Question

After how many place the decimal expansion of 7/80 will terminate​

Answer 1

The decimal expansion of 7/80 will terminate after four decimal places

Given :

The fraction 7/80

To find :

After how many place the decimal expansion of 7/80 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 fraction

The given fraction is 7/80

Step 2 of 3 :

Simplify the given fraction

$\displaystyle \sf{ \frac{7}{ 80 } }$

$\displaystyle \sf{ = \frac{7}{ {2}^{4} \times 5 } }$

Step 3 of 3 :

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

Numerator = 7

Denominator = 2⁴ × 5

Since the prime factorisation of the denominator contains only prime factors as 2 and 5

So the given fraction is terminating

Since the exponent of 2 is 4 and exponent of 5 is 1

Hence decimal expansion of 7/80 will terminate after four decimal places

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