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Sagot :
To determine the fractional form of the repeating decimal [tex]\( 0.\overline{8} \)[/tex], follow these steps:
1. Let the repeating decimal be represented by [tex]\( x \)[/tex]:
[tex]\[ x = 0.\overline{8} \][/tex]
2. Express the repeating decimal by multiplying [tex]\( x \)[/tex] by 10:
[tex]\[ 10x = 8.8888\ldots \][/tex]
Here, the decimal part is again [tex]\( 0.\overline{8} \)[/tex].
3. Subtract the original equation from this new equation:
[tex]\[ 10x = 8.8888\ldots \][/tex]
[tex]\[ - (x = 0.8888\ldots) \][/tex]
[tex]\[ 9x = 8 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{8}{9} \][/tex]
Thus, the fractional form of [tex]\( 0.\overline{8} \)[/tex] is:
[tex]\[ \frac{8}{9} \][/tex]
The correct answer is:
C. [tex]\(\frac{8}{9}\)[/tex]
1. Let the repeating decimal be represented by [tex]\( x \)[/tex]:
[tex]\[ x = 0.\overline{8} \][/tex]
2. Express the repeating decimal by multiplying [tex]\( x \)[/tex] by 10:
[tex]\[ 10x = 8.8888\ldots \][/tex]
Here, the decimal part is again [tex]\( 0.\overline{8} \)[/tex].
3. Subtract the original equation from this new equation:
[tex]\[ 10x = 8.8888\ldots \][/tex]
[tex]\[ - (x = 0.8888\ldots) \][/tex]
[tex]\[ 9x = 8 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{8}{9} \][/tex]
Thus, the fractional form of [tex]\( 0.\overline{8} \)[/tex] is:
[tex]\[ \frac{8}{9} \][/tex]
The correct answer is:
C. [tex]\(\frac{8}{9}\)[/tex]
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