Estimating means rounding every value in a calculation to make the arithmetic quick and approximate, then calculating with those rounded values — it's not the same as finding the exact answer. Unless told otherwise, round every number in the calculation to 1 significant figure before doing anything else.

1. The first significant figure is the first non-zero digit (reading left to right).
2. Zeros between non-zero digits count as significant: $402$ has 3 s.f.
3. Leading zeros (before the first non-zero digit) are never significant: $0.000002$ has 1 s.f.
4. Trailing zeros only count if there's a decimal point: $1000$ has 1 s.f., but $1050.$ has 4 s.f.

When rounding, use placeholder zeros to keep the number's scale correct: $34{,}568$ to 2 s.f. is $35{,}000$ (not $35$).

Round every number to 1 s.f., then apply BIDMAS to the simplified expression — do not round partway through a calculation.

Example: Estimate $9.04 + 19.85 \times 2.99 - 5.03$.

For division, round the denominator carefully — never let it round to zero. Dividing by $0.5$ is the same as multiplying by $2$, which is a useful shortcut when a rounded value lands on $0.5$.

Round each given value to 1 s.f., calculate, then interpret the result sensibly in context (correct units, whole numbers where the context demands it).

Example: Estimate the cost of $197$ packets of crisps at $45$p each. Round to $200 \times 50\text{p} = 10{,}000\text{p} = £100$.

Find the two perfect squares either side of the number, then judge which one it's closer to.

Example: Estimate $\sqrt{70}$. Since $8^2=64$ and $9^2=81$, the answer is between $8$ and $9$. As $70$ is closer to $64$ (difference $6$) than to $81$ (difference $11$), $\sqrt{70}$ is a little closer to $8$ than $9$ — about $8.4$.

It depends on which way each number was rounded:

For subtraction and division, rounding both numbers in the same direction makes the effect impossible to determine without checking — the two roundings pull in opposite directions on the result.

$52$ is rounded to $1$ s.f. as $50$, and $7.8$ is rounded to $1$ s.f. as $8$. Is the estimate of $52 \div 7.8$ using these roundings an overestimate or underestimate?

1. The first number ($52 \to 50$) was rounded down.
2. The second number ($7.8 \to 8$) was rounded up.
3. For division, "first down, second up" gives an underestimate — dividing a smaller numerator by a larger denominator makes the result smaller than the true value.