Decimal Fractions
Decimal Fractions
Convert between decimals, fractions, and recurring decimals fluently \u2014 this skill underpins every percentage, ratio, and interest calculation. SSC CHSL and RRB papers test direct decimal simplification, while banking exams embed decimal operations inside larger DI and approximation sets. Master terminating-vs-recurring recognition and the multiply-subtract trick for recurring decimals.
Key Idea
Decimals are just fractions with powers of 10 as denominator. Every decimal operation maps to a fraction operation — use whichever is more convenient.
Core Formulas
Decimal to Fraction
Move digits over power of 10, simplify. 0.ab = ab/100
Place the decimal digits over the matching power of 10 and simplify \u2014 use this whenever a question gives a terminating decimal and asks for the fraction form
Fraction to Decimal
Divide numerator by denominator
Divide directly to convert any fraction into its decimal equivalent \u2014 stop once the remainder repeats or terminates
Recurring decimal
x = 0.abab... → 100x − x = ab → x = ab/99
To convert pure recurring decimal to fraction
Decimal multiplication
Count total decimal places in factors; place decimal in product from right
Multiplying decimal numbers
Decimal comparison
Align decimal points, compare digit by digit from leftmost
Comparing two decimal numbers
Relevant Exams
Direct calculation questions in SSC CHSL and RRB exams. Forms the basis for all percentage, ratio, and interest calculations. Tested as simplification questions in banking exams.