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# Fractions as Decimals

## Dividing the denominator into the numerator

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Fractions as Decimals

Have you ever completed a survey?

After the sixth grade social, the students were given a survey. The survey asked the students about their favorite events and whether or not they had a terrific time. Some of the students wished there had been more dancing, some wished there had been more games, and some wished they could have attended at all. For different reasons, 6A had 40 out of 48 students attend and 6B had 42 out of 44 students attend.

After going through the surveys, Wendy, the class secretary, has tallied the results. She is most interested in figuring out which cluster has more students who say that they had a terrific time at the social.

Here are the results.

In 6A, \begin{align*}\frac{36}{40}\end{align*} said that they had a terrific time.

In 6B, \begin{align*}\frac{35}{42}\end{align*} said that they had a terrific time.

Wendy thinks that 6A has more students who say that they had a terrific time. Is she correct?

To figure out whether or not Wendy is correct, it would help to learn how to convert fractions to decimals. Once you have learned these skills, you can come back to this problem and figure out if Wendy has accurately analyzed the situation.

### Guidance

Previously we worked on converting decimals to fractions. Now we are going to work the other way around.

How do we convert a fraction to a decimal?

There are two ways to convert a fraction to a decimal.

The first way is to think in terms of place value. If we have a fraction that has ten as a denominator, we can think of that fraction as tenths. Now we can figure out how to write the decimal.

\begin{align*}\frac{6}{10}=.6\end{align*}

There is one decimal place in tenths, so this decimal is accurate.

\begin{align*}\frac{125}{1000}\end{align*}

There are three decimal places in a thousandths decimal. There are three digits in the numerator. We can easily convert this to a decimal.

The second way is to use division. We can take the numerator of a fraction and divide it by the denominator. The denominator is the divisor and the numerator is the dividend.

\begin{align*}\frac{3}{5}\end{align*}

We want to change \begin{align*}\frac{3}{5}\end{align*} to a decimal. We can do this by dividing the numerator by the denominator. We will be adding a decimal point and zero placeholders to help us with this division. Let’s take a look.

\begin{align*}& \overset{ \quad \ .6}{5 \overline{ ) {3.0 \;}}}\\ & \ \underline{-30}\\ & \quad \ \ 0\end{align*}

Now it is time for you to try a few. Convert each fraction to a decimal.

#### Example A

\begin{align*}\frac{8}{10}\end{align*}

Solution: \begin{align*}0.8\end{align*}

#### Example B

\begin{align*}\frac{5}{100}\end{align*}

Solution: \begin{align*}0.05\end{align*}

#### Example C

\begin{align*}\frac{3}{5}\end{align*}

Solution: \begin{align*}0.6\end{align*}

Now back to the survey!

If you look at the survey results for 6A and 6B you will see that they both have different denominators. Their denominators aren’t base ten denominators either.

We need to convert both fractions into decimals to be able to compare them. The easiest way to do this is to divide using a decimal point and zero placeholders.

\begin{align*}& 6A = \overset{ \qquad \ .9}{40 \overline{ ) {36.0 \;}}}\\ & \qquad \quad \ \underline{-360}\\ & \qquad \qquad \quad 0\end{align*}

6A has .9 or \begin{align*}\frac{9}{10}\end{align*} of the students who say that they had a terrific time.

\begin{align*}& 6B = \overset{ \qquad \ .833}{42 \overline{ ) {35.000 \;}}}\\ & \qquad \quad \ \underline{-336\;}\\ & \qquad \qquad \ \ 140\\ & \qquad \qquad \underline{-126\;}\\ & \qquad \qquad \quad \ 140 \end{align*}

6B has a repeating decimal of \begin{align*}.8\bar{3}\end{align*} .

Now we can compare the two decimals.

\begin{align*}.9 > .83\end{align*}

Wendy was correct. 6A does have more students who say that they had a terrific time!!

### Guided Practice

Here is one for you to try on your own.

Write the following fraction as a decimal.

\begin{align*} \frac{1}{4}\end{align*}

To write this as a decimal, we must first convert it into a denominator of 100.

\begin{align*} \frac{1}{4} = \frac{25}{100}\end{align*}

Now we can write it as a decimal.

\begin{align*}0.25\end{align*}

### Explore More

Directions: Write the following fractions as decimals.

1. \begin{align*}\frac{3}{10}\end{align*}
2. \begin{align*}\frac{23}{100}\end{align*}
3. \begin{align*}\frac{9}{100}\end{align*}
4. \begin{align*}\frac{8}{10}\end{align*}
5. \begin{align*}\frac{182}{1000}\end{align*}
6. \begin{align*}\frac{25}{100}\end{align*}
7. \begin{align*}\frac{6}{10}\end{align*}
8. \begin{align*}\frac{125}{1000}\end{align*}
9. \begin{align*}\frac{1}{10}\end{align*}
10. \begin{align*}\frac{2}{100}\end{align*}
11. \begin{align*}\frac{1}{2}\end{align*}
12. \begin{align*}\frac{1}{4}\end{align*}
13. \begin{align*}\frac{3}{4}\end{align*}
14. \begin{align*}\frac{3}{6}\end{align*}
15. \begin{align*}\frac{3}{5}\end{align*}

### Vocabulary Language: English

Decimal

Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).
Equivalent

Equivalent

Equivalent means equal in value or meaning.
fraction

fraction

A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar. It is also called a rational number.
Irrational Number

Irrational Number

An irrational number is a number that can not be expressed exactly as the quotient of two integers.
Place Value

Place Value

The value of given a digit in a multi-digit number that is indicated by the place or position of the digit.