https://file.aiquickdraw.com/mathbot/file/1725498885276oj63ftj5.jpg

The image contains the following recurring decimals to be converted into fractions:

- 53. \(0.\overline{6}\)
- 54. \(0.4\)
- 55. \(0.\overline{12}\)
- 56. \(0.\overline{43}\)
- 57. \(0.1\overline{34}\)
- 58. \(0.\overline{731}\)
- 59. \(0.25\)
- 60. \(0.6\overline{17}\)

Let's start by converting these recurring decimals to fractions:

### 1. \(0.\overline{6}\) (53)
Let \(x = 0.\overline{6}\). 
Multiply by 10: 
\[
10x = 6.\overline{6}
\]
Now subtract \(x = 0.\overline{6}\):
\[
10x - x = 6.\overline{6} - 0.\overline{6}
\]
\[
9x = 6
\]
\[
x = \frac{6}{9} = \frac{2}{3}
\]

### 2. \(0.4\) (54)
This is a terminating decimal, so:
\[
0.4 = \frac{4}{10} = \frac{2}{5}
\]

### 3. \(0.\overline{12}\) (55)
Let \(x = 0.\overline{12}\). 
Multiply by 100: 
\[
100x = 12.\overline{12}
\]
Now subtract \(x = 0.\overline{12}\):
\[
100x - x = 12.\overline{12} - 0.\overline{12}
\]
\[
99x = 12
\]
\[
x = \frac{12}{99} = \frac{4}{33}
\]

### 4. \(0.\overline{43}\) (56)
Let \(x = 0.\overline{43}\). 
Multiply by 100: 
\[
100x = 43.\overline{43}
\]
Now subtract \(x = 0.\overline{43}\):
\[
100x - x = 43.\overline{43} - 0.\overline{43}
\]
\[
99x = 43
\]
\[
x = \frac{43}{99}
\]

### 5. \(0.1\overline{34}\) (57)
Let \(x = 0.1\overline{34}\). First express as:
\[
x = 0.1 + 0.\overline{34}
\]
\(0.\overline{34}\) can be converted using the method above, where \(x = \frac{34}{99}\):
\[
x = 0.1 + \frac{34}{99}
\]
Convert 0.1 to a fraction:
\[
x = \frac{1}{10} + \frac{34}{99}
\]
Find a common denominator:
\[
x = \frac{99 + 340}{990} = \frac{439}{990}
\]
Simplify:
\[
x = \frac{439}{990}
\]

### 6. \(0.\overline{731}\) (58)
Let \(x = 0.\overline{731}\). 
Multiply by 1000:
\[
1000x = 731.\overline{731}
\]
Now subtract \(x = 0.\overline{731}\):
\[
1000x - x = 731.\overline{731} - 0.\overline{731}
\]
\[
999x = 731
\]
\[
x = \frac{731}{999}
\]

### 7. \(0.25\) (59)
This is a terminating decimal, so:
\[
0.25 = \frac{25}{100} = \frac{1}{4}
\]

### 8. \(0.6\overline{17}\) (60)
Let \(x = 0.6\overline{17}\). First express as:
\[
x = 0.6 + 0.\overline{17}
\]
\(0.\overline{17}\) can be converted similarly:
\[
0.\overline{17} = \frac{17}{99}
\]
Convert 0.6 to a fraction:
\[
x = \frac{6}{10} + \frac{17}{99}
\]
Find a common denominator:
\[
x = \frac{594 + 170}{990} = \frac{764}{990}
\]
Simplify:
\[
x = \frac{382}{495}
\]

Would you like more details on any of these conversions, or have any other questions?

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Here are 5 related questions to consider:
1. How do you convert any recurring decimal into a fraction?
2. What is the difference between terminating and recurring decimals?
3. How do you simplify fractions to their lowest terms?
4. What are the properties of repeating decimal patterns?
5. Can every repeating decimal be expressed as a fraction?

**Tip:** Always simplify fractions after converting from decimals to ensure the result is in its simplest form.

Convert the following recurring decimals to fractions: 53. 0.6̅, 54. 0.4, 55. 0.1̅2̅, 56. 0.4̅3̅, 57. 0.1̅34̅, 58. 0.7̅31̅, 59. 0.25, 60. 0.6̅17̅.

Learn how to convert recurring decimals such as 0.6̅, 0.4̅3̅, and 0.1̅2̅ into fractions. This guide provides a step-by-step breakdown of converting recurring decimals and simplifying them into their simplest fractional form, suitable for Grades 7-10.

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