nearest label without thinking.
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.
- Find the two multiples of 10 that 5,764 is between. Rounding to the nearest 10 means choosing the closest multiple of 10.5,760 < 5,764 < 5,770
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.4 is 4 or less, so round down.
- Write the rounded number. Digits to the right of the tens column become zeros.5,764 ≈ 5,760 (to the nearest 10)
Check. Distances: 5,764 − 5,760 = 4 and 5,770 − 5,764 = 6. 5,760 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.
- Find the two multiples of 100 that 5,764 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.5,700 < 5,764 < 5,800
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.6 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the hundreds column become zeros.5,764 ≈ 5,800 (to the nearest 100)
Check. Distances: 5,764 − 5,700 = 64 and 5,800 − 5,764 = 36. 5,800 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.
- Find the two multiples of 1,000 that 5,764 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.5,000 < 5,764 < 6,000
- 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 7.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.7 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the thousands column become zeros.5,764 ≈ 6,000 (to the nearest 1,000)
Check. Distances: 5,764 − 5,000 = 764 and 6,000 − 5,764 = 236. 6,000 is the nearer one. ✓
Watch out. Only the digit just to the right decides. Do not look at digits further along.
Method. The tens digit decides if we round up or down to the nearest 100. Try each digit.
- Look at what 4,400 needs. The number 4,3_6 is between 4,300 and 4,400. To round to 4,400 it must be at least halfway, which is 4,350.Halfway = (4,300 + 4,400) ÷ 2 = 4,350
- Try each tens digit. A tens digit of 5 or more rounds up.4,306: tens digit 0 → round down to 4,300
4,316: tens digit 1 → round down to 4,300
4,326: tens digit 2 → round down to 4,300
4,336: tens digit 3 → round down to 4,300
4,346: tens digit 4 → round down to 4,300
4,356: tens digit 5 → round up to 4,400
4,366: tens digit 6 → round up to 4,400
4,376: tens digit 7 → round up to 4,400
4,386: tens digit 8 → round up to 4,400
4,396: tens digit 9 → round up to 4,400 - Write the digits that work. 5, 6, 7, 8 or 9
Check. 4,356 > 4,350, so it is past halfway and rounds up. 4,346 < 4,350, so it rounds down. ✓
Watch out. Only the tens digit matters here. The ones digit 6 does not change the answer.
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.
- Find the two multiples of 1,000 that 5,610 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.5,000 < 5,610 < 6,000
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.6 is 5 or more, so round up.
- Write the rounded number. Digits to the right of the thousands column become zeros.5,610 ≈ 6,000 (to the nearest 1,000)
Check. Distances: 5,610 − 5,000 = 610 and 6,000 − 5,610 = 390. 6,000 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.
- Find the two multiples of 1,000 that 5,390 is between. Rounding to the nearest 1,000 means choosing the closest multiple of 1,000.5,000 < 5,390 < 6,000
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.3 is 4 or less, so round down.
- Write the rounded number. Digits to the right of the thousands column become zeros.5,390 ≈ 5,000 (to the nearest 1,000)
Check. Distances: 5,390 − 5,000 = 390 and 6,000 − 5,390 = 610. 5,000 is the nearer one. ✓
Watch out. Only the digit just to the right decides. Do not look at digits further along.
Method. Compare the real numbers, not the rounded ones.
- Look at the real crowds. The rounded numbers are 6,000 and 5,000, but we need the real ones.5,610 and 5,390
- Are they equal? Compare from the left. The hundreds digits are 6 and 3.5,610 > 5,390
- Write the answer. No. The crowds were different. 5,610 is 220 more than 5,390.
Check. 5,610 − 5,390 = 220. ✓
Watch out. Rounding can make different numbers look the same, or look more different than they really are.
Method. Round both numbers to the nearest 1,000, then do the easy calculation.
- Round the first number. Look at the digit just to the right of the thousands column.4,968 ≈ 5,000
- Round the second number. Do the same.3,012 ≈ 3,000
- Do the easy calculation. Rounded numbers are easy to add and take away.5,000 + 3,000 = 8,000
Check. The exact answer is 7,980, which is close to 8,000. ✓
Watch out. Estimates are not exact. The answer is close to the real answer.
Method. Round both numbers to the nearest 1,000, then do the easy calculation.
- Round the first number. Look at the digit just to the right of the thousands column.7,098 ≈ 7,000
- Round the second number. Do the same.2,947 ≈ 3,000
- Do the easy calculation. Rounded numbers are easy to add and take away.7,000 − 3,000 = 4,000
Check. The exact answer is 4,151, which is close to 4,000. ✓
Watch out. Estimates are not exact. The answer is close to the real answer.
