# The decimal expansion of rational numbers $\dfrac{{49}}{{40}}$ will terminate after how many places of decimal?

Last updated date: 23rd Mar 2023

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Answer

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Hint: The decimal expansion of a number consists of a decimal point followed by several digits. Whenever we try to convert a fraction to numerical value, we get a decimal value.

Complete step-by-step answer:

The given rational number = $\dfrac{{49}}{{40}}$

Multiplying and dividing the above fraction with ‘25’.

$ \Rightarrow \dfrac{{49}}{{40}} \times \dfrac{{25}}{{25}}$

$ = \dfrac{{1225}}{{1000}}$

In the denominator we have 1000 (three zeros), so when dividing a number by thousand we get a decimal point followed by three digits.

$ = 1.225$

After the decimal point we got three digits.

$\therefore $ The given rational number $\dfrac{{49}}{{40}}$ terminates after 3 places of the decimal.

Note: Whenever we want to convert any rational number to a decimal value without using a calculator, we need to convert the denominator into a form of ${10^n}\left[ {n > 0} \right]$. If ‘k’ zeros are present in the denominator, then we will have ‘k’ digits after the decimal point in the numerator.

For example take $\dfrac{9}{{100}}$, this value equals 0.09, sometimes we may encounter non-terminating values after the decimal point, eg: $\dfrac{1}{3} = 0.33333333333.......$

Complete step-by-step answer:

The given rational number = $\dfrac{{49}}{{40}}$

Multiplying and dividing the above fraction with ‘25’.

$ \Rightarrow \dfrac{{49}}{{40}} \times \dfrac{{25}}{{25}}$

$ = \dfrac{{1225}}{{1000}}$

In the denominator we have 1000 (three zeros), so when dividing a number by thousand we get a decimal point followed by three digits.

$ = 1.225$

After the decimal point we got three digits.

$\therefore $ The given rational number $\dfrac{{49}}{{40}}$ terminates after 3 places of the decimal.

Note: Whenever we want to convert any rational number to a decimal value without using a calculator, we need to convert the denominator into a form of ${10^n}\left[ {n > 0} \right]$. If ‘k’ zeros are present in the denominator, then we will have ‘k’ digits after the decimal point in the numerator.

For example take $\dfrac{9}{{100}}$, this value equals 0.09, sometimes we may encounter non-terminating values after the decimal point, eg: $\dfrac{1}{3} = 0.33333333333.......$

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