If $\frac{18}{91}$ = 0.00112233445566778899………., then what is the value of $\frac{198}{891}$ ?

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0.222….

0.111….

0.3232….

0.4242….

answer is A.

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Detailed Solution

⇒

\frac{18}{91}

= 0.00112233445566778899………. (1)
We have to find the decimal value of another fraction i.e.

\frac{198}{891}

Split this fraction in integer number and fraction as given below
⇒

\frac{198}{891} = 198 \times \frac{1}{891}

………… (2)
Comparing equation (1) and (2), we get
⇒

\frac{198}{891}

198 \times

0.00112233445566778899
As it takes time to multiply these two numbers and chances of errors are there. So, we can also solve it by splitting the decimal number as follows:
⇒ 0.00112233445566778899… = 0.0011 + 0.000022 + 0.00000033…….
⇒ 198×0.00112233445566778899… = 198 × (0.0011 + 0.000022 + 0.00000033…)
Now to find 198 × 0.0011, we can do multiplication of 198 × 11. Here to multiply with 11 we can use a trick given as follow
seo

Therefore, 198 × 0.0011 = 0.2178
⇒198 × 0.000022 = 0.004356
So on.
⇒ 198 × 0.00112233445566778899…... = 198 × 0.0011 + 198 × 0.000022 +…..
= 0.2178 + 0.004356 +………..
⇒ 198 × 0.00112233445566778899…….. = 0.222
Hence, option (1) is the correct option.

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