Method. Round both numbers to the nearest 100, then do the easy calculation.
- Round the first number. Look at the digit just to the right of the hundreds column.6,214 ≈ 6,200
- Round the second number. Do the same.2,788 ≈ 2,800
- Do the easy calculation. Rounded numbers are easy to add and take away.6,200 + 2,800 = 9,000
Check. The exact answer is 9,002, which is close to 9,000. ✓
Watch out. Estimates are not exact. The answer is close to the real answer.
Method. Round each number to the nearest 1000 by looking at the hundreds digit.
- Round each number. The hundreds digit tells us: 5 or more rounds up, 4 or less rounds down.4,501: hundreds digit 5 → 5,000
5,499: hundreds digit 4 → 5,000
5,500: hundreds digit 5 → 6,000
4,999: hundreds digit 9 → 5,000 - Find the one that is not 5,000. 5,500 rounds to 6,000.
- Write the answer. 5,500
Check. 5,500 is exactly halfway between 5,000 and 6,000, and halfway rounds up. ✓
Watch out. Numbers ending in 500 are halfway, and halfway rounds up.
Method. Round 3,456 to the nearest 10 yourself and compare it with Aisha’s answer.
- Round 3,456 to the nearest 10. Look at the ones digit: 6 is 5 or more, so round up.3,460 (3,456 ≈ 3,460)
- Round 3,456 to the nearest 100. Look at the tens digit: 5, so round up.3,456 ≈ 3,500
- Say what Aisha did. Her answer, 3,500, is 3,456 rounded to the nearest 100.She rounded to the nearest 100. The question asked for the nearest 10, so the answer is 3,460.
Check. 3,460 is only 4 away from 3,456, but 3,500 is 44 away. ✓
Watch out. Check which place the question asks you to round to.
Method. Test the numbers on each edge: 649, 650, 749 and 750.
- Test the bottom edge. Look at the tens digit: 5 or more rounds up.649: tens digit 4 → rounds to 600
650: tens digit 5 → rounds to 700 - Test the top edge. Do the same for the numbers just below and above 750.749: tens digit 4 → rounds to 700
750: tens digit 5 → rounds to 800 - Write the answer. The smallest is 650 and the largest is 749.Yes. Tom is right.
Check. The numbers from 650 to 749 are all within 50 of 700 (and 650 is exactly 50 away, which rounds up). ✓
Watch out. A number exactly halfway rounds up. That is why 650 rounds to 700 but 749 is the last one.
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.
- Find the two multiples of 100 that 3,845 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.3,800 < 3,845 < 3,900
- 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.
- Decide: round up or round down? 5 or more: round up. 4 or less: round down.4 is 4 or less, so round down.
- Write the rounded number. Digits to the right of the hundreds column become zeros.3,845 ≈ 3,800 (to the nearest 100)
Check. Distances: 3,845 − 3,800 = 45 and 3,900 − 3,845 = 55. 3,800 is the nearer one. ✓
Watch out. Only the digit just to the right decides. Do not look at digits further along.
Method. Round to the nearest 1000 and then change metres to kilometres.
- Round 3,845 to the nearest 1000. The hundreds digit is 8, which is 5 or more, so round up.3,845 ≈ 4,000
- Change metres to kilometres. 1,000 m = 1 km.4,000 ÷ 1,000 = 4 km
- Write the answer. 4,000 m = 4 km
Check. 3,845 m is a bit less than 4 km, so about 4 km is sensible. ✓
Watch out. There are 1,000 metres in a kilometre.
Method. A number rounds to 7,000 if it is between 6,500 and 7,499. With these digits, the first digit must be 7 and the hundreds digit must be 4 or less.
- Choose the thousands digit. Rounding to 7,000 means the number must start with 7 (6 is not one of our digits).Thousands digit = 7
- Choose the hundreds digit. It must be 4 or less so the number rounds down to 7,000. From 5, 3, 2 that means 3 or 2.Hundreds digit = 3 or 2
- Arrange the last two digits. For each hundreds digit, the other two digits can go in either order.7,235
7,253
7,325
7,352 - Write the numbers. 7,235, 7,253, 7,325, 7,352
Check. 7,5xx would round up to 8,000, so 5 cannot be the hundreds digit. ✓
Watch out. Check each answer. A hundreds digit of 5 rounds up, so those numbers do not work.