Question

प्रश्न 2 रा : सोडवा. 16 1) ही संख्या दशांश रुपात लिहा. 3 2) सोबतच्या आकृतीवरून mLABD काढा 10 D 30 व या दोन्ही संख्यांनी नि:शेष भाग जाईल अशी एक​

Answer 1

SOLUTION

TO DETERMINE

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

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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