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Math · Number Sense

Rounding to 10, 100 and 1000: Then Estimate and Check

Round whole numbers to the nearest 10, 100 or 1000 on a number line, use the halfway rule, avoid rounding twice, and estimate to check answers.

Grades 3–5 · 32 practice questions · Original material
Learning objectiveRound whole numbers to the nearest 10, 100 and 1000 by finding the two benchmarks and the halfway mark on a number line, connect this to the digit one place to the right, round halfway numbers up, round once from the original number, and use rounded numbers to estimate sums and differences and decide whether an answer is reasonable.

The idea

Rounding swaps a number for a nearby friendly number that is easier to think with. If 47 people are coming to a class party, “about 50” is close enough for a quick plan. A rounded number is an estimate, not the exact amount, so we round when “about” is good enough.

A number line shows what rounding really means. To round 47 to the nearest ten, find the two tens it sits between: 40 and 50. The halfway mark between them is 45. 47 is past 45, so it is closer to 50: it is 3 away from 50 but 7 away from 40. So 47 rounds to 50.

There is a digit shortcut that matches the number line. Find the place you are rounding to, then look at the digit one place to its right. If that digit is 0, 1, 2, 3 or 4, the rounding digit stays the same. If it is 5, 6, 7, 8 or 9, the rounding digit goes up by one. Every digit after the rounding place becomes 0. To round 362 to the nearest hundred, look at the tens digit, 6, so 362 rounds up to 400.

A number exactly on the halfway mark, such as 45, 350 or 4500, is the same distance from both benchmarks. We need a rule for it, and the common rule, used in this lesson, is to round halfway numbers up: 45 → 50 and 350 → 400. Some calculators and sciences use other rules, but school arithmetic usually rounds halfway up.

Always round once, starting from the original number. 4449 rounded to the nearest thousand is 4000, because its hundreds digit is 4 and it is less than the halfway mark 4500. If you round to 4450, then 4500, then 5000, each step moves the number a little until it crosses a halfway mark it never really reached.

Rounding is most useful for estimating. Before or after an exact calculation, round each number and do the easy version. 612 + 289 is about 600 + 300 = 900, so an exact answer of 901 makes sense, but an answer of 8101 or 711 tells you to check your work. An estimate checks the size of an answer; it does not replace the exact answer when you need one.

Worked examples

Rounding on a number line to the nearest ten, hundred and thousandThree number lines. Line 1 runs from 40 to 50 with the halfway mark 45. The number 47 is past the halfway mark, so it rounds to 50. Line 2 runs from 300 to 400 with the halfway mark 350. The number 362 is past the halfway mark, so it rounds to 400. Line 3 runs from 4000 to 5000 with the halfway mark 4500. The number 4449 is before the halfway mark, so it rounds down to 4000, not 5000. Numbers in the left half round down to the lower benchmark; numbers on or past the halfway mark round up. To use digits, look at the digit one place to the right of the rounding place: 0 to 4 stays, 5 to 9 rounds up. Round once, from the original number.Rounding: find the benchmarks and the halfway markGreen half: round down to the lower benchmark. Orange half (from halfway on): round up. Original schematic.1 · Nearest ten405045halfway47→ 50ones digit 72 · Nearest hundred300400350halfway362→ 400tens digit 63 · Nearest thousand400050004500halfway4449→ 4000hundreds digit 4Look one place to the right of the rounding place: 0–4 stays, 5–9 rounds up.Round once, from the original number: 4449 → 4000, not 4450 → 4500 → 5000.
Original schematic, drawn to the labelled values. Each number line runs between two benchmarks with the halfway mark in the middle. Numbers before the halfway mark round down to the lower benchmark; numbers on or past it round up. This lesson uses the common school rule that halfway numbers round up.

Example 1 · Use a number line

Round 47 to the nearest ten.

  1. 47 is between 40 and 50.
  2. The halfway mark is 45. 47 is past 45.
  3. 47 is 3 away from 50 and 7 away from 40, so it is closer to 50.

47 rounds to 50.

Example 2 · Use the digit to the right

Round 362 to the nearest hundred.

  1. The rounding place is hundreds (the 3). The benchmarks are 300 and 400.
  2. Look one place to the right: the tens digit is 6.
  3. 6 is 5 or more, so the 3 goes up to 4 and the digits after it become 0.

