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 $100.$

Example 3: rounding to the nearest 1000

Round $29,862$ to the nearest $1000.$

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

Show step

$8 > 5, \; (8$ 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 $2.$

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

Round $25.67$ to the nearest whole number

Step-by-step guide: Estimation

Example 5: rounding a decimal number to the nearest tenth

Round $7.542$ to the nearest tenth.

Step-by-step-guide: Rounding decimals

Example 6: rounding a decimal number to the nearest hundredth

Round $408.095$ to the nearest hundredth.

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

Show step

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

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.

The next lessons are

• Factors and multiples
• Fractions
• Fractions operations

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