Question

The decimal expansion of the rational number 587/250 will terminate after decimal places​

Answer 1

after 3 decimal places is the answer

Step-by-step explanation:

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Answer 2

The decimal expansion of the rational number 587/250 will terminate after three decimal places

Given : The rational number 587/250

To find : The number of decimal places after which the decimal expansion of the rational number 587/250 will terminate

Concept :

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

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 }

Solution :

Step 1 of 3 :

Write down the given number

The given number is 587/250

Step 2 of 3 :

Prime factorise denominator of the number

Denominator of the rational number = 250

We now prime factorise the denominator

250

= 2 × 5 × 5 × 5

$\sf = {2}^{1} \times {5}^{3}$

Step 3 of 3 :

Find the number of decimal places after which the decimal expansion terminates

Exponent of 2 = 1

Exponent of 5 = 3

Max { 1 , 3 } = 3

Hence the decimal expansion of the rational number 587/250 will terminate after three decimal places

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