Question

after how many decimal places the rational number 13/2^4×5^3 will terminate​

Answer 1

Answer:

13/2^4 x 5^3 will terminate after 4 decimal places.

Step-by-step explanation:

13/2^4 x 5^3

= 13 x 5^3 / 2^4

Multiply numerator and denominator by 5^4

= 13 x 5^3 x 5^4 / 2^4 x 5^4

= 13 x 5^3 x 5^4 / 10^4

= 1,015,625 / 10^4

= 101.5625

Thus, it will terminate after 4 decimal places.

Answer 2

SOLUTION

TO DETERMINE

After how many decimal places the below rational number will terminate

$\displaystyle \sf{ \frac{13}{ {2}^{4} \times {5}^{3} } }$

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

$\displaystyle \sf{ \frac{13}{ {2}^{4} \times {5}^{3} } }$

Numerator = 13

Denominator = 2⁴ × 5³

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 = 4

The exponent of 5 = 3

Max{ 4 , 3 } = 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