Discover new knowledge and insights with IDNLearn.com's extensive Q&A platform. Discover detailed and accurate answers to your questions from our knowledgeable and dedicated community members.
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]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.