362 rounds to 400 (it is past the halfway mark 350).

Example 3 · Round once

Round 4449 to the nearest thousand.

  1. The benchmarks are 4000 and 5000, and the halfway mark is 4500.
  2. Look at the hundreds digit: 4. Four is less than 5, so the 4 thousands stays.
  3. Do not round to 4450, then 4500, then 5000. Each extra step starts from a new number, not from 4449.

4449 rounds to 4000.

Example 4 · When a 9 rounds up

Round 2960 to the nearest hundred.

  1. 2960 has 29 hundreds. The benchmarks are 2900 and 3000.
  2. The tens digit is 6, so round up: 29 hundreds + 1 hundred = 30 hundreds.
  3. 30 hundreds is 3000, so the thousands digit changes too.

2960 rounds to 3000.

Example 5 · Estimate to check

Leo says 703 − 288 = 585. Is that reasonable?

  1. Round each number to the nearest hundred: 703 → 700 and 288 → 300.
  2. Estimate: 700 − 300 = 400.
  3. 585 is far from 400, so check again. The exact answer is 415, which is close to the estimate.

585 is not reasonable; 415 is.

Common mistakes

These are tempting because they use familiar operations. Check what the question is actually measuring.

Looking at the wrong digit.

Why this fails: Look at the digit one place to the right of the rounding place. To round 386 to the nearest hundred, look at the 8 tens, not the 6 ones: 386 → 400, not 390.

Rounding again and again.

Why this fails: 4449 → 4450 → 4500 → 5000 is wrong. Round once from the original number: the hundreds digit is 4, so 4449 → 4000.

Thinking “round down” means make the digit smaller.

Why this fails: Rounding down goes to the lower benchmark, which keeps the rounding digit: 43 → 40, not 30.

Forgetting to carry when a 9 rounds up.

Why this fails: 2960 to the nearest hundred is 29 hundreds + 1 hundred = 30 hundreds = 3000, not 2100 or 21000.

Chopping off digits instead of rounding.

Why this fails: 498 is almost 500, not 400. Dropping the tens and ones gives 400 + 300 = 700 for 498 + 397, but rounding gives 500 + 400 = 900, much closer to the exact 895.

Trusting an estimate when you need enough.

Why this fails: 487 + 342 rounds to 500 + 300 = 800, but the exact total is 829. If every person needs a chair, use the exact total or round up.

Foundation

Foundation practice

Find the benchmarks and the halfway mark, then round.

Number line

1. On a number line from 40 to 50, the number 47 is marked. Rounded to the nearest ten, 47 is …

  1. 40
  2. 50
  3. 45
  4. 100
Nearest ten

2. Round 83 to the nearest ten.

  1. 80
  2. 90
  3. 85
  4. 100
Find the benchmarks

3. Which two hundreds does 362 sit between?

  1. 360 and 370
  2. 350 and 400
  3. 300 and 400
  4. 0 and 1000
Halfway mark

4. What number is exactly halfway between 300 and 400?

  1. 340
  2. 305
  3. 399
  4. 350
Nearest hundred

5. Round 362 to the nearest hundred.

  1. 400
  2. 300
  3. 360
  4. 460
Halfway

6. Round 45 to the nearest ten.

  1. 40
  2. 45
  3. 50
  4. It cannot be rounded
Which digit?

7. You want to round 6274 to the nearest thousand. Which digit tells you whether to round up or stay?

  1. The 6 (thousands digit)
  2. The 7 (tens digit)
  3. The 4 (ones digit)
  4. The 2 (hundreds digit)
Nearest thousand

8. Round 6274 to the nearest thousand.

  1. 7000
  2. 6000
  3. 6300
  4. 6270

Practice

Practice practice

Round to 10, 100 and 1000, including halfway numbers, and estimate sums and differences.

Nearest ten

9. Round 518 to the nearest ten.

  1. 520
  2. 510
  3. 500
  4. 600
Halfway

10. Round 750 to the nearest hundred.

  1. 700
  2. 750
  3. 800
  4. 760
Nearest thousand

11. Round 3501 to the nearest thousand.

  1. 3000
  2. 3500
  3. 3600
  4. 4000
Carrying over

12. Round 2960 to the nearest hundred.

  1. 2900
  2. 3000
  3. 2100
  4. 2970
Which rounds?

