# 4.12: Decimal Rounding and Division

**At Grade**Created by: CK-12

**Practice**Decimal Rounding and Division

Have you ever had to divide a very small decimal? It can be tricky business.

Let's say you have the following decimal.

\begin{align*}.9873429 \div 8\end{align*}

What would the quotient be? Can you round this to the nearest thousandth?

**This Concept is all about dividing and rounding decimals. By the end of it, you will know how to accomplish this task.**

### Guidance

You have learned how to divide decimals by whole numbers and how to use zero placeholders to find the most accurate decimal quotient. We can also take a decimal quotient and round it to a specific place. Let’s say we have a decimal like this one.

.3456210

**Wow! That is a mighty long decimal. It is so long that it is difficult to decipher the value of the decimal.**

**If we were to round the decimal to the thousandths place, that would make the size of the decimal a lot easier to understand.**

.3456210 Five is in the thousandths place. The number after it is a six, so we round up.

.346

**Our answer is .346.**

**Now let’s try it with an example. Divide and round this decimal quotient to the nearest ten-thousandth.**

1.26484 \begin{align*}\div\end{align*} 4 = ______

Use a piece of paper to complete this division.

**Our answer is .31621.**

**Now we want to round to the nearest ten-thousandth.**

**.31621 Two is in the ten-thousandths place. The number after this is a one so our two does not round up.**

**Our answer is .3162.**

Now it's time for you to practice. Divide these decimals and whole numbers and then round each to the nearest thousandth.

#### Example A

**.51296 \begin{align*}\div\end{align*} 2 \begin{align*}=\end{align*} _____**

**Solution: .256**

#### Example B

**10.0767 \begin{align*}\div\end{align*} 3 \begin{align*}=\end{align*} _____**

**Solution: 3.359**

#### Example C

\begin{align*}.48684 \div 2\end{align*}

**Solution: .243**

Now back to the original problem.

Have you ever had to divide a very small decimal? It can be tricky business. Let's say you have the following decimal.

\begin{align*}.9873429 \div 8\end{align*}

What would the quotient be? Can you round this to the nearest thousandth?

First we divide the decimal by 8.

\begin{align*}.1234178\end{align*}

This is the quotient.

Now to get a better sense of this decimal, we can round it to the nearest thousandth. To do this, we look at the value to the right of the thousandths place. It is a 4.

So, we round up.

\begin{align*}.123\end{align*}

**This is our answer.**

### Vocabulary

**Here are the vocabulary words used for this Concept.**

- Divide
- to split up into groups evenly.

- Divisor
- a number that is doing the dividing. It is found outside of the division box.

- Dividend
- the number that is being divided. It is found inside the division box.

- Quotient
- the answer to a division problem

### Guided Practice

Here is one for you to try on your own.

Divide the following and then round the quotient to the nearest thousandth.

\begin{align*}.45622 \div 4\end{align*}

**Answer**

To do this, we simply divide. Here is the quotient.

\begin{align*}.114055\end{align*}

Next, we round to the nearest thousandth.

The 4 is in the thousandths place. Because the digit to the right of the 4 is a zero, we don't round up.

**Our answer is .114.**

### Video Review

Here are videos for review.

Khan Academy Dividing Decimals 2

James Sousa Example of Dividing a Decimal by a Whole Number

### Practice

Directions: Divide and round each quotient to the nearest thousandth.

1. \begin{align*}.54686 \div 2\end{align*}

2. \begin{align*}.84684 \div 2\end{align*}

3. \begin{align*}.154586 \div 2\end{align*}

4. \begin{align*}.34689 \div 3\end{align*}

5. \begin{align*}.994683 \div 3\end{align*}

6. \begin{align*}.154685 \div 5\end{align*}

7. \begin{align*}.546860 \div 5\end{align*}

8. \begin{align*}.25465 \div 5\end{align*}

9. \begin{align*}.789003 \div 3\end{align*}

10. \begin{align*}.18905 \div 5\end{align*}

11. \begin{align*}.27799 \div 9\end{align*}

12. \begin{align*}.354680 \div 10\end{align*}

13. \begin{align*}.454686 \div 6\end{align*}

14. \begin{align*}.954542 \div 2\end{align*}

15. \begin{align*}.8546812 \div 4\end{align*}

Divide

To divide is split evenly into groups. The result of a division operation is a quotient.Dividend

In a division problem, the dividend is the number or expression that is being divided.divisor

In a division problem, the divisor is the number or expression that is being divided into the dividend. For example: In the expression , 6 is the divisor and 152 is the dividend.Quotient

The quotient is the result after two amounts have been divided.### Image Attributions

Here you'll learn how to divide and round decimals.

## Concept Nodes:

Divide

To divide is split evenly into groups. The result of a division operation is a quotient.Dividend

In a division problem, the dividend is the number or expression that is being divided.divisor

In a division problem, the divisor is the number or expression that is being divided into the dividend. For example: In the expression , 6 is the divisor and 152 is the dividend.Quotient

The quotient is the result after two amounts have been divided.