Estimation

Keep the first non-zero digit and inspect the next digit.

The zeros before 8 are placeholders.

Round both inputs before multiplying.

Keep the hundreds place for both numbers.

Round each number, then keep the subtraction.

Write the division using one-significant-figure values.

1. 418\approx400 and 5.2\approx5.
2. The estimate is 400\div5=80.

Keep the decimal place value when rounding 0.31.

1. 7.7\approx8 and 0.31\approx0.3.
2. The estimate is 8\times0.3=2.4.

How many tenths are in each rounded number?

1. 6.12\approx6 and 0.29\approx0.3.
2. 6\div0.3=60\div3=20.

Multiply the rounded values that Nia uses.

1. 30\times50=1500.
2. The original numbers were changed, so use \approx: 32\times48\approx1500.

Work out the rounded numerator before dividing.

1. \dfrac{39.2\times21.1}{8.3}\approx\dfrac{40\times20}{8}.
2. 40\times20=800, then 800\div8=100.

Estimate the number of folders and the price separately.

1. 19\approx20 and 3.90\approx4.
2. Estimated cost: 20\times4=80, or £80.

Keep the brackets. Add inside them before multiplying.

1. The rounded calculation is (50+20)\times4.
2. 50+20=70 and 70\times4=280.

The area of a rectangle is length multiplied by width.

1. 18.7\approx20 m and 9.6\approx10 m.
2. Estimated area: 20\times10=200 square metres.

Round each original number to one significant figure without changing its place value.

1. 6.14\approx6 and 0.398\approx0.4.
2. 6\div0.4=15, so the answer should be near 15, not near 0.15.

Consider the effect of changing 61 to 60, then separately consider changing 3.9 to 4.

1. Changing 61 to 60 lowers the answer. Changing the number you divide by from 3.9 to 4 also lowers it.
2. Both changes reduce the result, so 15 is an underestimate.

Estimate the fuel used for the whole journey before finding its cost. The rate is given per 100 km.

1. Round the journey distance to 200 km, the fuel consumption to 8 litres per 100 km, and the price to £2 per litre.
2. The estimated fuel used is (200\div100)\times8=2\times8=16 litres. The 100 km reference in the rate stays unchanged.
3. Estimated cost: 16\times2=32, or £32. This uses rounded inputs rather than rounding an exact final cost.

Use the stated rounding for the estimate. Then return to the original values for the budget decision.

Part (a)

1. 48\approx50, 2.10\approx2 and 19\approx20.
2. 50\times2+20=120, so the estimate is £120.

Part (b)

1. 48\times2.10+19=100.80+19=119.80.
2. 120-119.80=0.20, so there is £0.20 left.

Use the requested estimate first, then decide the claim using the original values.

Part (a)

1. 11.8\approx12 km and 3.9\approx4 hours.
2. Estimated speed: 12\div4=3 kilometres per hour.

Part (b)

1. At exactly 3 km/h, the distance in 3.9 hours would be 3\times3.9=11.7 km.
2. The walker covers 11.8 km in that time, which is more than 11.7 km. The actual average speed is therefore above 3 km/h.
3. The claim is true. The rough estimate alone was not accurate enough to settle it.

Work out the exact product and compare it with the stated estimate.

1. 52\times19=52\times(20-1)=1040-52=988.
2. The difference is 1000-988=12, so the estimate exceeds the exact value by 12.
3. One factor was rounded down and the other up. Those opposing changes alone do not establish the direction of the error; the comparison settles this case.

An estimate may not be enough to decide a purchase. Check how much ribbon whole rolls actually contain.

1. Nine rolls contain 9\times9.6=86.4 m, which is less than 94 m.
2. Ten rolls contain 10\times9.6=96 m, which is enough. The fewest number of rolls is 10.
3. The estimate reduced the required length and increased the length per roll, so it underestimated the number of rolls required.