Civil Service Numerical Test key terms

The value a digit has because of its position inside a number. In 4,702 the 7 stands for seven hundreds, while in 7,420 the same digit stands for seven thousands.

The agreed sequence for working out an expression: brackets first, then powers or roots, then multiplication and division, then addition and subtraction, working left to right within each level.

A whole number that divides another number exactly, leaving no remainder. For example, 1, 2, 3, 4, 6 and 12 are all factors of 12.

The result of multiplying a number by a whole number. The multiples of 6 include 6, 12, 18 and 24, and every number is a multiple of itself.

A whole number greater than 1 whose only factors are 1 and itself, such as 2, 3, 5, 7, 11 and 13. The number 1 is not counted as prime.

The amount left over when one whole number cannot be divided exactly by another. Dividing 17 by 5 gives 3 with a remainder of 2.

A way of showing part of a whole, written as one number over another. The bottom number gives how many equal parts there are; the top gives how many are taken.

A position to the right of the decimal point showing tenths, hundredths, thousandths and so on. The number 3.472 has three decimal places.

A fraction expressed out of one hundred and written with the % sign. Fifty per cent means 50 out of every 100, which is the same as one half.

The size of an increase or decrease shown as a percentage of the original amount. Divide the change by the starting value, then multiply by 100.

The plain arithmetic difference between two percentages. A rate rising from 4% to 6% has risen by 2 percentage points, even though that is a 50% increase.

A comparison of the sizes of two or more quantities, written with colons such as 3:2. It shows how many parts of one item there are for each part of another.

A statement that two ratios are equal, or a share of a total worked out from a ratio. If 2 of every 5 staff are part-time, the proportion is two fifths.

A technique for solving proportion problems by first finding the value of a single unit. If 4 pens cost £6, one pen costs £1.50, so 7 pens cost £10.50.

A shortcut for solving an equation between two fractions. Multiply the top of one fraction by the bottom of the other to produce a simple equation without fractions.

The total of a set of values divided by how many values there are. For 4, 7, 9 and 12 the total is 32, so the mean is 8.

The middle value once a set of numbers is arranged in order. When the count is even, take the mean of the two middle values.

The value that appears most often in a set of data. A list may have one mode, several modes, or no mode at all when every value is different.

The difference between the largest and the smallest values in a data set. It is a quick measure of how widely the data is spread.

An average in which some values count for more than others. Multiply each value by its weight, add the results, then divide by the total of the weights.

A comparison of two quantities measured in different units, such as miles per hour or cost per kilogram. It states how much of one thing matches one unit of another.

A rate expressed for a single unit of the second quantity, such as £3.20 per litre or 60 words per minute. Unit rates make comparisons between offers straightforward.

Changing a measurement from one unit to another without altering the amount, for example turning 1.5 kilometres into 1,500 metres by multiplying by 1,000.

A figure given for each person, found by dividing a total by the population or group size. It allows fair comparison between groups of different sizes.

A circle divided into sectors, where each sector's angle is proportional to its share of the total. All sectors together make a full 360 degrees.

A graph using rectangles of equal width whose heights show the size of each category. It is useful for comparing amounts across a small number of groups.

A chart that plots points and joins them with straight lines, usually to show how a value changes over time or across a continuous scale.

One of the two reference lines on a graph. The horizontal axis usually shows categories or time, while the vertical axis usually shows the measured value.

The general direction in which data moves over a period, such as rising, falling or staying level, ignoring short-term ups and downs.

Replacing a number with a nearby simpler one of similar size, often to a set number of decimal places or significant figures, to make calculation easier.

Finding a quick answer close to the exact one, usually by rounding numbers to convenient values. It is used to check answers and to save time in tests.

The digits in a number that carry meaningful information about its precision, counted from the first non-zero digit. Rounding 4,782 to two significant figures gives 4,800.

A plan showing expected income and planned spending over a period. Comparing actual figures with the budget shows whether money is being overspent or saved.

A reduction from the normal price, often stated as a percentage. A 20% discount on £80 takes off £16, leaving a sale price of £64.

Interest calculated only on the original amount, never on interest already added. Multiply the principal by the annual rate and by the number of years.

The money left when total costs are subtracted from total revenue. If a stall takes £450 and costs £300 to run, the profit is £150.

Gross means a total before deductions such as tax; net means the amount left after those deductions. Gross pay of £2,000 with £300 tax gives net pay of £1,700.

How much of a task is completed in a given time. If two people work at known rates, adding those rates shows how quickly they finish the job together.