Question

1) 16 ही संख्या दशांश रुपात लिहा.

Answer 1

SOLUTION

TO DETERMINE

The decimal expansion of $\displaystyle \sf{ \frac{16}{3} }$

CONCEPT TO BE IMPLEMENTED

$\displaystyle\sf{Fraction = \frac{Numerator}{Denominator} }$

A fraction is said to be terminating if prime factorisation of the denominator contains only prime factors 2 and 5

If the denominator is of the form

$\sf{Denominator = {2}^{m} \times {5}^{n} }$

Then the fraction terminates after N decimal places

Where N = max { m , n }

EVALUATION

Here the given number is

$\displaystyle \sf{ \frac{16}{3} }$

Numerator = 16

Denominator = 3

Since in the there is prime number 3

So the decimal expansion of the number is non terminating

Now

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:5.33 \:\:}}}\\ {\underline{\sf{3}}}&{\sf{\:\:16 \:\:}} \\{\sf{}}&\underline{\sf{\:\: \: \: \: \: \: \: \: \: \: \: 15 \: \: \: \: \: \: \: \:\: \: \:\:}} \\ {\underline{\sf{}}}&{\sf{\:\: \: \: \: \: \: \: \: \: \: \: \: \: \: 10 \: \: \: \: \: \: \: \:\:}} \\{\sf{}}&\underline{\sf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: 9 \: \: \: \: \: \:\:}} \\ {\underline{\sf{}}}& { \: \: \: \: \: \: \: \sf{10}} \\ {\sf{}}& \underline{\sf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 9 \: \: \: \: \: \:\:}} \\ {\underline{\sf{}}}& { \: \: \: \: \: \: \: \sf{1}} \end{array}\end{gathered}$

Thus we get

$\displaystyle \sf{ \frac{16}{3} }$

$\displaystyle \sf{ = 5.33...}$

$\displaystyle \sf{ = 5. \bar{3}}$

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