Selecting and carrying out calculations including multiplication and division, writing very large or very small numbers in scientific notation, and rounding answers to a given number of decimal places or significant figures.

What this dot point is asking

The SQA wants you to read a worded context, choose and carry out the right calculation (including multiplication and division of decimals), write very large or very small numbers in scientific notation, and round your answer to a stated number of decimal places or significant figures with a sensible degree of accuracy.

Selecting and carrying out a calculation

Applications questions are written in context, so the first job is to decide which operation answers the question. Sharing equally points to division; repeated groups point to multiplication; a total points to addition. On Paper 1 you must do this by hand, so keep your working tidy.

When multiplying decimals by hand, ignore the decimal points, multiply the whole numbers, then put the point back so the answer has as many decimal places as the two factors combined.

Scientific notation

Scientific notation (standard form) writes a number as a value between $1$ and $10$ multiplied by a power of ten. It is the compact way to handle the very large numbers (populations, distances) and very small numbers (measurements in metres) that appear in applied problems.

Rounding to decimal places and significant figures

Rounding turns a long or exact answer into a sensible one. The SQA expects you to round to a stated number of decimal places, or to a stated number of significant figures, and to choose a sensible accuracy when the question leaves it open.

Decimal places count digits after the decimal point. To round $3.847$ to $2$ decimal places, look at the third decimal ($7$); it is $5$ or more, so round up to $3.85$.

Significant figures count digits starting from the first non-zero digit. Leading zeros never count. To round $0.04063$ to $2$ significant figures, the first two significant digits are $4$ and $0$; the next digit ($6$) rounds the $0$ up, giving $0.041$.

A sensible degree of accuracy matches the context: money rounds to the nearest penny ($2$ decimal places), a length might round to the nearest centimetre, and a count of people must be a whole number.

Examples in context

Numeracy underpins every other area of the course. Working out fuel needed for a journey, the cost of carpet for a floor, or an average from a data set all start with choosing the operation and finishing with a sensibly rounded answer. Scientific notation appears when a problem quotes a distance such as $1.5 \times 10^8$ kilometres or a tiny measurement, and you must read it correctly before calculating.

Try this

Q1. Write $0.000805$ in scientific notation. [2 marks]

• Cue. $8.05 \times 10^{-4}$.

Q2. Round $7.0649$ to $2$ decimal places. [1 mark]

• Cue. $7.06$.

Q3. Round $134\,920$ to $3$ significant figures. [2 marks]

• Cue. $135\,000$.