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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?

A

Step 1

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B

Step 2

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C

Step 3

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D

Step 4

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Solution

The correct option is D Step 4

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Similar questions

Q. While converting

5 \frac{1}{2}

into an improper fraction, Ricky performed the following steps:

Step 1 : 5 \times 2 = 10

Step 2 : 10 + 1 = 11

Step 13 : \frac{11}{5}

In which step did he go wrong?

Q. The following steps are followed to solve the equation.
Step 1:

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

12 x - 4 x = 3

8 x = 3

x = 3 \times 8

Which one is the wrong step?

Q. While subtracting two mixed fractions, James performed the following steps:

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

Step 1: Conversion from mixed to improper fraction

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

Step 2: Taking the LCM of both the denominators. The LCM of 4 and 8 is 8.

Step 3: Subtraction:

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

Step 4: Conversion from improper to mixed fraction:

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

In which step did he go wrong?

Q. The density of wood is X

g c m^{- 3}

. Find [10X].{ Where , [] is a step function}

Q. A number consists of two digits whose sum is

9

27

is added to the number, its digits are interchanged. Are the given steps to find the number true?
Step

1

: Let the unit's digit be x
Step

2

: Then, ten's digit

= (9 - x)

∴

= 10 \times (9 - x) + x \Rightarrow 90 - 10 x + x = (90 - 9 x)

3

27

90 - 9 x

117 - 9 x

4

: Number with digits interchanged is

10 x + (9 - x) = 9 x + 9

5

117 - 9 x = 9 x + 9

6

: Therefore unit's digit

= 6

and ten's digit

= 3

7

: Hence the number

= 36

.

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