Rounding, Estimation & Bounds (AQA GCSE Maths)

When rounding a number to the nearest 100, the digit in the tens place value column determines how the number rounds.

E.g. when rounding 14, 578 to the nearest 100, the 7 in the tens column tells you to round up to 14, 600

The first significant figure of a number is the first non-zero digit of the number when reading from left to right.

For example, the first significant figure of 0.457 is 4.

False.

The second significant figure of 4.0051 is 0.

The number 0 can be a significant figure as long as there are non-zero values on either side of it.

To round a number to three significant figures:

1. Find the third significant figure

2. Check the digit to its right (the fourth significant figure)

   1. If this is 0, 1, 2, 3 or 4 then keep the third significant figure the same and (if necessary) fill the remaining place values with 0s

   2. If it is 5, 6, 7, 8 or 9 then round the third significant figure up to the next value and (if necessary) fill the remaining place values with 0s

E.g. the fourth significant figure of 40 529 is 2, this means the third significant figure (5) stays the same and it rounds down to 40 500.

When estimating a calculation, the general rule is to round each number to 1 significant figure first.

E.g. for the calculation , round to

Truncation is essentially the same as rounding down to a given degree of accuracy. You can think of it as "chopping off" the last parts of a number.

For example if the question is about the maximum number of people that can fit in a taxi and the answer is 4.6, the answer would be truncated to 4, rather than rounded to 5.

False.

Truncating a number to 3 decimal places will often produce a different result to rounding a number to 3 decimal places.

E.g.
Rounding 3.57867 to 3 decimal places would be 3.579
Truncating 3.57867 to 3 decimal places would be 3.578

If you round both numbers up in an addition, the answer will be an overestimate.

E.g. estimate the calculation 288 + 962.
Each value rounds up to 1 significant figure, 300 + 1000 = 1300.
(This gives an overestimate 288 + 962 = 1250).

If you round both numbers down in a multiplication, the answer will be an underestimate.

E.g. estimate the calculation 621 × 438.
Each value rounds down to 1 significant figure, 600 × 400 = 240 000.
(This gives an underestimate 621 × 438 = 271 998.)

False.

If you round both numbers up when estimating a division, it is not easy to tell whether the the answer be an overestimate or an underestimate.