Question

Let x =7/20×25 be a rational number. Then x has decimal expansion, which terminates:

(a) after four places of decimal. (b) after three places of decimal
(c) after two places of decimal. (d) after five places of decimal​

Answer 1

Answer:

terminates after 3places of decimal

Step-by-step explanation:

let x=7/29×25 be rational number . then x haa has decimal expansion

x=7/(20*25)

20*25=20*5*5

=100 * 5

x= 7/(100*5)

multiply numerator &denominator by 2

x =14/ (100*5*2)

x=14/1000

x=0.014

decimal expansion terminates after 3places of decimal

Answer 2

if $\bf x = \frac{7}{20 \times 25}$ then, it terminates after 3 decimal places.

Option (b) is correct.

Given:$x = \frac{7}{20 \times 25}$ be a rational number.

To find:

Then x has decimal expansion, which terminates:

(a) after four places of decimal.

(b) after three places of decimal.

(c) after two places of decimal.

(d) after five places of decimal.

Solution:

Let us understand first, how one can find without actually division that after how many decimal places a rational number will terminate.

If a rational number p/q is in standard form, i.e. p and q are co-prime integers and q≠0.

Then,

The rational number have terminating decimal expansion, if q is in the form

$\bf { 2}^{n} \times {5}^{m}$

where, n and m are non-negative integers.

Step 1: Checking for standard form.

First check for numerator and denominator of x, whether both have any common factor.

it is clear that 7 and 20×25=500 are co-prime numbers.

Step 2: Do prime factors of denominator.

$500 = 2\times 2 \times5 \times 5 \times 5$

$500 = {2}^{2} \times {5}^{3}$

It satisfies the condition of terminating decimal.

Step 3: Multiply numerator and denominator by 2.

The step is necessary, so that powers of 2 and 5 will be equal, in order to do the division without actually division.

So,

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

or

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

or

$x = \frac{14}{ {2}^{3} \times {5}^{3} }$

or

$x = \frac{14}{ {(2 \times 5)}^{3} }$

or

$x = \frac{14}{ {(10)}^{3} }$

or

$x = \frac{14}{1000 }$

or

$\bf x = 0.014$

Thus,

Decimal expansion of x terminates after 3 decimal places.

Option (b) is correct.

Learn more:

1) 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

2) without actual division show that 171 by 800 is a terminating decimal. express it in decimal form.

https://brainly.in/question/3303413