Question

The decimal expansion of the rational number 64/16×125 will terminate after how many places of decimals
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Answer 1

Answer:

the decimal places will terminate after 4 decimal places

Answer 2

The decimal form of the given rational number terminates after 3 decimal places.

Given :

The rational number = 64/(16 * 125)

To Find :

Number of terminating decimals

Solution :

The numerator of the given rational number = 64

The denominator of the given rational number = 16 * 125

Firstly, we factorize the denominator to prime numbers (especially 2 and 5),

              $16 * 125 = ( 2 * 2 * 2* 2)*(5*5*5)$

                            $= 2^{4} * 5^{3}$

                            $= (2*5)^{3} * 2$

Secondly, we want the denominator in the form of 10 to get the decimal digits. for this, we need to multiply by 5 on both sides to form 10 with the extra "2" left in the denominator.

                  $64/(16*125) = 64/(10^{3} * 2)$

                                        $= (64*5) / (10^{3} *2*5)$

                                         $= 320 / 10^{4}$

                                         $= 32/10^{3}$

Now as the denominator is a multiple of 10, we can easily find the decimal form without actual division i.e.

                       $32/10^{3} = 32/1000$

                                   $= 0.032$

Thus, the decimal terminates after 3 digits for the given rational number.

To learn more about Terminating Decimals, visit

https://brainly.in/question/6852141

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