# Rounding numbers

Here you will learn how to round numbers to the nearest 10, 100, and 1000 as well as how to round decimal numbers to the nearest tenth, hundredth and thousandth.

Students will first learn about rounding numbers as part of their work with place value in the 3rd grade. They build upon this knowledge as they progress through 4th and 5th grade.

## What is rounding numbers?

Rounding a number means to simplify it by scaling it up or down.

Rounding is a type of estimation used to make calculations easier.

To round numbers, you can use a number line or you can apply a rule.

For example, let’s look at several rounding samples with and without a number line.

Rounding \bf{14\underline{7}8} to the nearest \bf{10} with a number line

1478 is to the right of the halfway point and closer to
1480 than 1470. It will round to be 1480.

Rounding \bf{14\underline{7}8} to the nearest \bf{10} with the rule

7 tens is in the rounding place, and 8 ones is to the right of 7.

The rule says that if the number to the right of the rounding digit is greater
or equal to 5 \, (5, 6, 7, 8, 9), round up by adding 1 to the rounding digit.

7 tens becomes 8 tens, and the rest of the digits to the right change to be 0’ s.

14\underline{7}8 → Rounded to the nearest ten is 1480

Rounding \bf{1\underline{4}78} to the nearest \bf{100} with a number line

1478 is to the right of the halfway point and closer to
1500 than 1400. It will round to be 1500.

Rounding \bf{1\underline{4}78} to the nearest \bf{100} with the rule

4 hundreds is in the rounding place, and 7 tens is to the right of 4.

The rule says that if the number to the right of the rounding digit is greater
than or equal to 5 \, (5, 6, 7, 8, 9), round up by adding 1 to the rounding digit.

7 is greater than 5, so 4 hundreds will become a 5 hundreds.

1\underline{4}78 → Rounded to the nearest 100 is 1500

Rounding \bf{\underline{1}478} to the nearest \bf{1000} with a number line

1478 is to the left of the halfway point and closer to
1000 than 2000. It will round to be 1000.

Rounding \bf{\underline{1}478} to the nearest \bf{1000} with the rule

1 thousand is in the rounding place, and 4 hundred is to
the right of the rounding digit.

The rule says that if the number to the right of the rounding digit is less than
5 \, (5, 6, 7, 8, 9), round down by leaving the rounding digit alone.

4 is less than 5, so the digit 1 will remain as a 1.

\underline{1}478 → Rounded to the nearest 1000 is 1000

Rounding \bf{147\underline{8}.5} to the nearest whole number with a number line

1478 is the halfway point between 1478 and 1479 and the same distance
away from either number. When this happens, you will round up 1479.

Rounding \bf{147\underline{8}.5} to the nearest whole number with the rule

8 ones is in the rounding place, and 5 tenths is to the right of the rounding digit.

The rule says that if the number to the right of the rounding digit is greater than
or equal to 5 \, (5, 6, 7, 8, 9), round up by adding one to the rounding digit.

5 is equal to 5, so 8 ones becomes 9 ones.

147\underline{8}.5 → Rounded to the nearest whole number is 1479

### What is rounding numbers? ## Common Core State Standards

How does this relate to 4th grade math and 5th grade math?

• Grade 3 – Number and Operations – Base Ten (3.NBT.A.1)
Use place value understanding to round whole numbers to the nearest 10 or 100.

• Grade 4 – Number and Operations – Base Ten (4.NBT.A.3)
Use place-value understanding to round multi-digit whole numbers to any place.

• Grade 5 – Number and Operations – Base Ten (5.NBT.A.4)
Use place value understanding to round decimals to any place.

## How to round numbers

In order to round a whole number:

1. Find the rounding place and look at the digit immediately to the right of the rounding place.
2. When that digit is 5 or greater, add 1 to the rounding digit. When it is less than 5, leave the rounding digit alone.
3. Change all the digits to the right or the rounding place to 0’s.
4. Write the rounded number.

In order to round a decimal number:

1. Find the rounding place and look at the digit immediately to the right of the rounding place.
2. When that digit is 5 or greater, add 1 to the rounding digit. When it is less than 5, leave the rounding digit alone.
3. Drop all the digits to the right of the rounded digit.
4. Write the rounded number.

## Rounding numbers examples

### Example 1: rounding to the nearest 10

Round 382 to the nearest 10.

1.  Find the rounding place and look at the digit immediately to the right of the rounding place.

3\underline{8}2 → 8 is in the rounding place (tens place)

3\underline{8}2 → 2 is the digit immediately to the right of 8 which is in the ones place.

2When that digit is 5 or greater, add 1 to the rounding digit. When it is less than 5, leave the rounding digit alone.

2 < 5 \; (2 is less than 5), so keep the digit as an 8.

3Change all the digits to the right or the rounding place to 0’s.

382 → change the 2 to a 0

4Write the rounded number.

382 rounded to the nearest 10 is 380.

383 is to the left of the halfway point and closer to 380. It will round to be 380.

### Example 2: rounding to the nearest 100

Round 573 to the nearest 100.

\underline{5}73 → 5 is in the rounding place (hundreds place)

\underline{5}73 → 7 is the digit immediately to the right of 5 which is in the tens place.

7 > 5, \; (7 is greater than 5), add 1 to the rounding digit, 5 will become 6.

\underline{5}73 → 600 – change the 7 and 3 to 0 ’s.

573 rounded to the nearest 100 is 600.

### Example 3: rounding to the nearest 1000

Round 29,862 to the nearest 1000.

2\underline{9},862 → 9 is the digit in the rounding place

2\underline{9},862 → 8 is the digit immediately to the right of 9 (hundreds place).

8 > 5, \; (8 is greater than 5), add 1 to the rounding digit, 9 will become 10.

Place a 0 where the 9 is, add 1 to the digit 2.

2\underline{9},862 → 30,000

29,862 rounded to the nearest 1000 is 30,000.

### Example 4: rounding a decimal number to the nearest whole number

Round 25.67 to the nearest whole number

2\underline{5}.67 → 5 is in the rounded place (ones place)

2\underline{5}.67 → 6 is the digit immediately to the right of 5 (tenths place)

6 > 5, \; (6 is greater than 5), add 1 to the rounding digit, 5 will become 6.

2\underline{5}.67 → drop the digits 6 and 7

25.67 rounded to the nearest whole number is 26

Step-by-step guide: Estimation

### Example 5: rounding a decimal number to the nearest tenth

Round 7.542 to the nearest tenth.

7.\underline{5}42 → 5 is in the rounded place (tenth place)

7.\underline{5}42 → 4 is the digit immediately to the right of 5 (hundredths place)

4 < 5, \; (4 is less than 5), leave the rounding digit alone.

7.542 → drop the digits 4, 2

7.542 rounded to the nearest tenth is 7.5

Step-by-step-guide: Rounding decimals

### Example 6: rounding a decimal number to the nearest hundredth

Round 408.095 to the nearest hundredth.

408.0\underline{9}5 → 9 is in the rounded place (hundredths place)

408.0\underline{9}5 → 5 is the digit immediately to the right of 9 (thousandths place)

5 = 5, so add 1 to the rounded digit, and 9 becomes 10. Replace the 9 with a 0, add 1 to the digit 0.

408.0\underline{9}5 → drop the digits 5 and 6

408.095 rounded to the nearest hundredth is 408.10

### Teaching tips for rounding numbers

• Reinforce rounding with the number line. It gives students a visual representation of what rounding means.

• You can also utilize math videos for rounding in math centers to help students review concepts.

• Emphasize place value to help students with rounding. Provide a place value chart as a visual aide.

• To help students understand why the rule requires the number to be rounded up when there is a 5 to the right of the rounded digit, give them grouping visuals.

