Step-by-step Maths Level 4 Comparing, ordering and rounding: check-up and practice test questions

Method. Round to the nearest 10: look at the digits to the right of the ten place.

1. Look at the ones digit. The digits on the right tell us which way to go.
   the ones digit is 1
2. Decide: less than 5. Half of 10 is 5. 5 or more rounds up; less than 5 rounds down.
   1 is less than 5
3. Round down. Keep the same tens, and the digits to the right become 0.
   7301 rounds down to 7300
4. Write the answer. This is the nearest multiple.
   7300

Check. Check: 7300 is a multiple of 10, and it is the closest one to 7301.

Watch out. Exactly 5 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.

Method. The first column that is different decides which number is greater.

1. Compare the thousands. Look at the first digit on the left.
   3 and 4
2. Compare the thousands. This is the first column that is different.
   3 and 4
3. Write the greater number. The larger digit makes the larger number.
   4141

Check. Check: 4141 > 3773.

Watch out. Do not compare the last digits first.

Method. Round to the nearest 10: look at the digits to the right of the ten place.

1. Look at the ones digit. The digits on the right tell us which way to go.
   the ones digit is 8
2. Decide: 5 or more. Half of 10 is 5. 5 or more rounds up; less than 5 rounds down.
   8 is at least 5
3. Round up. Add one more ten, and the digits to the right become 0.
   2308 rounds up to 2310
4. Write the answer. This is the nearest multiple.
   2310

Check. Check: 2310 is a multiple of 10, and it is the closest one to 2308.

Watch out. Exactly 5 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.

Method. Find the two labelled thousands on either side of the dot.

1. Find the thousand just below the dot. Look for the labelled number on the left.
   7000 is just below 7895
2. Find the thousand just above the dot. Look for the labelled number on the right.
   8000 is just above 7895
3. Write the two numbers. The dot is between them.
   Between 7000 and 8000

Check. Check: 7000 < 7895 < 8000.

Watch out. The dot is between two labels, not on one of them.

Method. Compare the numbers column by column, starting with the thousands.

1. Look at the thousands. Numbers with fewer thousands are smaller.
   2319: 2, 7139: 7, 1606: 1, 6388: 6, 6087: 6
2. Look at the hundreds for numbers with the same thousands. Compare the next column only when the first is the same.
   Put them in groups by thousands first
3. Order the numbers. Put them largest to smallest.
   7139, 6388, 6087, 2319, 1606
4. Write the answer in order. Write each number once.
   7139, 6388, 6087, 2319, 1606

Check. Check: each number is greater than the next one in the list.

Watch out. Compare the thousands first, then the hundreds, then the tens, then the ones.

Method. Round to the nearest 10: look at the digits to the right of the ten place.

1. Look at the ones digit. The digits on the right tell us which way to go.
   the ones digit is 3
2. Decide: less than 5. Half of 10 is 5. 5 or more rounds up; less than 5 rounds down.
   3 is less than 5
3. Round down. Keep the same tens, and the digits to the right become 0.
   8433 rounds down to 8430
4. Write the answer. This is the nearest multiple.
   8430

Check. Check: 8430 is a multiple of 10, and it is the closest one to 8433.

Watch out. Exactly 5 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.

Method. Halfway between two numbers is half of their total.

1. Add the two numbers. The total of the two ends is shared equally in the middle.
   4000 + 4400 = 8400
2. Halve the total. Halfway is half of the sum of the two numbers.
   8400 ÷ 2 = 4200
3. Write the answer. This number is the same distance from both ends.
   4200

Check. Check: 4200 - 4000 = 4400 - 4200, the same distance each way.

Watch out. Halfway is not the same as adding a fixed amount. Find the total, then halve it.

Method. Round to the nearest 1000: look at the digits to the right of the thousand place.

1. Look at the hundreds, tens and ones together. The digits on the right tell us which way to go.
   the last three digits are 755
2. Decide: 500 or more. Half of 1000 is 500. 500 or more rounds up; less than 500 rounds down.
   755 is at least 500
3. Round up. Add one more thousand, and the digits to the right become 0.
   8755 rounds up to 9000
4. Write the answer. This is the nearest multiple.
   9000

Check. Check: 9000 is a multiple of 1000, and it is the closest one to 8755.

Watch out. Exactly 500 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.

Method. Compare the numbers column by column, starting with the thousands.

1. Look at the thousands. Numbers with fewer thousands are smaller.
   8313: 8, 4783: 4, 2907: 2, 5592: 5
2. Look at the hundreds for numbers with the same thousands. Compare the next column only when the first is the same.
   Put them in groups by thousands first
3. Order the numbers. Put them largest to smallest.
   8313, 5592, 4783, 2907
4. Write the answer in order. Write each number once.
   8313, 5592, 4783, 2907

Check. Check: each number is greater than the next one in the list.

Watch out. Compare the thousands first, then the hundreds, then the tens, then the ones.

Method. Round to the nearest 10: look at the digits to the right of the ten place.

1. Look at the ones digit. The digits on the right tell us which way to go.
   the ones digit is 2
2. Decide: less than 5. Half of 10 is 5. 5 or more rounds up; less than 5 rounds down.
   2 is less than 5
3. Round down. Keep the same tens, and the digits to the right become 0.
   8612 rounds down to 8610
4. Write the answer. This is the nearest multiple.
   8610

Check. Check: 8610 is a multiple of 10, and it is the closest one to 8612.

Watch out. Exactly 5 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.