13. Which number rounds to 70 when rounded to the nearest ten?

  1. 64
  2. 75
  3. 65
  4. 79
Estimate a sum

14. Estimate 612 + 289 by rounding each number to the nearest hundred first.

  1. 900
  2. 800
  3. 1000
  4. 901
Estimate a difference

15. Estimate 832 − 417 by rounding each number to the nearest hundred first.

  1. 500
  2. 415
  3. 300
  4. 400
Round once

16. Round 4449 to the nearest thousand.

  1. 5000
  2. 4000
  3. 4400
  4. 4500

Think

Think practice

Each question shows a tempting mistake. Explain why it fails.

Spot the error

17. Sam rounds 4449 to the nearest thousand like this: 4449 → 4450 → 4500 → 5000. What went wrong?

  1. Nothing; every step follows the rule
  2. He should stop at 4500
  3. He rounded his rounded answer again and again instead of rounding 4449 once
  4. He should look at the ones digit, 9, so 5000 is right
Spot the error

18. Ava says 43 rounded to the nearest ten is 30, because “rounding down makes the tens digit smaller.” What is the mistake?

  1. Rounding down keeps the tens digit; 43 rounds to 40
  2. She is right
  3. 43 should round up to 50
  4. 43 should round to 45
Spot the error

19. Noah rounds 386 to the nearest hundred. He looks at the 6 and writes 390. What went wrong?

  1. Nothing; 390 is correct
  2. He rounded to the nearest ten; for hundreds, look at the 8 tens: 400
  3. It should be 300, because 3 is less than 5
  4. It should be 380
Check with an estimate

20. Leo says 703 − 288 = 585. Use an estimate to decide whether his answer is reasonable.

  1. Reasonable: it is between 288 and 703
  2. Not reasonable: the answer must be more than 703
  3. You cannot tell without working out the exact answer
  4. Not reasonable: about 700 − 300 = 400, so 585 is too big
Spot the error

21. Maya estimates 498 + 397 as 400 + 300 = 700. What went wrong?

  1. She dropped the tens and ones instead of rounding; 500 + 400 = 900 is much closer
  2. Nothing; 700 is a good estimate
  3. She should have rounded both to 1000
  4. She should add first, then round 895 down to 800
Two roundings

22. Which number rounds to 450 to the nearest ten AND to 500 to the nearest hundred?

  1. 446
  2. 452
  3. 455
  4. 549
Explain

23. Is 350 closer to 300 or to 400? Explain why the rule in this lesson rounds it to 400.

True or false?

24. Ben says, “A rounded number is always bigger than the number you started with.” Is he right?

  1. Yes, always
  2. Yes, except for halfway numbers
  3. No: 83 rounds down to 80
  4. No: rounded numbers are always smaller

Challenge

Challenge practice

Work backwards, find ranges and decide when an estimate is safe.

Estimate a total

25. At a school concert there are 487 students and 312 family members. Estimate the total by rounding each to the nearest hundred.

  1. 700
  2. 900
  3. 799
  4. 800
When is an estimate not enough?

26. For another concert there are 487 students and 342 family members. Ravi rounds to 500 + 300 and sets out 800 chairs. Explain why some people will not have a seat.

Smallest

27. What is the smallest whole number that rounds to 600 to the nearest hundred?

  1. 550
  2. 500
  3. 549
  4. 599
Largest

28. What is the largest whole number that rounds to 600 to the nearest hundred?

  1. 650
  2. 649
  3. 699
  4. 600
Work backwards

29. A whole number rounded to the nearest ten is 80. Which could be the number?

  1. 74
  2. 86
  3. 75
  4. 85
Estimate a bigger sum

30. Estimate 3812 + 2409 by rounding each number to the nearest thousand.

  1. 5000
  2. 7000
  3. 6221
  4. 6000
Check with an estimate

31. Ella works out 1975 + 2046 and gets 3021. Is her answer reasonable?

  1. No: about 2000 + 2000 = 4000
  2. Yes: about 1000 + 2000 = 3000
  3. Yes: it is close to 3000
  4. No: the sum must be more than 5000
Work backwards

32. A news report says “about 3000 people” came to a parade, rounded to the nearest thousand. What are the fewest and the most people who could have come?

