Math, asked by DurgaSai2004, 11 months ago

after how many decimal places will the decimal representation of the rational number 229/(2^2 x 5^7) terminate ?​

Answers

Answered by aamodvarma
28

Answer:

After 7 decimal places

Step-by-step explanation:

First we have to make the base a power of 10  , that is we know 5 * 2 is 10 so we have to make the powers of exponets of 2 and 5 in the denominator same so we multiply 2^5 on both numerator and denominator

229/2^2*5^7  * 2^5/2^5

which becomes

->229*2^5/2^(2+5)*5^7

here in the denominator as 2 and 5 have the same powers we can take 2 and 5 common into (2*5)^7 -> 10^7

Here as base is 10 followed by 7 zeroes , the decimal will terminate after 7 places

Answered by codiepienagoya
36

Given:

\bold{\frac{229}{2^2\times 5^7}}

To find:

The decimal representation of the rational number.

Solution:

\Rightarrow \frac{299}{2^2\times 5^7}\\\\\Rightarrow \frac{299}{4\times 78,125}\\\\\Rightarrow \frac{299}{312,500}\\\\\Rightarrow \frac{299}{3125 \times 100}\\\\\Rightarrow \frac{299}{3125 \times 10^2}\\\\\Rightarrow \frac{299\times 10^{-2}}{3125 }\\\\\Rightarrow 0.09568 \times 10^{-2}\\\\\Rightarrow 09568 \times 10^{-7}\\\\\Rightarrow 9568 \times 10^{-7}\\\\

The decimal place of the given value use in -7th place.

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