2 Negative numbers

Negative numbers arise in any situation in which we need to talk about numbers that are less than some agreed reference point (labelled zero). For example, on the Celsius temperature scale, the reference point 0 °C (said as ‘zero degrees Celsius’) is the temperature at which pure water freezes under normal atmospheric conditions. When the temperature falls five degrees below 0 °C, then we say that it is minus five degrees Celsius, or -5 °C, and if it falls even further to ten degrees below zero then it is -10 °C. So the minus sign in front of a temperature tells you that it is ‘less than zero’ and the number tells you how many degrees less than zero. In other words, the larger the number that follows the minus sign, the further the temperature is below zero degrees.

Mathematically, five degrees below zero means 0 °C - 5 °C, and if you do this subtraction the answer is -5 °C.

If you are not used to thinking about negative numbers, then it may help to think in terms of money. If your account is overdrawn by £50, then it has ‘£50 less than nothing’ in it, and your balance is -£50. You would have to add £50 to bring the balance up to zero. In a similar way, if the temperature is -50 °C (i.e. 50 °C ‘less than nothing’), then you would have to increase the temperature by 50 °C to bring it up to zero.

A wide range of Celsius temperatures is shown in Figure 2.1. The highest temperature marked is that of boiling water. When temperatures fall below zero, they are represented by negative numbers; the lower the temperature, the larger the number following the minus. At the lowest temperature shown, -196 °C (i.e. 196 degrees Celsius below zero), nitrogen gas, which is the main component of the air we breathe, condenses and becomes a liquid.

Figure 2.1 Temperatures on the Celsius scale. Note that we always use minus signs to denote negative temperatures, but we do not generally use plus signs in front of positive temperatures.