Rounding to the Nearest 10 and 100 - Third Grade Mathematics

Rounding is a powerful mathematical tool that replaces an exact number with a friendlier, easier-to-use number that is close in value. When you go shopping, plan a party, or estimate travel distances, you usually do not need the exact number down to the single digit; rounding to the nearest ten or hundred lets you calculate quickly in your head while staying very accurate.

What Does Rounding Really Mean?

Rounding means finding which benchmark number (such as a multiple of 10 or a multiple of 100) an exact number is closest to on a number line.

Think about walking along a path between two mileposts. If you are closer to milepost 30 than to milepost 40, you round to 30. If you have walked more than halfway toward milepost 40, you round to 40!

20        22             25                  28        30
+----------+--------------+-------------------+---------+
         (closer to 20)  (halfway)         (closer to 30)

Rounding to the Nearest Ten

When rounding to the nearest ten, your target benchmarks are multiples of 10 (such as 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110...).

Using a Number Line to Round to the Nearest Ten

Let us round 63 to the nearest ten:
- Between which two tens does 63 live? It lives between 60 and 70.

- What is the exact halfway point between 60 and 70? The halfway point is 65.


60         63            65                            70
+-----------+-------------+-----------------------------+
<-- 3 units --><------------------- 7 units ----------->

Because 63 is only 3 units away from 60, but 7 units away from 70, it is much closer to 60. Therefore, 63 rounded to the nearest ten is 60.

The Rounding Rule for Tens

Instead of drawing a number line every time, you can follow this simple rule:
1. Underline the tens digit (this is the place you are rounding to).

2. Look at the neighbor digit directly to its right (the ones digit).

3. If the ones digit is 4 or less (0, 1, 2, 3, 4), round down (keep the tens digit the same).

4. If the ones digit is 5 or more (5, 6, 7, 8, 9), round up (increase the tens digit by 1).

5. Change all digits to the right of the tens place to 0.


Why does 5 round up? The number 5 is exactly in the middle. By universal mathematical agreement, when a number is exactly halfway, we always round up!

Worked Examples: Rounding to the Nearest Ten

Example 1: Round 87 to the nearest ten.
- Underline tens: 8

- Neighbor to the right: 7

- 7 is 5 or greater, so round up! The 8 becomes 9.

- Answer: 90.


Example 2: Round 245 to the nearest ten.
- Underline tens: 4 (in 245)

- Neighbor to the right: 5

- 5 is halfway, so round up! The 4 becomes 5. The hundreds digit stays 2.

- Answer: 250.


Rounding to the Nearest Hundred

When rounding to the nearest hundred, your benchmark numbers are multiples of 100 (100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000...).

Using a Number Line to Round to the Nearest Hundred

Let us round 368 to the nearest hundred:
- 368 lives between 300 and 400.

- The halfway point between 300 and 400 is 350.


300                      350         368               400
+-------------------------+-----------+-----------------+
                          (halfway)   (past halfway mark)

Because 368 is past the halfway mark of 350, it is closer to 400 than to 300. Therefore, 368 rounded to the nearest hundred is 400.

The Rounding Rule for Hundreds

  1. Underline the hundreds digit.
  2. Look at the neighbor directly to its right (the tens digit).
  3. If the tens digit is 0, 1, 2, 3, or 4, round down (keep hundreds the same).
  4. If the tens digit is 5, 6, 7, 8, or 9, round up (add 1 to the hundreds digit).
  5. Change both the tens and ones digits to 0.

Worked Examples: Rounding to the Nearest Hundred

Example 1: Round 629 to the nearest hundred.
- Underline hundreds: 6

- Look at tens digit: 2

- Since 2 is 4 or less, round down. The hundreds digit stays 6.

- Answer: 600.


Example 2: Round 1,750 to the nearest hundred.
- Underline hundreds: 7 (in 1,750)

- Look at tens digit: 5

- Since 5 is halfway, round up. The 7 becomes 8. The thousands digit stays 1.

- Answer: 1,800.


Comparing Rounding to 10 vs. Rounding to 100

Notice how the same number gives different results depending on which place value you round to!

Take the number 473:
- Nearest ten: 473 is between 470 and 480. Look at the 3 ones -> round down to 470.

- Nearest hundred: 473 is between 400 and 500. Look at the 7 tens -> round up to 500.


Always read problem directions carefully so you know which place value to target!

Chapter Practice Exercises

  1. Round each number to the nearest ten: a. 48 b. 72 c. 35 d. 184 e. 596
  2. Round each number to the nearest hundred: a. 319 b. 782 c. 450 d. 1,248 e. 2,685
  3. A school library has 438 science books. a. What is this number rounded to the nearest ten? b. What is this number rounded to the nearest hundred?
  4. A farmer harvested 895 apples. Round this number to the nearest ten and to the nearest hundred. What do you notice?
  5. Write two different whole numbers that both round to 70 when rounded to the nearest ten.

Solutions and Step-by-Step Answers

  1. Round to nearest ten: a. 48 -> look at 8 (>=5) -> rounds up to 50. b. 72 -> look at 2 (<=4) -> rounds down to 70. c. 35 -> look at 5 (halfway) -> rounds up to 40. d. 184 -> look at 4 (<=4) -> rounds down to 180. e. 596 -> look at 6 (>=5) -> 9 tens becomes 10 tens, which regroups to 6 hundreds -> rounds up to 600.
  2. Round to nearest hundred: a. 319 -> look at tens digit 1 (<=4) -> rounds down to 300. b. 782 -> look at tens digit 8 (>=5) -> rounds up to 800. c. 450 -> look at tens digit 5 (halfway) -> rounds up to 500. d. 1,248 -> look at tens digit 4 (<=4) -> rounds down to 1,200. e. 2,685 -> look at tens digit 8 (>=5) -> rounds up to 2,700.
  3. For 438 books: a. Nearest ten: look at 8 ones -> rounds up to 440. b. Nearest hundred: look at 3 tens -> rounds down to 400.
  4. For 895 apples:
  5. Nearest ten: 5 ones rounds up, making 9 tens become 10 tens -> 900.
  6. Nearest hundred: 9 tens rounds up, making 8 hundreds become 9 hundreds -> 900. Both roundings result in 900 because 895 is very close to 900 in both scales.
  7. Any whole number from 65 to 74 rounds to 70. Two possible answers are 68 and 73.