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# The decimal expansion of rational numbers $\dfrac{{49}}{{40}}$ will terminate after how many places of decimal?  Answer Verified
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: $\dfrac{1}{3} = 0.33333333333.......$
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Decimal Expansion of Rational Numbers  Rational Numbers and Their Properties  Rational Numbers  Rational Numbers Between Two Rational Numbers  Rational and Irrational Numbers  Operations on Rational Numbers  Decimal Numbers Standard Form  Difference Between Rational and Irrational Numbers  Rational Numbers on a Number line  Binary to Decimal Conversion  