Question

1) In which the folloing rational number can be expressed as a terminating decimal.
a)77/210
b)13/125
c)2/15
d)17/18

Answer 1

Answer:

OPTION B= 13/125

Step-by-step explanation:

Because the Denominator can be expressed in terms of 2^m*5^n.

That is 5^3 * 2^0.

Answer 2

Option b-  $\frac{13}{125}=0.104$  is expressed as a terminating decimal.

Step-by-step explanation:

To find : In which the following rational number can be expressed as a terminating decimal ?

Solution :

A rational number can be expressed as a terminating decimal when the denominator is in the form of $2^m\times 5^n$.

a)  $\frac{77}{210}$

$\frac{77}{210}=\frac{77}{2\times 3\times 5\times 7}$

$\frac{77}{210}=\frac{11}{2\times 3\times 5}$

No, it is not terminating.

b)  $\frac{13}{125}$

$\frac{13}{125}=\frac{13}{5^3}$

Multiply and divide by $2^3$,

$\frac{13}{125}=\frac{13\times 2^3}{2^3\times 5^3}$

$\frac{13}{125}=\frac{104}{10^3}$

$\frac{13}{125}=0.104$

It is terminating.

c)  $\frac{2}{15}$

$\frac{2}{15}=\frac{2}{3\times 5}$

No, it is not terminating.

d)  $\frac{17}{18}$

$\frac{17}{18}=\frac{17}{2\times 3\times 3}$

No, it is not terminating.

#Learn more

4. If 13/125 is a rational number, find the decimal expansion of it, which terminates.

https://brainly.in/question/4217897