Decimals and Fractions — Study Notes

Overview

Decimals and fractions are two different ways to represent parts of a whole, and mastery of both is essential for SSC GD Elementary Mathematics. This topic typically accounts for 3–5 direct questions in the exam, but the concepts appear indirectly in almost every other area—percentage, ratio, interest, and mensuration all require fluent conversion and calculation with decimals and fractions.

Students must be able to convert between decimal and fraction forms quickly, perform all four operations (addition, subtraction, multiplication, division) on both, and simplify answers to their lowest terms. Many errors occur when students mix operations or forget place values in decimals. The key is to build mechanical fluency: know the standard conversions (like 0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4) by heart and practice the algorithms until they become automatic.

In SSC GD, questions are straightforward but require accuracy under time pressure. You will see problems asking you to add mixed fractions, multiply decimals, or convert a recurring decimal to a fraction. A single calculation mistake costs marks, so systematic working and double-checking are non-negotiable.

Key Concepts

• **Fraction basics**: A fraction a/b has numerator a (top) and denominator b (bottom). Proper fractions have a < b; improper fractions have a ≥ b. A mixed number combines a whole number and a proper fraction (e.g. 2 1/3).

• **Decimal place value**: In 45.678, the 6 is in the tenths place (6/10), 7 in hundredths (7/100), and 8 in thousandths (8/1000). Understanding place value prevents errors when adding or comparing decimals.

• **Equivalent fractions**: Multiplying or dividing both numerator and denominator by the same nonzero number gives an equivalent fraction. Example: 2/3 = 4/6 = 6/9. Simplification means reducing to lowest terms by dividing by the greatest common divisor.

• **Conversion fraction to decimal**: Divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75. Some fractions give terminating decimals (like 1/2 = 0.5), others give recurring decimals (like 1/3 = 0.333...).

• **Conversion decimal to fraction**: Write the decimal as a fraction over the appropriate power of 10, then simplify. Example: 0.36 = 36/100 = 9/25 after dividing numerator and denominator by 4.

• **Operations on fractions**: For addition/subtraction, find a common denominator, convert both fractions, then add/subtract numerators. For multiplication, multiply numerators and denominators directly. For division, multiply by the reciprocal of the divisor.

• **Operations on decimals**: Align decimal points for addition and subtraction. For multiplication, ignore decimals initially, multiply as whole numbers, then count total decimal places in factors and place the decimal in the product. For division, make the divisor a whole number by shifting decimals in both dividend and divisor.