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Conversion of Recurring Decimals to Fractions

While convert...

Question

While converting $2. ¯ ¯ ¯ 3$ into a fraction, Garry performed the following steps:

Step 1: $x = 2.333333...$
Step 2: $10 x = 23.333333...$
Step 3: $10 x - x = 21$
Step 4: $x = \frac{21}{3}$

In which step did Garry go wrong?

Step 1

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Step 2

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Step 3

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Step 4

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Solution

The correct option is D Step 4

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Similar questions

2. ¯ ¯ ¯ 3

x = 2.333333...

10 x = 23.333333...

10 x - x = 21

x = \frac{21}{3}

5 \frac{1}{2}

Step 1 : 5 \times 2 = 10

Step 2 : 10 + 1 = 11

Step 13 : \frac{11}{5}

5 x + 7 x - 4 x + 2 = 5

12 x - 4 x = 3

8 x = 3

x = 3 \times 8

3 \frac{5}{8} - 1 \frac{1}{4}

3 \frac{5}{8} = \frac{29}{8}, 1 \frac{1}{4} = \frac{5}{4}

\frac{29}{8} - \frac{5}{4} = \frac{29 \times 1 - 5 \times 2}{8} = \frac{19}{8}

\frac{19}{8} = 2 \frac{5}{8}

g c m^{- 3}

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