Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals.
$- \frac{33}{20}$

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Solution

Given that $- \frac{33}{20}$
Here $3$ and $20$ have no common factors and $33$ and $20$ are co-prime
for denominator $= 20$
$= 5 \times 4$
$= 2^{2} . 5^{1}$
Here $n = 2, m = 1$
$∴$ the denominator is form of $2^{n} . 5^{m}$
$∴$ $- \frac{33}{20}$ is a terminating decimal

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Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals.−3320

Given that −3320Here 3 and 20 have no common factors and 33 and 20 are co-primefor denominator =20=5×4=22.51Here n=2,m=1∴ the denominator is form of 2n.5m∴ −3320 is a terminating decimal

Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals.
$- \frac{33}{20}$

Given that $- \frac{33}{20}$
Here $3$ and $20$ have no common factors and $33$ and $20$ are co-prime
for denominator $= 20$
$= 5 \times 4$
$= 2^{2} . 5^{1}$
Here $n = 2, m = 1$
$∴$ the denominator is form of $2^{n} . 5^{m}$
$∴$ $- \frac{33}{20}$ is a terminating decimal