Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Certainly! Let's transform the repeating decimal [tex]\( 2.\overline{81} \)[/tex] into a fraction.
1. Let [tex]\( x \)[/tex] represent the repeating decimal:
[tex]\[ x = 2.818181\ldots \][/tex]
2. To eliminate the repeating part, multiply both sides of the equation by 100 (since 81 repeats every two decimal places):
[tex]\[ 100x = 281.818181\ldots \][/tex]
3. Now subtract the original [tex]\( x \)[/tex] from this equation:
[tex]\[ 100x - x = 281.818181\ldots - 2.818181\ldots \][/tex]
4. This simplifies to:
[tex]\[ 99x = 279 \][/tex]
5. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{279}{99} \][/tex]
6. Simplify the fraction by finding the greatest common divisor (GCD) of 279 and 99. The GCD of 279 and 99 is 9.
7. Divide the numerator and the denominator by their GCD:
[tex]\[ \frac{279 \div 9}{99 \div 9} = \frac{31}{11} \][/tex]
Therefore, the repeating decimal [tex]\( 2.\overline{81} \)[/tex] expressed as a quotient of two integers is [tex]\( \frac{31}{11} \)[/tex].
1. Let [tex]\( x \)[/tex] represent the repeating decimal:
[tex]\[ x = 2.818181\ldots \][/tex]
2. To eliminate the repeating part, multiply both sides of the equation by 100 (since 81 repeats every two decimal places):
[tex]\[ 100x = 281.818181\ldots \][/tex]
3. Now subtract the original [tex]\( x \)[/tex] from this equation:
[tex]\[ 100x - x = 281.818181\ldots - 2.818181\ldots \][/tex]
4. This simplifies to:
[tex]\[ 99x = 279 \][/tex]
5. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{279}{99} \][/tex]
6. Simplify the fraction by finding the greatest common divisor (GCD) of 279 and 99. The GCD of 279 and 99 is 9.
7. Divide the numerator and the denominator by their GCD:
[tex]\[ \frac{279 \div 9}{99 \div 9} = \frac{31}{11} \][/tex]
Therefore, the repeating decimal [tex]\( 2.\overline{81} \)[/tex] expressed as a quotient of two integers is [tex]\( \frac{31}{11} \)[/tex].
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.