Simplification & Surds · Topic 7 of 8

• Decimal Simplification

1 exam question type, fully solved

Decimals follow all the same rules as whole numbers — you just have to keep track of the point. And like everywhere else in this chapter, the exam usually hides an identity to make the numbers cancel.

How to handle decimals fast

• Add / subtract: line up the decimal points (pad with zeros), then add column by column.

• Multiply: ignore the points, multiply as whole numbers, then place the point so the answer has as many decimal places as both numbers together.

• Recurring decimals: turn them into fractions — 0.333… = , 0.999… = 1 exactly (a classic trap).

• Spot the identity: has the shape , which cancels straight to a+b = 1. Never cube the decimals.

And BODMAS still rules the order, exactly as with integers.

🔢BODMAS Step-by-StepReveal one step at a time

12 + 6 ÷ 2 × 3 − 4

0.7 + 0.07 + 0.007 = (line up the points).

Q1Find 0.6 + 0.06 + 0.006:

Q2The value of (1.5)² − (0.5)² is:

Q30.333… equals which fraction?

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Real exam questions — Decimal Simplification

1 question types · 4 solved examples from real SSC papers

Line up the points, or spot the hidden identity. Most exam decimals are picked to collapse to a clean number.

How to solve this type

For plain adding or subtracting, write the numbers in a column with the decimal points lined up, padding with zeros so every number has the same count of decimal places, then add as usual. To multiply, ignore the points and multiply as whole numbers, then count the total decimal places in both factors and place the point that many digits from the right. Convert a recurring decimal to a fraction before heavy work — for example 0.333… = 1/3, 0.444… = 4/9, and a two-digit repeat like 0.121212… = 12/99 — or simply expand it to six places and compute. Most exam decimals hide an identity such as (a + b)², a² − b² = (a + b)(a − b), or a³ ± b³, so check for that before grinding out squares and cubes. Finally obey BODMAS: brackets and orders first, then division and multiplication, then addition and subtraction.

Find 0.5 + 0.55 + 0.555 + 0.5555

A1.5555B1.4405C2.1605D1.0555

Find $\sqrt{1.44 + 0.81 + 2\times 1.2\times 0.9}$

A1.5B2.4C1.8D2.1

The value of $\dfrac{0.96^3+0.04^3}{0.96^2-0.96\times0.04+0.04^2}$ is:

A0B1C2D0.82

The value of 22.444… + 11.567676… − 33.5999… is:

A0.323232…B0.412121…C0.313131…D0.412412…