Decimal Expansion


 
 
Concept Explanation
 

Decimal Expansion

Decimal Expansion : When we convert a fraction in the  decimal expansion.

large Example: ;Find ;decimal ;expansion ;of; frac{5}{16};and ;frac{17}{8}

Solution       On dividing 5 by 16.

                        large therefore frac{5}{16}=0.3125

                    (ii) we divide 17 by 8.

                      large therefore frac{17}{8}=2.125

large Thus ;frac{5}{16}; and;frac{17}{8} ;can ;be ;represented ;by ;terminating; decimals,

large but; there; are; certain; cases ;which; do ;not; terminate; such; as;frac{1}{7}

We note that if the denominator in the lowest form has some prime factors other than 2 or 5 then it cannot be expressed as a terminating decimals.

Inserting Irrational Numbers Between two Numbers: We can write any non terminating non recurring decimals between those numbers.

Example: Insert three rational numbers between 0.2 and 0.3.

Solution: Three rational numbers between 0.2 and 0.3

0.2101001000...., 0.211011001100011...., 0.21100110001100001111....

 
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