Decimal Fractions
Decimal Fractions
A decimal fraction is a fraction whose denominator is a power of 10. The number of decimal places equals the power of 10 in the denominator (0.375 = 375/1000). To convert a fraction to a decimal, divide numerator by denominator. To convert a terminating decimal to a fraction, write the digits over the appropriate power of 10 and simplify (0.125 = 125/1000 = 1/8). A recurring decimal repeats infinitely — 1/3 = 0.333… — and can be converted to a fraction by multiplying by the appropriate power of 10 and subtracting. For comparison, align decimal points and compare digit by digit from the left. For arithmetic: addition and subtraction require aligned decimal points; multiplication requires counting total decimal places in both factors; division requires making the divisor a whole number first.
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
To convert terminating decimal to fraction
Fraction to Decimal
Divide numerator by denominator
To convert fraction to decimal
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.