Method. Halfway between two numbers is half of their total.

1. Add the two numbers. The total of the two ends is shared equally in the middle.
   6800 + 7200 = 14000
2. Halve the total. Halfway is half of the sum of the two numbers.
   14000 ÷ 2 = 7000
3. Write the answer. This number is the same distance from both ends.
   7000

Check. Check: 7000 - 6800 = 7200 - 7000, the same distance each way.

Watch out. Halfway is not the same as adding a fixed amount. Find the total, then halve it.

Method. Round to the nearest 100: look at the digits to the right of the hundred place.

1. Look at the tens and ones together. The digits on the right tell us which way to go.
   the last two digits are 20
2. Decide: less than 50. Half of 100 is 50. 50 or more rounds up; less than 50 rounds down.
   20 is less than 50
3. Round down. Keep the same hundreds, and the digits to the right become 0.
   5320 rounds down to 5300
4. Write the answer. This is the nearest multiple.
   5300

Check. Check: 5300 is a multiple of 100, and it is the closest one to 5320.

Watch out. Exactly 50 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.

Method. Round to the nearest 10: look at the digits to the right of the ten place.

1. Look at the ones digit. The digits on the right tell us which way to go.
   the ones digit is 5
2. Decide: 5 or more. Half of 10 is 5. 5 or more rounds up; less than 5 rounds down.
   5 is at least 5
3. Round up. Add one more ten, and the digits to the right become 0.
   1305 rounds up to 1310
4. Write the answer. This is the nearest multiple.
   1310

Check. Check: 1310 is a multiple of 10, and it is the closest one to 1305.

Watch out. Exactly 5 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.

Method. Compare the thousands first, then the hundreds, then the tens, then the ones.

1. Compare the thousands. The first column that is different decides the order.
   4 and 1: 4 is more
2. Write the sign between the numbers. The sign points to the smaller number.
   >

Check. Check: read the sign as words. 4967 is greater than 1228.

Watch out. The arrow always points to the smaller number. Compare the thousands first, not the last digits.

Method. Round to the nearest 1000: look at the digits to the right of the thousand place.

1. Look at the hundreds, tens and ones together. The digits on the right tell us which way to go.
   the last three digits are 729
2. Decide: 500 or more. Half of 1000 is 500. 500 or more rounds up; less than 500 rounds down.
   729 is at least 500
3. Round up. Add one more thousand, and the digits to the right become 0.
   9729 rounds up to 10000
4. Write the answer. This is the nearest multiple.
   10000

Check. Check: 10000 is a multiple of 1000, and it is the closest one to 9729.

Watch out. Exactly 500 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.

Method. Round to the nearest 1000: look at the digits to the right of the thousand place.

1. Look at the hundreds, tens and ones together. The digits on the right tell us which way to go.
   the last three digits are 508
2. Decide: 500 or more. Half of 1000 is 500. 500 or more rounds up; less than 500 rounds down.
   508 is at least 500
3. Round up. Add one more thousand, and the digits to the right become 0.
   6508 rounds up to 7000
4. Write the answer. This is the nearest multiple.
   7000

Check. Check: 7000 is a multiple of 1000, and it is the closest one to 6508.

Watch out. Exactly 500 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.

Method. Round to the nearest 100: look at the digits to the right of the hundred place.

1. Look at the tens and ones together. The digits on the right tell us which way to go.
   the last two digits are 45
2. Decide: less than 50. Half of 100 is 50. 50 or more rounds up; less than 50 rounds down.
   45 is less than 50
3. Round down. Keep the same hundreds, and the digits to the right become 0.
   4645 rounds down to 4600
4. Write the answer. This is the nearest multiple.
   4600

Check. Check: 4600 is a multiple of 100, and it is the closest one to 4645.

Watch out. Exactly 50 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.

Method. Compare the numbers column by column, starting with the thousands.

1. Look at the thousands. Numbers with fewer thousands are smaller.
   6754: 6, 5628: 5, 8465: 8, 2664: 2
2. Look at the hundreds for numbers with the same thousands. Compare the next column only when the first is the same.
   Put them in groups by thousands first
3. Order the numbers. Put them largest to smallest.
   8465, 6754, 5628, 2664
4. Write the answer in order. Write each number once.
   8465, 6754, 5628, 2664

Check. Check: each number is greater than the next one in the list.

Watch out. Compare the thousands first, then the hundreds, then the tens, then the ones.

Method. Compare the numbers column by column, starting with the thousands.

1. Look at the thousands. Numbers with fewer thousands are smaller.
   2886: 2, 1650: 1, 3963: 3, 4857: 4, 2897: 2
2. Look at the hundreds for numbers with the same thousands. Compare the next column only when the first is the same.
   Put them in groups by thousands first
3. Order the numbers. Put them smallest to largest.
   1650, 2886, 2897, 3963, 4857
4. Write the answer in order. Write each number once.
   1650, 2886, 2897, 3963, 4857

Check. Check: each number is less than the next one in the list.

Watch out. Compare the thousands first, then the hundreds, then the tens, then the ones.

Method. Find the two labelled thousands on either side of the dot.

1. Find the thousand just below the dot. Look for the labelled number on the left.
   2000 is just below 2020
2. Find the thousand just above the dot. Look for the labelled number on the right.
   3000 is just above 2020
3. Write the two numbers. The dot is between them.
   Between 2000 and 3000

Check. Check: 2000 < 2020 < 3000.

Watch out. The dot is between two labels, not on one of them.