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sahilsahh
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­Which of the following fractions is equal to 0.10101010... ? 01 Jul 2024, 22:23
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73% (00:56) correct 27% (00:44) wrong based on 127 sessions

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­Which of the following fractions is equal to 0.10101010... ?

A. 10/999
B. 1/90
C. 5/99
D. 10/99
E. 1/9
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Bunuel
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­Which of the following fractions is equal to 0.10101010... ? 02 Jul 2024, 08:15
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sahilsah456
­Which of the following fractions is equal to 0.10101010... ?

A. 10/999
B. 1/90
C. 5/99
D. 10/99
E. 1/9
Show more
We are given the recurring decimal \(0.\overline{10}\) and want to convert it to a fraction. There are several methods to do this.

APPROACH 1. Put the recurring number in the numerator and put as many nines in the denominator as there are digits in the recurring number. Hence, for \(0.\overline{10}\), we put 10 in the numerator and 99 (two 9's) in the denominator, since there are two recurring digits. Thus, \(0.\overline{10}=\frac{10}{99}\). 

P.S. You won't need this for the GMAT, but if you're still interested, here is how to convert mixed recurring decimals such as \(0.2\overline{18}\), into fractions. First, write a number, consisting of the non-repeating digits and the repeating digits together, which in this case is 218. Next, subtract the non-repeating digits (2) from this number to get 216, and put it in the numerator. To form the denominator, put as many nines as there are repeating digits, followed by as many zeros as there are non-repeating digits. For \(0.2\overline{18}\), there are two repeating digits and one non-repeating digit, so the denominator would be 990. We get \(0.2\overline{18}=\frac{218-2}{990}=\frac{216}{990}=\frac{12}{55}\).

APPROACH 2. Equate the recurring decimal to \(x\). We get \(x = 0.\overline{10}\). Multiply \(x\) by a power of 10, such that only the recurring part appears after the decimal point. For \(0.\overline{10}\), it would mean multiplying it by 100 to get \(100x=10.\overline{10}\). Subtract \(x\) from this equation to eliminate the recurring part: \(100x - x = 99x=10.\overline{10}-0.\overline{10}=10\). Therefore, we get that \(x = 0.\overline{10}=\frac{10}{99}\).

P.S. You won't need this for the GMAT, but if you're still interested, here is how to convert mixed recurring decimals such as \(0.2\overline{18}\), into fractions with this approach. Equate the recurring decimal to \(x\). We get \(x = 0.2\overline{18}\). Next, multiply the recurring decimal by a power of 10 so that only the recurring numbers appear after the decimal point. For \(0.2\overline{18}\), this means multiplying by 10, giving \(10x=2.\overline{18}\). Then, multiply the recurring decimal by a power of 10 so that the recurring numbers also appear before the decimal point. For \(0.2\overline{18}\), this means multiplying by 1000, giving \(1000x=218.\overline{18}\). Subtracting one from the other yields \(1000x-10x=218.\overline{18}-2.\overline{18}\), which simplifies to \(990x=216\). Therefore, we can write \(x=\frac{216}{990}=\frac{12}{55}\).


Answer: B­
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soniasw16
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­Which of the following fractions is equal to 0.10101010... ? 21 Jul 2025, 04:50
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"Next, subtract the non-repeating digits (2) from this number to get 216, and put it in the numerator." --> What are the 2 non-repeating digits in this number?
Bunuel
sahilsah456
­Which of the following fractions is equal to 0.10101010... ?

A. 10/999
B. 1/90
C. 5/99
D. 10/99
E. 1/9
We are given the recurring decimal \(0.\overline{10}\) and want to convert it to a fraction. There are several methods to do this.

APPROACH 1. Put the recurring number in the numerator and put as many nines in the denominator as there are digits in the recurring number. Hence, for \(0.\overline{10}\), we put 10 in the numerator and 99 (two 9's) in the denominator, since there are two recurring digits. Thus, \(0.\overline{10}=\frac{10}{99}\).

P.S. You won't need this for the GMAT, but if you're still interested, here is how to convert mixed recurring decimals such as \(0.2\overline{18}\), into fractions. First, write a number, consisting of the non-repeating digits and the repeating digits together, which in this case is 218. Next, subtract the non-repeating digits (2) from this number to get 216, and put it in the numerator. To form the denominator, put as many nines as there are repeating digits, followed by as many zeros as there are non-repeating digits. For \(0.2\overline{18}\), there are two repeating digits and one non-repeating digit, so the denominator would be 990. We get \(0.2\overline{18}=\frac{218-2}{990}=\frac{216}{990}=\frac{12}{55}\).

