Throw the calculator in dustbin- 2

Number Theory Level 3

Find the value of $\dfrac{1}{49}$ up to 6 decimal places.

Provide your answer as: $\color{#D61F06}{\text{answer}}\times 10^6$ round to the nearest integer.

Hint : Read the Mental Math Tricks .

The answer is 20408.

1 solution

Sravanth C.
Feb 8, 2016

From the Mental Math Tricks wiki, we can find the value of $\dfrac 1{49}$ in this way:

$\begin{aligned}&&\dfrac 15\quad \, \, &=& \color{#D61F06}{0} \text{ remainder 1} \\ \dfrac{10(1)+0}{5} \quad &=& \dfrac{10}{5} \quad \, \, &=& \color{#D61F06}{2} \text{ remainder 0} \\ \dfrac{10(0)+2}{5} \quad &=& \dfrac{2}{5} \quad &=& \color{#D61F06}{0} \text{ remainder 2} \\ \dfrac{10(2)+0}{5} \quad &=& \dfrac{20}{5} \quad &=& \color{#D61F06}{4} \text{ remainder 0} \\ \dfrac{10(0)+4}{5} \quad &=& \dfrac{4}{5} \quad &=& \color{#D61F06}{0} \text{ remainder 4} \\ \dfrac{10(4)+0}{5} \quad &=& \dfrac{40}{5} \quad &=& \color{#D61F06}{8} \text{ remainder 0} \\\end{aligned}$

Therefore we can say $\dfrac{1}{49}=\color{#D61F06}{0.020408}$

Hence the answer is, $\color{#D61F06}{0.020408}\times 10^6=\boxed{20408}$

Another quick way to do this is to note that $\frac{1}{49} = \frac{1}{50} + \frac{1}{50^2} + \frac{1}{50^3} + \ldots = \frac{2}{10^2} + \frac{2^2}{10^4} + \frac{2^3}{10^6} + \ldots + \frac{2^n}{10^{2n}} + \ldots.$

Eli Ross Staff - 5 years, 4 months ago

Great! Nice way to do it.

Sravanth C. - 5 years, 4 months ago

Super solution sir

Raghu Ram - 5 years, 3 months ago

Throw the calculator in dustbin- 2

The answer is 20408.

1 solution

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