To convert the decimal \( 17.153163153153 \) into a fraction, we first observe that it has a repeating part, which is \( 163 \). This means the number can be written as:

\[
17.153163163163\ldots
\]

Let's represent this number as \( x \):

\[
x = 17.153163163163\ldots
\]

### Step 1: Remove the whole number part
Subtract the whole number part \( 17 \) from \( x \):

\[
x - 17 = 0.153163163163\ldots
\]

### Step 2: Express the decimal part as a fraction
Let \( y = 0.153163163163\ldots \). Now, multiply \( y \) by \( 1000 \) to move the decimal point to the right of the first repeating sequence:

\[
1000y = 153.163163163\ldots
\]

Now, subtract \( y \) from \( 1000y \):

\[
1000y - y = 153.163163163\ldots - 0.153163163\ldots
\]

This simplifies to:

\[
999y = 153
\]

So,

\[
y = \frac{153}{999}
\]

Now, simplify the fraction:

\[
y = \frac{153 \div 9}{999 \div 9} = \frac{17}{111}
\]

### Step 3: Add back the whole number
Now add back the whole number part:

\[
x = 17 + \frac{17}{111} = \frac{17 \times 111 + 17}{111} = \frac{1887 + 17}{111} = \frac{1904}{111}
\]

Thus, the fraction form of \( 17.153163153153 \) is:

\[
\frac{1904}{111}
\]

This is the simplest fraction that represents the decimal \( 17.153163153153 \).

---

Would you like a detailed breakdown of the steps or any further clarifications? Here are some related questions to explore:

1. How do you convert other repeating decimals to fractions?
2. Can you express non-repeating decimals as fractions?
3. How do you simplify fractions?
4. What are some practical uses of repeating decimals in real life?
5. Can every decimal be converted to a fraction?

**Tip:** Always check if a fraction can be simplified by finding the greatest common divisor of the numerator and denominator.

This guide explains how to convert the repeating decimal 17.153163153153 into a fraction. Learn the steps involved, including removing the whole number, expressing the repeating part as a fraction, and simplifying. The final fraction is 1904/111. Suitable for Grades 9-12.

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