Answer key

  1. 1. 50
    47 is 3 away from 50 and 7 away from 40, so it is closer to 50. 40 is the farther ten, 45 is the halfway mark (not a ten), and 100 is the nearest hundred, not the nearest ten.
  2. 2. 80
    83 sits between 80 and 90. The ones digit is 3, which is less than 5, so it stays at 80. 90 rounds the wrong way, 85 is the halfway mark, and 100 is the nearest hundred.
  3. 3. 300 and 400
    362 has 3 hundreds, so it is more than 300 and less than 400. 360 and 370 are the two tens around it, 350 is the halfway mark, not a hundred, and 0 and 1000 are thousands.
  4. 4. 350
    The gap from 300 to 400 is 100, and half of 100 is 50, so the halfway mark is 300 + 50 = 350. 305 adds half of 10 instead of half of 100, 340 is not in the middle, and 399 is next to 400.
  5. 5. 400
    Look at the tens digit, 6. Six is 5 or more, so 362 rounds up to 400. It is past the halfway mark 350. 300 just drops the digits, 360 is the nearest ten, and 460 adds 1 to the hundreds but keeps the old digits.
  6. 6. 50
    45 is exactly halfway between 40 and 50. The common rule, used in this lesson, is that a number on the halfway mark rounds up, so 45 rounds to 50. 40 rounds the wrong way, and 45 is not a ten. Halfway numbers can still be rounded; we just need the rule.
  7. 7. The 2 (hundreds digit)
    Look one place to the right of the place you are rounding to. Thousands is the rounding place, so look at the hundreds digit, 2. The 6 is the digit that may change, not the one that decides. The 7 and the 4 are too far to the right.
  8. 8. 6000
    The hundreds digit is 2, which is less than 5, so 6274 rounds to 6000. 7000 rounds the wrong way, 6300 is the nearest hundred, and 6270 is the nearest ten.
  9. 9. 520
    518 is between 510 and 520. The ones digit is 8, so round up to 520. 510 rounds the wrong way, 500 is the nearest hundred, and 600 rounds up to the wrong hundred.
  10. 10. 800
    750 is exactly halfway between 700 and 800. Halfway rounds up, so 750 rounds to 800. 700 rounds down, 750 is the halfway mark, not a hundred, and 760 is not a hundred either.
  11. 11. 4000
    The hundreds digit is 5, so round up: 3501 → 4000. It is just past the halfway mark 3500. 3000 rounds the wrong way, 3500 is the halfway mark (not a thousand), and 3600 is not a thousand.
  12. 12. 3000
    The tens digit is 6, so round up. 29 hundreds plus 1 hundred is 30 hundreds, which is 3000. 2900 rounds down, 2100 changes only one digit and forgets that 9 + 1 makes a new thousand, and 2970 is not a hundred.
  13. 13. 65
    65 is halfway between 60 and 70, and halfway rounds up, so 65 → 70. 64 rounds to 60. 75 and 79 both round to 80, because they are at or past the halfway mark between 70 and 80.
  14. 14. 900
    612 rounds to 600 and 289 rounds to 300, so the estimate is 600 + 300 = 900. 800 rounds 289 down to 200, 1000 rounds 612 up to 700, and 901 is the exact sum, not the rounded estimate.
  15. 15. 400
    832 rounds to 800 and 417 rounds to 400, so 800 − 400 = 400. 500 comes from rounding 832 up to 900, 300 from rounding 417 up to 500, and 415 is the exact answer, not the estimate.
  16. 16. 4000
    The hundreds digit is 4, so 4449 stays at 4000; it is less than the halfway mark 4500. 5000 comes from rounding again and again (4450, 4500, 5000). 4400 is the nearest hundred and 4500 is the halfway mark.
  17. 17. He rounded his rounded answer again and again instead of rounding 4449 once
    Round once, from the original number. The hundreds digit of 4449 is 4, so it rounds to 4000. Each extra step moved the number a little, until it crossed a halfway mark it never really reached. 4500 is not a thousand, and the ones digit does not decide rounding to the nearest thousand.
  18. 18. Rounding down keeps the tens digit; 43 rounds to 40
