To solve the problem of converting each fraction to a decimal, we will divide the numerator by the denominator for each fraction. If the resulting decimal repeats or continues indefinitely, we will round it to the nearest thousandth place (three decimal places). Let's go through each fraction step by step.
---
1. \( \frac{4}{10} \)
- Divide 4 by 10:
\[
4 \div 10 = 0.4
\]
- The decimal is already exact and does not need rounding.
-
Answer: \( 0.4 \)
---
2. \( \frac{2}{3} \)
- Divide 2 by 3:
\[
2 \div 3 = 0.6666\ldots
\]
- The decimal repeats as \( 0.\overline{6} \).
- Round to the nearest thousandth:
\[
0.6666\ldots \approx 0.667
\]
-
Answer: \( 0.667 \)
---
3. \( \frac{5}{6} \)
- Divide 5 by 6:
\[
5 \div 6 = 0.8333\ldots
\]
- The decimal repeats as \( 0.8\overline{3} \).
- Round to the nearest thousandth:
\[
0.8333\ldots \approx 0.833
\]
-
Answer: \( 0.833 \)
---
4. \( \frac{7}{9} \)
- Divide 7 by 9:
\[
7 \div 9 = 0.7777\ldots
\]
- The decimal repeats as \( 0.\overline{7} \).
- Round to the nearest thousandth:
\[
0.7777\ldots \approx 0.778
\]
-
Answer: \( 0.778 \)
---
5. \( \frac{1}{5} \)
- Divide 1 by 5:
\[
1 \div 5 = 0.2
\]
- The decimal is already exact and does not need rounding.
-
Answer: \( 0.2 \)
---
6. \( \frac{3}{7} \)
- Divide 3 by 7:
\[
3 \div 7 = 0.428571\ldots
\]
- The decimal repeats as \( 0.\overline{428571} \).
- Round to the nearest thousandth:
\[
0.428571\ldots \approx 0.429
\]
-
Answer: \( 0.429 \)
---
Final Answers:
\[
\begin{array}{|c|c|}
\hline
\text{Fraction} & \text{Decimal} \\
\hline
\frac{4}{10} & 0.4 \\
\hline
\frac{2}{3} & 0.667 \\
\hline
\frac{5}{6} & 0.833 \\
\hline
\frac{7}{9} & 0.778 \\
\hline
\frac{1}{5} & 0.2 \\
\hline
\frac{3}{7} & 0.429 \\
\hline
\end{array}
\]
Boxed Final Answer:
\[
\boxed{0.4, 0.667, 0.833, 0.778, 0.2, 0.429}
\]
Parent Tip: Review the logic above to help your child master the concept of how to convert fractions to decimals worksheet.
