Question

the decimal expansion of the rational number 658/25 will terminate​

Answer 1

Given :- the decimal expansion of the rational number 658/25 will terminate ?

Answer :-

Concept used :- we have to check prime factors of denominators of given fraction .

• if Prime factor are 2, or 5 , or 2 and 5 both . Than the given fraction is a terminating decimal expansion .
• if prime factors are other than 2 or 5 , than the given fraction is a non - terminating decimal expansion .

so,

→ 658/25

→ Denominator = 25

→ Prime factors of denominator = 5 * 5 = Only 5 .

therefore, we can conclude that, the given fraction (658/25) is a terminating decimal expansion .

Learn more :-

(3) निम्न के स्थानीय मान लिखिये-

(अ)43.24

(स)884.20

(ब) 534.34

(द) 178.34

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Answer 2

SOLUTION

COMPLETE QUESTION

The decimal expansion of the rational number 658/25 will terminate after how many places of decimal ?

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 rational number is

$\displaystyle\sf{ \frac{658}{25} }$

So denominator = 25

Now 25 = 5 × 5 = 5²

Since the prime factorisation of the denominator contains only prime factors as 5

So the given rational number is terminating

Since the exponent of 5 = 2

Hence the given rational number terminates after 2 decimal places

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