Question

without actually dividing,determines,after how many places,the decimal form of 125/2⁴.5³ will terminate?​

Answer 1

Answer:

after four decimal places it will terminate

Step-by-step explanation:

check the exponents of 2 and 5.

the exponent which is greater. the number terminate d after so many places

Answer 2

The decimal form of 125/2⁴.5³ will terminate after four decimal places

Given :

The fraction 125/2⁴.5³

To find :

The number of decimal places after which the decimal form of 125/2⁴.5³ will terminate without actually dividing

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 fraction

The given fraction is

$\displaystyle \sf{ \frac{125}{ {2}^{4}. {5}^{3} } }$

Step 2 of 3 :

Simplify the given fraction

$\displaystyle \sf{ \frac{125}{ {2}^{4}. {5}^{3} } }$

$\displaystyle \sf{ = \frac{125}{ {2}^{4} \times 125 } }$

$\displaystyle \sf{ = \frac{1}{ {2}^{4} } }$

Step 3 of 3 :

Find the number of decimal places after which the decimal form will terminate

Numerator = 1

Denominator = 2⁴

Since the prime factorisation of the denominator contains only prime factors as 2

So the given rational number is terminating

Since the exponent of 2 = 4

Hence the given rational number terminates after four decimal places

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