Question

Without actually dividing find which of the following are terminating decimals

3/25
11/18
13/20
41/42

Answer 1

If denominator is in the form of 2^n × 5^m .Then it is terminating otherwise non terminating.

25=5×5

So 3/25 is terminating.

18=2×3×3

11/18 is non terminating.

20=2×2×5

13/20 is terminating.

42=2×3×7

41/42 is non terminating.

Answer 2

The  terminating decimals are  $\frac{3}{25}$ and $\frac{11}{18}$.

Step-by-step explanation:

Consider the provided information.

If Denominator is in the form of 2ⁿ × 5ⁿ then decimals are terminating.

Consider the fraction:  $\frac{3}{25}$

The above fraction can be written as: $\frac{3}{25} =\frac{3}{5^2}=\frac{3}{2^0\times5^2}$

Since, the denominator is in the form of 2ⁿ × 5ⁿ, therefore the decimal is terminating.

Consider the fraction:  $\frac{11}{18}$

The above fraction can be written as: $\frac{11}{18} =\frac{11}{2\times3^2}$

Since, the denominator is not in the form of 2ⁿ × 5ⁿ, therefore the decimal is not terminating.

Consider the fraction:  $\frac{13}{20}$

The above fraction can be written as: $\frac{13}{20} =\frac{13}{2^2\times5}$

Since, the denominator is in the form of 2ⁿ × 5ⁿ, therefore the decimal is terminating.

Consider the fraction:  $\frac{41}{42}$

The above fraction can be written as: $\frac{41}{42} =\frac{41}{2\times3\times7}$

Since, the denominator is not in the form of 2ⁿ × 5ⁿ, therefore the decimal is not terminating.

#Learn more

Without actually dividing find the which of the following are terminating decimals 3/25

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