Question

The decimal expansion of the rational number 33/22.5 will terminates after .How many places of decimal

Answer 1

33/22.5 = 4.666666........
6 is repeat
So, it terminates after 2 decimal places

Answer 2

It is non-terminating - $\dfrac{33}{22.5}=1.4666666666...$

Step-by-step explanation:

Given : The decimal expansion of the rational number 33/22.5 will terminates

To find : How many places of decimal places ?

Solution :

Number,  $\frac{33}{22.5}$

Write the number as,

$\dfrac{33}{22.5}=\dfrac{33\times 10}{225}$

$\dfrac{33}{22.5}=\dfrac{330}{3^2\times 5^2}$

As the denominator is not in form of $2^n\times 5^n$ it will not terminating.

It is an irrational number.

$\dfrac{33}{22.5}=1.4666666666...$

#Learn more

The rational numbers 7 by 25 will have a terminating decimal expansion or non terminating repeating decimal expansion

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