Simplification

What is an approximation question?

The question says "what approximate value comes in place of ?" — the numbers are deliberately awkward (1199.8, 24.98%, √2303.9) and the options are far apart. You are allowed to round every number to a friendly value, compute, and pick the closest option. Perfection is not wanted; speed is.

The rounding rules

• Decimals round to the nearest whole number: 49.98 → 50, 15.02 → 15, 23.9 → 24.
• Percentages become fractions: 24.9% ≈ $\frac{1}{4}$, 33.3% ≈ $\frac{1}{3}$, 16.7% ≈ $\frac{1}{6}$, 12.5% = $\frac{1}{8}$, 19.9% ≈ $\frac{1}{5}$, 66.6% ≈ $\frac{2}{3}$.
• Near-perfect squares: √2303.9 ≈ 48 (since $48^2 = 2304$), √3968.9 ≈ 63, √625 ≈ 25.
• Near-perfect cubes: ∛29791.03 ≈ 31 ($31^3 = 29791$).
• Multiplying two rounded numbers? Round one up and the other down when you can — the errors cancel.

The fraction–percentage anchors (learn cold)

So "16.98% of 800" → $\frac{1}{6} \times 800 ≈ 133$ — no pen needed.

The usual question shapes

1. One expression: 29.9% of 1199.8 + 15.02 × 23.9 → $360 + 360 = 720$.
2. Find ?: 34.9% of 599.8 + ? = 299.9 → $210 + ? = 300$ → ? = 90.
3. Roots and powers mixed: (23.98)² + √2303.9 − 4.99 × 8.01 → $576 + 48 - 40 = 584$.
4. Equation in ?: (?)% of 650 + 40 = 350 → ? = 310/650 × 100 ≈ 48.

How precise must you be?

Work to the nearest ten (or nearest hundred for big numbers), then choose the option nearest to your answer. If two options are close, redo only the step that separates them.

Two worked mini-examples

• $\sqrt{3968.9} + \sqrt[3]{29791.03}$: $63^2 = 3969$ and $31^3 = 29791$, so the value is $63 + 31 = 94$. Both roots were placed next to perfect powers on purpose — that is how the setter builds the question.
• $\sqrt[3]{729.05} \times 12.99 ≈ 18.02\%$ of ?: left side $= 9 \times 13 = 117$. Then $? = 117 \times \frac{100}{18} ≈ 650$. When ? is on the right of a percentage, divide by the fraction instead of multiplying.

Sanity checks that save marks

• Size first: decide whether the answer is in the tens, hundreds or thousands before computing — one option in each region is usually a decoy.
• Direction of %: "18% of ? = 117" means $? = 117 \div 0.18$ (bigger than 117); "?% of 650 = 310" means ? is a percentage (around 48). Mixing these two up flips the answer by orders of magnitude.
• Balanced rounding: for $15.02 \times 23.9$ use $15 \times 24$ — you rounded one factor down and the other up, so the error largely cancels.

Quick revision

• Round everything; options are spaced 5–10% apart.
• Percent → fraction anchors; squares/cubes nearby.
• Round up-and-down pairs for products.
• Then pick the closest option, never recompute from scratch.