Question
Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non terminating repeating decimal expansion.
$\frac{125}{441}$
$\frac{125}{441}$
✓
Answer
The given number is $\frac{125}{441}$
Here, $441 = 3^2 \times 7^2 441 = 32 \times 72$ and none of $3$ and $7$ is a factor of $125.$
So, the given number is in its simplest form.
Now, $441 = 3^2 \times 7^2$ is not of the form $2^m \times 5^n.$
So, the given number has a non-terminating repeating decimal expansion.
Here, $441 = 3^2 \times 7^2 441 = 32 \times 72$ and none of $3$ and $7$ is a factor of $125.$
So, the given number is in its simplest form.
Now, $441 = 3^2 \times 7^2$ is not of the form $2^m \times 5^n.$
So, the given number has a non-terminating repeating decimal expansion.
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