Foundation and Higher · estimation

Estimate the answer.
Round everything
to 1 significant figure.

then it is
mental maths

when the question says —

Estimate

do not work out the exact answer

round first, then calculate

step 1 of 4

Round each number

1. Round every number to 1 s.f.

2. Write the rounded numbers down.

✓ Use ≈, not =

4.8 × 21.30.52

≈ 5 × 200.5each to 1 s.f.

4.8 → 521.3 → 200.52 → 0.5

step 2 of 4

Work it out

1. Multiply the top: 5 × 20 = 100.

2. Then divide by 0.5.

✓ Estimate: 200

5 × 200.5

= 1000.5top first

= 200

step 3 of 4

Dividing by a decimal

1. Dividing by less than 1 makes it bigger.

2. There are two halves in every whole.

✓ 100 ÷ 0.5 = 200

100 ÷ 0.5

“how many halves in 100?”

= 200 not 50

÷ 0.5 is the same as × 2

step 4 of 4

Use it as a check

1. The exact answer is 196.6.

2. Your estimate should be close to it.

✓ Got 19.66 or 1966? Look for a slip

estimate: 200

calculator: 196.6…

close, so it is sensible

estimating —

Round

every number to 1 s.f.

Show it

write the rounded calculation

÷ 0.5

is the same as × 2

Never round to the nearest whole number:
0.52 would become 1.

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