APPROACH 2. Equate the recurring decimal to \(x\). We get \(x = 0.\overline{10}\). Multiply \(x\) by a power of 10, such that only the recurring part appears after the decimal point. For \(0.\overline{10}\), it would mean multiplying it by 100 to get \(100x=10.\overline{10}\). Subtract \(x\) from this equation to eliminate the recurring part: \(100x - x = 99x=10.\overline{10}-0.\overline{10}=10\). Therefore, we get that \(x = 0.\overline{10}=\frac{10}{99}\).

P.S. You won't need this for the GMAT, but if you're still interested, here is how to convert mixed recurring decimals such as \(0.2\overline{18}\), into fractions with this approach. Equate the recurring decimal to \(x\). We get \(x = 0.2\overline{18}\). Next, multiply the recurring decimal by a power of 10 so that only the recurring numbers appear after the decimal point. For \(0.2\overline{18}\), this means multiplying by 10, giving \(10x=2.\overline{18}\). Then, multiply the recurring decimal by a power of 10 so that the recurring numbers also appear before the decimal point. For \(0.2\overline{18}\), this means multiplying by 1000, giving \(1000x=218.\overline{18}\). Subtracting one from the other yields \(1000x-10x=218.\overline{18}-2.\overline{18}\), which simplifies to \(990x=216\). Therefore, we can write \(x=\frac{216}{990}=\frac{12}{55}\).


Answer: B­
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soniasw16
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­Which of the following fractions is equal to 0.10101010... ? 21 Jul 2025, 04:50
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"Next, subtract the non-repeating digits (2) from this number to get 216, and put it in the numerator." --> What are the 2 non-repeating digits in this number?
Bunuel
sahilsah456
­Which of the following fractions is equal to 0.10101010... ?

A. 10/999
B. 1/90
C. 5/99
D. 10/99
E. 1/9
We are given the recurring decimal \(0.\overline{10}\) and want to convert it to a fraction. There are several methods to do this.

APPROACH 1. Put the recurring number in the numerator and put as many nines in the denominator as there are digits in the recurring number. Hence, for \(0.\overline{10}\), we put 10 in the numerator and 99 (two 9's) in the denominator, since there are two recurring digits. Thus, \(0.\overline{10}=\frac{10}{99}\).

P.S. You won't need this for the GMAT, but if you're still interested, here is how to convert mixed recurring decimals such as \(0.2\overline{18}\), into fractions. First, write a number, consisting of the non-repeating digits and the repeating digits together, which in this case is 218. Next, subtract the non-repeating digits (2) from this number to get 216, and put it in the numerator. To form the denominator, put as many nines as there are repeating digits, followed by as many zeros as there are non-repeating digits. For \(0.2\overline{18}\), there are two repeating digits and one non-repeating digit, so the denominator would be 990. We get \(0.2\overline{18}=\frac{218-2}{990}=\frac{216}{990}=\frac{12}{55}\).

APPROACH 2. Equate the recurring decimal to \(x\). We get \(x = 0.\overline{10}\). Multiply \(x\) by a power of 10, such that only the recurring part appears after the decimal point. For \(0.\overline{10}\), it would mean multiplying it by 100 to get \(100x=10.\overline{10}\). Subtract \(x\) from this equation to eliminate the recurring part: \(100x - x = 99x=10.\overline{10}-0.\overline{10}=10\). Therefore, we get that \(x = 0.\overline{10}=\frac{10}{99}\).

P.S. You won't need this for the GMAT, but if you're still interested, here is how to convert mixed recurring decimals such as \(0.2\overline{18}\), into fractions with this approach. Equate the recurring decimal to \(x\). We get \(x = 0.2\overline{18}\). Next, multiply the recurring decimal by a power of 10 so that only the recurring numbers appear after the decimal point. For \(0.2\overline{18}\), this means multiplying by 10, giving \(10x=2.\overline{18}\). Then, multiply the recurring decimal by a power of 10 so that the recurring numbers also appear before the decimal point. For \(0.2\overline{18}\), this means multiplying by 1000, giving \(1000x=218.\overline{18}\). Subtracting one from the other yields \(1000x-10x=218.\overline{18}-2.\overline{18}\), which simplifies to \(990x=216\). Therefore, we can write \(x=\frac{216}{990}=\frac{12}{55}\).


Answer: B­
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