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.

**Our answer is .125.**

**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*}

**Our answer is .6.**

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*}.8\end{align*}**

#### Example B

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

**Solution:\begin{align*}.05\end{align*}**

#### Example C

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

**Solution:\begin{align*}.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!!**

### Vocabulary

- Decimal
- a part of a whole written using place value and a decimal point.

- Fraction
- a part of a whole written with a fraction bar dividing the numerator and the denominator.

- Equivalent
- means equal

### 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*}

**Answer**

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*}.25\end{align*}

**This is our answer.**

### Interactive Practice

### Video Review

Khan Academy Converting Fractions to Decimals

James Sousa Fractions to Decimals

### Practice

Directions: Write the following fractions as decimals.

- \begin{align*}\frac{3}{10}\end{align*}
- \begin{align*}\frac{23}{100}\end{align*}
- \begin{align*}\frac{9}{100}\end{align*}
- \begin{align*}\frac{8}{10}\end{align*}
- \begin{align*}\frac{182}{1000}\end{align*}
- \begin{align*}\frac{25}{100}\end{align*}
- \begin{align*}\frac{6}{10}\end{align*}
- \begin{align*}\frac{125}{1000}\end{align*}
- \begin{align*}\frac{1}{10}\end{align*}
- \begin{align*}\frac{2}{100}\end{align*}
- \begin{align*}\frac{1}{2}\end{align*}
- \begin{align*}\frac{1}{4}\end{align*}
- \begin{align*}\frac{3}{4}\end{align*}
- \begin{align*}\frac{3}{6}\end{align*}
- \begin{align*}\frac{3}{5}\end{align*}