Decimals are a way of representing numbers. They have a whole number part and a fractional (or decimal) part, which are separated by a decimal point.
So that’s the basics covered. But here are some lesser known, and rather curious, facts about decimals:
The ‘dec’ in decimal means ten, and refers to the fact that each position in a decimal number corresponds to ten times more than the next position along. For example, the number 325.31 means 3 hundreds, 2 tens, 5 ones, 3 tenths and 1 hundredth. Humans decided to group in tens because that’s how many fingers/thumbs we have. It made counting and arithmetic a whole lot easier. Three-fingered aliens might well group in threes!
Have you ever been told that ‘to multiply by ten, just add a zero at the end’? If so, you’ve been misled! Here’s an example: 2.3 x10 is not 2.30, it is 23.0. What’s actually happening when you multiply by ten is that every digit shifts along one place to the left because there are now ten times as many of each digits. In our example, there are now 2 tens rather than 2 ones.
Some decimal expansions go on forever: for example, 1/3 = 0.333… where the ‘…’ means that the 3s never end.
0.999…. = 1
This can’t be true, surely? It is, and we’re going to prove it:
Let x = 0.999…
Then 10x = 9.999…
So 9x = 10x – x
= 9.999… – 0.999…
Which means x=1.
Here’s another way to convince yourself: try plotting the value 0.999… on the number line. It has to be greater than 0.9, but also greater than 0.99, and 0.999 and so on. You don’t have any space to squeeze it before the 1 which must mean it is actually equal to 1!
Every fraction is a decimal. A fraction is one whole number divided by another (but we can’t divide by zero). Every fraction, small or large, positive or negative, can be written as a decimal. For example, 1/2 = 0.5, 1/3 = 0.333… and 1/7 = 0.142857142857… – where the ‘142857’ repeats forever!
But not every decimal is a fraction. Some numbers are so strange that they can’t be expressed as a fraction. The number π, for example, which we use to calculate circle measurements, has a decimal expansion that goes on forever and never repeats (it starts 3.14159). It cannot be written as a fraction.
Different countries and languages use different notation for the decimal point. For example, in Taiwan and Singapore the point is placed is placed mid-line, so 23·89 rather than 23.89. In many European countries, a comma is used instead: 23,89. Horses for courses!
Decimals are used in a range of real-world situations to represent different amounts. Money, weight and height all use decimal points. So does the Richter scale, which measures the strength of an earthquake.