Question

Can any fraction with a denominator of 20 be written as a terminating decimal? Explain.

Answer 1

Step-by-step explanation:

Given: Can any fraction with a denominator of 20 be written as a terminating decimal? Explain.

Explanation:

We know that a rational number have terminating decimal expansion if the rational number is written in its standard form;i.e. p and q are Co-prime numbers and then q have prime factors as $2^n\times5^m$, where n and m are positive integers.

Thus,

According to the situation take a rational number in its standard form.

Let say

$\frac{17}{20}$

here 17 and 20 are Co-prime numbers.

As 20 can be written in its prime factors as

20=2×2×5

or

20=2²×5

Here,

we can see that it follows this pattern $2^n\times5^m$, where n and m are positive integers.

Thus, 17/20 is having a terminating decimal expansion.

Verification:

$\frac{17}{20} = \frac{17}{ {2}^{2} \times 5} \\ \\ or \\ \\ \frac{17}{20} = \frac{17 \times 5}{ {2}^{2} \times {5}^{2} } \\ \\ or \\ \\ \frac{17}{20} = \frac{85}{( {2 \times 5)}^{2} } \\ \\ \frac{17}{20} = \frac{85}{( {10)}^{2} } \\ \\ \frac{17}{20} = \frac{85}{100} \\ \\ \frac{17}{20} = 0.85$

Hence verified.

Final answer:

Any rational number if written in its standard form and have denominator 20 is having a terminating decimal expansion.

Hope it helps you.

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Answer 2

Answer:

Step-by-step explanation: Yes becuase this and that