SSC CGL Preparation: Concepts and Practice

Learning outcome

Calculate with decimals using all four operations, explain the placement of the decimal point, and check whether an answer has a sensible size.

Understanding the operations

Addition and subtraction combine quantities with the same place value. Align decimal points so that tenths meet tenths and hundredths meet hundredths. Append zeros where helpful. Carrying and borrowing work because each place is worth ten of the next smaller place.

For multiplication, first multiply as integers, keeping any signs. Then use the total number of decimal places in both factors. This works because removing decimal points scales the factors by powers of ten; the product must be scaled back by their combined factor. Preserve zeros until the decimal point has been placed.

For division, the divisor must be nonzero. Multiply both dividend and divisor by the same power of ten until the divisor becomes an integer. Scaling both equally leaves the quotient unchanged. During long division, append zeros after the dividend’s decimal point when more digits are needed.

A useful check is to reverse the operation. Product divided by a nonzero factor should recover the other factor; quotient multiplied by divisor should recover the dividend. In expressions, retain the usual bracket and operation priorities.

Worked examples

Example 1: Calculate 12.6 + 3.85 - 0.47.

Align the places: 12.60 + 3.85 = 16.45. Then 16.45 - 0.47 = 15.98. Borrowing allows the hundredths subtraction without changing the overall quantity. Check: 15.98 + 0.47 = 16.45.

Example 2: Calculate 0.48 × 0.35.

Whole-number multiplication gives 48 × 35 = 1680. The factors have four decimal places altogether, so divide by 10000: 0.1680 = 0.168. Multiplication by a positive number below one makes the other positive factor smaller, so the size is sensible.

Example 3: Calculate 7.56 ÷ 0.24.

Multiply both numbers by 100: 756 ÷ 24. Since 24 × 31 = 744, the remainder is 12. Continue after the decimal point: 120 ÷ 24 = 5, giving the tenths digit. Therefore, the quotient is 31.5. Check: 31.5 × 0.24 = 7.56.

Common mistakes

Do not align final digits instead of decimal points for addition. Do not use that alignment rule to place a product’s decimal point. In division, scaling only one number changes the answer. Division by zero is undefined.

Practice questions

1. Calculate 8.07 + 0.9 - 2.365.
2. Calculate 2.4 × 0.065.
3. Calculate 0.864 ÷ 0.12.
4. Calculate 3.6 ÷ (0.4 + 0.5) + 0.25 × 0.8.

Worked answers

1. Use three decimal places: 8.070 + 0.900 = 8.970. Then 8.970 - 2.365 = 6.605.
2. Since 24 × 65 = 1560, four decimal places give 0.1560 = 0.156.
3. Scale both numbers by 100: 86.4 ÷ 12 = 7.2. Check: 7.2 × 0.12 = 0.864.
4. Brackets give 0.9. Then 3.6 ÷ 0.9 = 4 and 0.25 × 0.8 = 0.2. Finally, 4 + 0.2 = 4.2. These results are exact; no rounding was used.