There are ten numbers and these numbers are
divided into two groups. The first five digits are
used to round down and the second five digits
are used to round up.

### Our favorite mistakes

• Rounding errors occur when students do not have a strong understanding of place value.
For example, rounding 12.34 to the nearest tenth and a student rounds to the nearest whole number.

• Not rounding up appropriately when 9 is in the rounding digit.
For example, rounding 3.4973 to the nearest hundredth would be 3.49 or 3.40 instead of 3.50.

• When rounding decimal numbers be sure to represent the correct place value.
For example, when rounding the number 5.096 to the nearest hundredth, the rounded decimal number will be 5.10. Be sure to leave 0 as a placeholder.

### Rounding numbers practice questions

1. Round 193 to the nearest 100

100 200 1 2 \underline{1}93 → the digit immediately to the right of the rounding digit is 9.

Applying the rule, 9 > 5, add 1 to the rounded digit. 9 will become 10.

Change all digits to the right of the rounded digit to 0 ’s. 3 is to the right of the rounded digit, so it will become 0.

193 rounded to the nearest hundred, is 200.

2. Round 13.782 to the nearest hundredth.

13.79 13.70 13.80 13.78 13.7\underline{8}2 → 8 is in the rounded place and 2 immediately to the right of it.

Following the rule, 2 < 5, leave the rounded digit alone.

Drop all the digits to the right of the rounded digit, drop the 2.

13.782 rounded to the nearest hundredth is 13.78.

3. Round 25,592 to the nearest thousand.

26,000 25,700 25,600 25,690 2\underline{5},592 → 5 is in the rounded place and 5 is immediately to the right of it.

Following the rule, 5 = 5, so add 1 to the rounded digit. 8 will become 9.

Change all the digits to the right of the rounded digit to 0 ’s. 5, 9, 2 will become 0 ‘s.

25,592 rounded to the nearest thousand is 26,000.

4. Round 0.0364 to the nearest thousandth

0.03 0.36 0.036 0.037 0.036 → 6 is the rounded place and 4 is immediately to the right of it.

Following the rule, 4 < 5. Leave the rounded digit alone.

Drop the digits to the right of the rounded digit. Drop the digit 4.

0.0364 rounded to the nearest thousandth is 0.036

5. Round 77.552 to the nearest whole number.

78 77 77.6 78.6 7\underline{7}.552 → 7 is in the rounded place and 5 is immediately to the right of it.

Following the rule, 5 = 5, so add 1 to the rounded digit. 7 will become 8.

Drop the digits to the right of the rounded digit, so drop the digits 5, 5, and 2.

77.552 rounded to the nearest whole number is 78.

6. Round 2,689 to the nearest ten.

2700 2689 2680 2690 26\underline{8}9 → 8 is in the rounded place and 9 is the digit immediately to the right of it.

Following the rule, 9 > 5, so add 1 to the rounded digit. 8 will become 9.

Change the digits to the right of the rounded digit to 0 ’s. Change 9 to a 0.

2689 rounded to the nearest 10 is 2690.

## Rounding numbers FAQ’s

Is rounding numbers the same as estimation?

Both rounding and estimating are strategies used to approximate numbers so they are easier to calculate or conceptualize. Estimating is the process of making a guess or calculation, whereas rounding is the process of taking the given number and by scaling it up or down. Rounding can be considered a type of estimation.

What are significant figures?

Significant figures are the non-zero numbers in a rounded number. You can round a number to a specific number of significant digits.
For example, rounding 1645 to two significant figures would be 1600. This is the same as rounding 1645 to the nearest hundred.

Why is a number rounded up when there is a 5 after the rounding digit?

The rules for rounding determine that if the number to the right of the rounding digit is 5 or greater, round up. If the number to the right of the rounding digit is less than 5, round down. However, to help visualize this rule, think of the ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ) being divided into two groups. ## Still stuck?

At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.

Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.