# The A to Z of mathematics a basic guide - Sidebotham T.H.

ISBN 0-471-15045-2

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1. Qualitative data are descriptive data, for example, eye color, nationality, gender, types of jobs, attitudes toward politicians, and so on.

2. Quantitative data are numerical data, which are about numbers, for example, the number of workers in a factory, the number of children in a family, the temperature of a liquid, and so on. These data can be ranked in order of size.

3. Nominal data are qualitative data that cannot be ranked in order. For example, the color of cars cannot be ranked, since one color cannot be regarded as higher or lower than another color.

4. Ordinal data are qualitative data that can be ranked in some sort of order. For example, a person’s attitude toward television can be ranked as three levels: likes it, finds it OK, dislikes it.

5. Discrete data are quantitative data obtained by counting, and such that the items of data cannot be subdivided. For example the number of people in a family is a counting number and cannot be subdivided into half a person.

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146 DECILE

6. Continuous data are quantitative data obtained by measuring, with each item of measurement having an infinite number of possible values, restricted only by the limitations of the measuring device, for example, the speed of cars passing a certain mark on a highway.

References: Experiment, Population, Sample, Survey.

DECAGON

A decagon is a polygon with 10 sides. Figure a shows some decagons; the last one is a regular decagon. The regular decagon has 10 sides that are of equal length, and its 10 angles are each equal to 144°. It has 10 axes of symmetry, and the order of rotational symmetry is 10. The regular decagon is made up of 10 congruent isosceles triangles whose angles are 36°, 72°, and 72° (see figure b). The regular decagon will not tessellate.

References: Axis of symmetry, Congruent Figures, Isosceles Triangle, Order of Rotational Symmetry, Polygon, Regular Polygon, Tessellations.

(a)

(b)

DECAY

Reference: Exponential Decay.

DECILE

Reference: Percentiles.

DECIMAL 147

DECIMAL

A decimal is also known as a decimal fraction. A decimal is equivalent to a proper fraction that has a denominator of either 10,100,1000, or further powers of 10, but is written without a denominator and with a decimal point. A decimal can be negative.

Example 1. Write the fraction ^ in the form of a decimal.

Solution. This fraction has a denominator of 10, so it can readily be expressed in decimal form. As a decimal it is written without a denominator, but it does have a decimal point: ^ =0.3. The zero indicates there is no whole number, the 3 represents ^, and the decimal point separates them. Each figure that is written after the decimal point represents a proper fraction. The first figure after the decimal point represents

tenths. For example, 0.8 = ^ and 0.9 = ^. If there are two figures after the decimal

point, they are equivalent to hundredths. For example, 0.75 = 75/100, which cancels to |. Also, 0.08 = 08/100, which is written as 8/100, and cancels to 2/25.

If there are three figures after the decimal point they are equivalent to thousandths, and so on. For example, 0.257 = 257/1000.

Decimals involving two or more figures after the decimal point can be expressed as the sum of tenths, hundredths, thousandths, and so on. For example,

0 257 — — + — + —

— 10 t 100 -r 1000

If a fraction does not have a denominator of 10 or of powers of 10, it can still be converted into decimal form. The method is explained in the following example.

Example 2. Convert these fractions into decimal form: (a) |, (b) (c)

Solution. For (a), write

| = | x | Multiplying by | ensures that the denominator is 10 and the fraction has the same value

_ e_

~ 10

= 0.6 Which is in decimal form For (b),

25 = 25 X 4 Multiplying by | ensures that the denominator is 100

8

— 100

= 0.08

Which is in decimal form

148 DECIMAL

For (c),

j = 5 e-7 1 cannot be multiplied by a whole number to

obtain a power of 10, so the fraction is turned into a division

= 0.714285714... Using the calculator for division

= 0.714 (to 3 dp) See later in this entry for recurring decimals

Example (c) indicates that fractions can be changed into decimals using a calculator for dividing the numerator by the denominator. This means that the methods used in

(a) and (b) need only be employed if no calculator is available!

Decimals can be converted into fractions using the methods outlined in the following examples.

Example 3. Convert the following decimals into fractions, and leave your answers in their simplest form: (a) 0.25, (b) 0.80, (c) 2.857.

Solution. For (a), write

0.25 = ^ Two figures after the decimal point indicate that the

denominator of the fraction is 100

= | x || 25 is a common factor of 25 and 100

= j Canceling the 25’s

For (b),

0.80 = 0.8 The zero after the 8 indicates that there are no hundredths

One figure after the point indicates tenths

10 4 „

2 is a common factor of 8 and 10 Canceling the 2’s

For (c),

2.857 = 2 + The 2 is a whole number, because it is before the decimal point

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