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Approximating Fractions with Repeating Decimals

Write the fractions using decimal approximations. The example in the first row will guide you on how to enter your answers.

\begin{tabular}{|c|c|c|c|}
\hline
Fraction & Decimal to One Place Value & Decimal to Two Place Values & Decimal to Three Place Values \\
\hline
[tex]$\frac{1}{3}$[/tex] & 0.3 & 0.33 & 0.333 \\
\hline
[tex]$\frac{4}{9}$[/tex] & & & \\
\hline
[tex]$\frac{4}{13}$[/tex] & & & \\
\hline
[tex]$\frac{7}{24}$[/tex] & & & \\
\hline
\end{tabular}

Some questions may have textbook or video help available. To watch a quick refresher video on rounding, click the video link below.

Question Help:
Video

Sagot :

GinnyAnsweridn
Sure, let's go through the process of approximating each given fraction as a decimal to one, two, and three places.

### Fraction: [tex]\(\frac{1}{3}\)[/tex]
- Decimal to One Place: 0.3
- Decimal to Two Places: 0.33
- Decimal to Three Places: 0.333

These values are provided as an example.

### Fraction: [tex]\(\frac{4}{9}\)[/tex]
1. Decimal to One Place:
- [tex]\(\frac{4}{9}\)[/tex] ≈ 0.4 (rounded to one decimal place)

2. Decimal to Two Places:
- [tex]\(\frac{4}{9}\)[/tex] ≈ 0.44 (rounded to two decimal places)

3. Decimal to Three Places:
- [tex]\(\frac{4}{9}\)[/tex] ≈ 0.444 (rounded to three decimal places)

### Fraction: [tex]\(\frac{4}{13}\)[/tex]
1. Decimal to One Place:
- [tex]\(\frac{4}{13}\)[/tex] ≈ 0.3 (rounded to one decimal place)

2. Decimal to Two Places:
- [tex]\(\frac{4}{13}\)[/tex] ≈ 0.31 (rounded to two decimal places)

3. Decimal to Three Places:
- [tex]\(\frac{4}{13}\)[/tex] ≈ 0.308 (rounded to three decimal places)

### Fraction: [tex]\(\frac{7}{24}\)[/tex]
1. Decimal to One Place:
- [tex]\(\frac{7}{24}\)[/tex] ≈ 0.3 (rounded to one decimal place)

2. Decimal to Two Places:
- [tex]\(\frac{7}{24}\)[/tex] ≈ 0.29 (rounded to two decimal places)

3. Decimal to Three Places:
- [tex]\(\frac{7}{24}\)[/tex] ≈ 0.292 (rounded to three decimal places)

Now, let's fill in these values in the provided table:

[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Fraction} & \text{Decimal to One Place} & \text{Decimal to Two Places} & \text{Decimal to Three Places} \\ \hline \frac{1}{3} & 0.3 & 0.33 & 0.333 \\ \hline \frac{4}{9} & 0.4 & 0.44 & 0.444 \\ \hline \frac{4}{13} & 0.3 & 0.31 & 0.308 \\ \hline \frac{7}{24} & 0.3 & 0.29 & 0.292 \\ \hline \end{array} \][/tex]

By following these steps, you can determine the approximated decimal values for each fraction at different levels of precision.
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