Question

After how many decimal places will the rational number 7/80 be terminated? ​

Answer 1

Answer:

0.0875

Decimal will be after 4 places

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Answer 2

$\bf \red{\frac{7}{80} = 0.0875}$

it terminates after 4 decimal places.

Given:

• $\frac{7}{80}$

To find:

• After how many decimal places will the rational number 7/80 be terminated?

Solution:

Concept to be used:

• A rational number in the form p/q, where q≠0 and p and q are co-prime numbers, can be find as terminating or non- terminating without actual division.

1. Do prime factors of denominator.
2. A number is terminating,If it's denominator is in the form ${2}^{n} \times {5}^{m}$, where n and m are positive integers.

Step 1:

Check the given number.

As 7 and 80 are co-prime numbers, thus it is in standard form.

Step 2:

Do prime factors of 80.

$80 = 2 \times 2 \times 2 \times 2 \times 5$

or

$80 = {2}^{4} \times 5$

Thus,

Number is having terminating decimal expansion.

Step 3:

Multiply both numerator and denominator by 5³.

$\frac{7}{ {2}^{4} \times 5 } = \frac{7 \times {5}^{3} }{ {2}^{4} \times 5 \times {5}^{3} }$

or

$\frac{7}{ {2}^{4} \times 5 } = \frac{7 \times {5}^{3} }{ {2}^{4} \times {5}^{4} }$

or

$\frac{7}{ {2}^{4} \times 5 } = \frac{7 \times {5}^{3} }{ {( 2 \times 5)}^{4} }$

or

$\frac{7}{ {2}^{4} \times 5 } = \frac{7 \times {5}^{3} }{ {(10)}^{4} }$

or

$\frac{7}{ {2}^{4} \times 5 } = \frac{7 \times 125}{10000}$

or

$\frac{7}{ {2}^{4} \times 5 } = \frac{875}{ 10000}$

or

$\bf \frac{7}{80} = 0.0875$

Thus,

$\bf \frac{7}{80} = 0.0875$

it terminates after 4 decimal places.

Learn more:

1) 3/8 will terminate after how many decimal places

https://brainly.in/question/9415547

2) After how many decimal points, numbers 5/1600 terminate ?

a)5 b)6

c)7 d)8

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