Question

Q.1 Which of the following is equivalent to a decimal that terminates? *
1/2²3
1/5²7
1/5²11²
1/5²2²

Answer 1

4 th option
That is 1/5^2.2^2
Condition for decimal that terminates
Says that the numerator is in the form 2^m.5^n

Answer 2

Answer:

The fraction equivalent to a decimal that terminates from the options =   $\frac{1}{5^2X2^2}$

Step-by-step explanation:

Given fractions are

$\frac{1}{2^2X3} , \frac{1}{5^2X7}, \frac{1}{5^2X11^2}, \frac{1}{5^2X2^2}$

To find,

From the given options, the decimal terminates.

Solution:

Recall the concepts:

A fraction is a terminating decimal if the denominator of the fraction has no other prime factors other than 2 and 5.

The given fractions are $\frac{1}{2^2X3} , \frac{1}{5^2X7}, \frac{1}{5^2X11^2}, \frac{1}{5^2X2^2}$

In the given options, the fraction $\frac{1}{5^2X2^2}$has only prime factors 2 and 5.

Hence  $\frac{1}{5^2X2^2}$ is a terminating decimal.

∴ The fraction equivalent to a decimal that terminates from the options =   $\frac{1}{5^2X2^2}$

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