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# Decimal Rounding and Division

## Use digit following required place value for rounding

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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

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.

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.

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*}0.1234178\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*}0.123\end{align*}

### Vocabulary

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*}

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

\begin{align*}0.114055\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.

### 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*}

### Vocabulary Language: English

Divide

Divide

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

Dividend

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

divisor

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

Quotient

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