Answer :
Answer:
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Step-by-step explanation:
To convert the repeating decimal \( 0.63\overline{3} \) into a rational number, follow these steps:
Let \( x = 0.63\overline{3} \).
Step 1: Identify the repeating part and separate it.
- The repeating part is \( 0.3 \).
Step 2: Multiply \( x \) by 10 to shift the repeating part to the left of the decimal point:
\[
10x = 6.333\overline{3}
\]
Step 3: Subtract the original \( x \) from \( 10x \) to eliminate the repeating part:
\[
10x - x = 6.333\overline{3} - 0.63\overline{3}
\]
\[
9x = 5.7
\]
Step 4: Solve for \( x \):
\[
x = \frac{5.7}{9}
\]
Step 5: Simplify the fraction \( \frac{5.7}{9} \):
\[
x = \frac{57}{90}
\]
Step 6: Further simplify \( \frac{57}{90} \) by dividing numerator and denominator by their greatest common divisor, which is 3:
\[
x = \frac{57 \div 3}{90 \div 3} = \frac{19}{30}
\]
Therefore, the rational representation of the repeating decimal \( 0.63\overline{3} \) is \( \frac{19}{30} \).
Answer:
63/99
Step-by-step explanation:
0.63 bar
let x = 0.63... 1
multiple by 100 on both side
100 x = 63.63....... 2
subtracting 1 from 2
100x-x = 63.63-0.63
99x = 63
x = 63/99