    43 is between 40 and 50. Rounding down means going to the lower ten, 40, which keeps the 4. 30 is not even next to 43. 50 is the farther ten, and 45 is the halfway mark, not a ten.
  19. 19. He rounded to the nearest ten; for hundreds, look at the 8 tens: 400
    To round to the nearest hundred, look at the tens digit, 8, which is 5 or more, so 386 → 400. 390 is the nearest ten. The 3 is the digit that may change, not the one that decides, and 380 rounds the wrong way even for tens.
  20. 20. Not reasonable: about 700 − 300 = 400, so 585 is too big
    Rounded to the nearest hundred, 700 − 300 = 400, and 585 is far from that (the exact answer is 415). Being between the two numbers does not make an answer right. A difference of these two numbers cannot be more than 703, and the point of an estimate is to check without redoing all the exact work.
  21. 21. She dropped the tens and ones instead of rounding; 500 + 400 = 900 is much closer
    498 is almost 500 and 397 is almost 400, so both round up. Chopping off digits is not rounding. The exact sum is 895, which is 5 from 900 but 195 from 700. Rounding to 1000 is the wrong place, and 895 rounds to 900, not 800.
  22. 22. 452
    452 → 450 (ones digit 2) and 452 → 500 (tens digit 5). 446 rounds to 450 but to 400 for hundreds. 455 rounds to 460 for tens. 549 rounds to 550 for tens.
  23. 23. Neither. 350 is exactly 50 from 300 and 50 from 400, so it is on the halfway mark. Because it is not closer to either one, we need a rule; the common rule rounds halfway numbers up, so 350 rounds to 400.
    A strong answer shows both distances (50 and 50), uses the word halfway and names the round-up rule.
  24. 24. No: 83 rounds down to 80
    Rounding goes to whichever benchmark is closer, so it can go down (83 → 80) or up (87 → 90). It is not always bigger, and it is not always smaller either. Halfway numbers round up, so they are not an exception to “bigger.”
  25. 25. 800
    487 → 500 and 312 → 300, so about 500 + 300 = 800 people. 700 rounds 487 down, 900 rounds 312 up, and 799 is the exact total, not the estimate.
  26. 26. The exact total is 487 + 342 = 829, so 29 people would have no chair. 487 was rounded up by only 13, but 342 was rounded down by 42, so the estimate is too low. When you must have enough, round up or use the exact total.
    A strong answer finds the exact total (829), notices that one number was rounded down by more than the other was rounded up, and says an estimate is not safe when you need enough for everyone.
  27. 27. 550
    550 is the halfway mark between 500 and 600, and halfway rounds up, so 550 → 600. 549 rounds to 500 because its tens digit is 4. 500 is already a hundred and rounds to itself. 599 rounds to 600 but is not the smallest.
  28. 28. 649
    649 has a tens digit of 4, so it stays at 600. 650 is the halfway mark between 600 and 700, so it rounds up to 700, and 699 rounds to 700 too. 600 rounds to 600 but is not the largest.
  29. 29. 75
    75 is halfway between 70 and 80 and rounds up to 80. 74 rounds to 70. 85 is halfway between 80 and 90, so it rounds up to 90, and 86 rounds to 90 as well.
  30. 30. 6000
    3812 → 4000 and 2409 → 2000, so 4000 + 2000 = 6000. 5000 chops 3812 down to 3000, 7000 rounds 2409 up to 3000, and 6221 is the exact sum, not the estimate.
  31. 31. No: about 2000 + 2000 = 4000
    1975 → 2000 and 2046 → 2000, so the sum should be about 4000 (the exact sum is 4021). Ella probably forgot to regroup a thousand. 1000 + 2000 chops 1975 down instead of rounding, “close to 3000” compares her answer with itself, and two numbers near 2000 cannot add to more than 5000.
  32. 32. Fewest: 2500. Most: 3499. 2500 is the halfway mark and rounds up to 3000; 2499 would round to 2000, and 3500 would round to 4000.
    A strong answer finds both edges of the range and uses the halfway rule to explain why 2500 is in and 3500 is out.

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