RECURRING DECIMAL :- In a decimal fraction, if a figure or set of figures is repeated continuously then the number is called a recurring decimal.
Recurring is expressed by putting dot ( when one number is repeated ) on the number or by putting bar ( when a set of numbers is repeated ) on the numbers.
For eg. $\frac{1}{3}=0.3333....=0.\dot{3}$,
$\frac{1}{7}=0.142857142857142857...=0.\overline{142857}$
PURE RECURRING DECIMAL :- A decimal fraction in which all the figures after the decimal point are repeated, is called a pure recurring decimal.
For eg. $0.\overline{142857}$
CONVERTING A PURE RECURRING DECIMAL INTO VULGAR FRACTION :- Write the repeated figure once only in the numerator and put as many nines in the denominator as is the number of repeating figures in the given pure recurring decimal.
For eg. $0.\overline{45}= \frac{45}{99}$
MIXED RECURRING DECIMAL :- A decimal fraction in which some figures after the decimal point are not repeated and some of them are repeated are called mixed recurring decimal.
For eg. $0.29\overline{54}$
CONVERTING A MIXED RECURRING DECIMAL INTO VULGAR FRACTION :- For converting a mixed recurring decimal into vulgar fraction, take in the numerator, the difference between the number formed by all the digits after decimal point and that formed by non-repeating digits.
In the denominator, take as many nines as there are repeating digits and put as many zeros as is the number of non-repeating digits.
For eg. $0.1\overline{8}=\frac{(18-1)}{90}=\frac{17}{90}$
APPROXIMATION - ROUNDING TO THE NEAREST WHOLE NUMBER :-
RULE :- Increase the last figure by 1 if the succeeding figure be 5 or greater than 5.
For eg. The approximation value of 0.5848 up to three decimal places is 0.585
The approximation value of 0.438 up to one decimal place is 0.4
Recurring is expressed by putting dot ( when one number is repeated ) on the number or by putting bar ( when a set of numbers is repeated ) on the numbers.
For eg. $\frac{1}{3}=0.3333....=0.\dot{3}$,
$\frac{1}{7}=0.142857142857142857...=0.\overline{142857}$
PURE RECURRING DECIMAL :- A decimal fraction in which all the figures after the decimal point are repeated, is called a pure recurring decimal.
For eg. $0.\overline{142857}$
CONVERTING A PURE RECURRING DECIMAL INTO VULGAR FRACTION :- Write the repeated figure once only in the numerator and put as many nines in the denominator as is the number of repeating figures in the given pure recurring decimal.
For eg. $0.\overline{45}= \frac{45}{99}$
MIXED RECURRING DECIMAL :- A decimal fraction in which some figures after the decimal point are not repeated and some of them are repeated are called mixed recurring decimal.
For eg. $0.29\overline{54}$
CONVERTING A MIXED RECURRING DECIMAL INTO VULGAR FRACTION :- For converting a mixed recurring decimal into vulgar fraction, take in the numerator, the difference between the number formed by all the digits after decimal point and that formed by non-repeating digits.
In the denominator, take as many nines as there are repeating digits and put as many zeros as is the number of non-repeating digits.
For eg. $0.1\overline{8}=\frac{(18-1)}{90}=\frac{17}{90}$
APPROXIMATION - ROUNDING TO THE NEAREST WHOLE NUMBER :-
RULE :- Increase the last figure by 1 if the succeeding figure be 5 or greater than 5.
For eg. The approximation value of 0.5848 up to three decimal places is 0.585
The approximation value of 0.438 up to one decimal place is 0.4
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