Question

The decimal expansion of 13/1250 terminates after​

Answer 1

SOLUTION

TO DETERMINE

After how many decimal places the below rational number will terminate

$\displaystyle \sf{ \frac{13}{ 1250 } }$

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

$\displaystyle \sf{ \frac{13}{ 1250 } }$

Numerator = 13

Denominator = 1250 = 2 × 5⁴

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

So the given rational number is terminating

The exponent of 2 = 1

The exponent of 5 = 4

Max{ 1 , 4 } = 4

Hence the given rational number terminates after 4 decimal places

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. The decimal expansion of 49/2³5³

contains six digits after the decimal point.

https://brainly.in/question/36368731

2. Without actually dividing find which of the following are terminating decimals.

i. 3/25 ii. 11/18 iii. 13/20 iv. 41/42

https://brainly.in/question/135746

3. without actually performing the long division state whether 13/3125 and 13/343 will have a terminating decimal expansion...

https://brainly.in/question/23797327

Answer 2

Answer : given fraction is   $\frac{13}{1250}$

Numerator = 13

Denominator = 1250 = 2 × 5⁴

 prime factors of the denominator are  2 and 5

The exponent of 2 = 1

The exponent of 5 = 4

Max{ 1 , 4 } = 4

condition : if the denominator is of the form ,  denominator = $2^{m} \times5^{n}$,

then the fraction terminates after N decimal places.

Hence the given rational number terminates after 4 decimal places

Answer :

Step-by-step explanation: