1.2 Number formats and conventions

Ways of representing numbers (EMG4)

Convention

A standard way of doing something.

Format

The way that something appears or is set out.

Number formats and conventions refer to the different ways that we write numbers.

In South Africa the convention is to use the decimal comma to separate whole numbers from decimal fractions. We use spaces to separate groups of three digits. So we write one million rand as \(\text{R}\,\text{1 000 000,00}\). This makes big numbers easier to read. Compare 3000000 to \(\text{3 000 000}\).

You will sometimes see the use of the decimal point rather than the decimal comma, for example in account statements, bank statements and till slips. Also, sometimes people use commas to separate groups of three digits in very large numbers, for example one million rand is sometimes written as R1,000,000.00. These are all methods that make numbers easier to read. Using commas to separate groups is not common in South Africa however, and so this convention should be avoided - rather use spaces.

A calculator display shows a decimal point, with no spaces to separate the groups of three digits.

Numbers in different situations (EMG5)

We use different kinds of numbers in different situations. Sometimes these represent counting numbers or measurement values; sometimes they represent order, and sometimes they are just codes for identification.

Think about the numbers you see around you all the time:

These numbers include:

• measurements, such as lengths and masses.
• numbers of houses and flat numbers, which represent where to find them.
• numbers for counting, such as the number of people on a bus.
• numbers for representing order (for example: Sophie won 1st prize and James won 2nd prize).
• numbers for amounts of money.
• the rate of unemployment, as a percentage.
• numbers that represent a code rather than a value, for example, telephone numbers, car registration plate numbers, PINs, etc.

Notice that the numbers are represented in different ways.

• We use whole numbers for counting exact numbers of things, for example, a person has exactly \(\text{10}\) toes.

• Things that are ordered in a particular way are given whole numbers, but these numbers do not represent a number value. Ordering of things can also be indicated by 1st, 2nd, 3rd, etc.

• Numbers can also be used to represent position. For example, a house or flat number.

Not all of these kinds of numbers can be used in calculations. We can only calculate with numbers that represent a value and not with numbers that are used for naming, ordering or classifying things. For example, it doesn't make sense to use a telephone number in a calculation - if you multiplied a telephone number, you would just get the wrong number!

Writing whole numbers in words (EMG6)

Digit

One of \(\text{0}\); \(\text{1}\); \(\text{2}\); \(\text{3}\); \(\text{4}\); \(\text{5}\); \(\text{6}\); \(\text{7}\); \(\text{8}\); \(\text{9}\); used to make up a number.

To convert a number that is written in digits into words, use the following method:

• Beginning at the right and working from right to left, separate the number into groups by inserting spaces after every three digits (e.g. “123456” becomes “\(\text{123 456}\)”).
• Beginning at the left, read each group individually, saying the name of the group.

Here are a few examples for writing the numbers as words.

Place value of large numbers (EMG7)

It is easier to read large numbers written in symbols than numbers written out in words, because the place value of the symbols makes the value of the number clear.

For example: \(\text{65 781}\) is written out in full as sixty-five thousand, seven hundred and eighty-one.

Note the comma after the thousands and the hyphen between the tens and the units. This is similar to the thousands space we use when writing numbers in numerals.

It is useful to write large numbers in a place value table to compare them:

Arranging numbers in order (EMG8)

Here is a method for writing whole numbers from smallest to biggest (ascending order):

• Draw up a table with enough place value columns for all of the digits.
• Write in all the numbers. Put the units in the column on the right-hand side.
• Compare all of the numbers, starting from the first column on the left.
• If the digits are the same, look at the next column to the right until you find a digit that is different from the others.
• Write down the smallest number first, then the next smallest, and so on.

We use a similar method for writing numbers from biggest to smallest (descending order): compare them in the same way and write down the biggest number first.