Name: Place Value of Digits in a Decimal Fraction
Uploaded: 2019-07-19
Duration: 3 min 24 s
Description: You must have seen people fill fuel in their vehicles. Have you observed the price is always different with different decimal points? Watch this video to lea...

Question

Find the decimal form of

\frac{1}{11}

.

Accepted Answer

Given fraction is $\frac{1}{11}$ .

Therefore, $\frac{1}{11} = \frac{1 \times 10}{11 \times 10} = \frac{1}{10} \times \frac{10}{11}$

Now, $\frac{1}{10} \times \frac{10}{11} = \frac{1}{10} \times 0 \frac{10}{11}$ ( by converting $\frac{10}{11}$ into mixed fraction)

$\frac{1}{10} \times 0 \frac{10}{11} = \frac{1}{10} \times (0 + \frac{10}{11})$ $= (\frac{1}{10} \times 0) + (\frac{1}{10} \times \frac{10}{11}) = \frac{0}{10} + \frac{10}{110}$

Thus, $\frac{1}{11} = \frac{0}{10} + \frac{10}{110}$

So, $\frac{1}{11} - \frac{0}{10} = \frac{10}{110} . . . . (1)$

Now, like the above we can find a fraction with denominator $100$ , which is close to $\frac{1}{11}$ .

$\frac{1}{11} = \frac{1 \times 100}{11 \times 100} = \frac{1}{100} \times \frac{100}{11}$

Now, $\frac{1}{100} \times \frac{100}{11} = \frac{1}{100} \times 9 \frac{1}{11}$ ( by converting $\frac{100}{11}$ into mixed fraction)

So, $\frac{1}{100} \times 9 \frac{1}{11} = \frac{1}{100} \times (9 + \frac{1}{11}) = \frac{9}{100} + \frac{1}{1100}$

Thus, $\frac{1}{11} = \frac{9}{100} + \frac{1}{1100}$

$\Rightarrow \frac{1}{11} - \frac{9}{100} = \frac{1}{1100} . . . . . (2)$

Similarly like above we can find a fraction with denominator $1000$ , which is close to $\frac{1}{11}$ .

Thus, $\frac{1}{11} = \frac{1 \times 1000}{11 \times 1000} = \frac{1}{1000} \times \frac{1000}{11}$

Now, $\frac{1}{1000} \times \frac{1000}{11} = \frac{1}{1000} \times 90 \frac{10}{11}$ (by converting $\frac{1000}{11}$ into mixed fraction)

Also, $\frac{1}{1000} \times 90 \frac{10}{11} = \frac{1}{1000} \times (90 + \frac{10}{11}) = (\frac{1}{1000} \times 90) + (\frac{1}{1000} \times \frac{10}{11}) = \frac{90}{1000} + \frac{10}{11000}$

Therefore, $\frac{1}{11} = \frac{90}{1000} + \frac{10}{11000}$

So, $\frac{1}{11} - \frac{90}{1000} = \frac{10}{11000} . . . . . (3)$

Thus, the fraction $\frac{0}{10}, \frac{9}{100}, \frac{90}{1000}, . . . .$ and so on get closer and closer to $\frac{5}{6}$ .

Now, $\frac{9}{100} = 0.9, \frac{90}{1000} = 0.090, . . . .$ and so on.

Therefore, the decimal form of $\frac{1}{11} = 0.0909 . . . . . .$

Kerala Board Solutions for Chapter: Decimal Forms, Exercise 2: Exercise 2

Kerala Board Mathematics Solutions for Exercise - Kerala Board Solutions for Chapter: Decimal Forms, Exercise 2: Exercise 2

Questions from Kerala Board Solutions for Chapter: Decimal Forms, Exercise 2: Exercise 2 with Hints & Solutions

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