Linking fractions and decimals
Sometimes we need to refer to amounts that are in between whole numbers.
For example, a builder might need a piece of timber cut to a length longer than two meters
but shorter than three meters. In instances such as this, when we need to refer to a number that
isn't a whole number, we have a choice: we can use a fraction, or we can use a decimal.
Fractions and decimals do the same job, they just do it in different ways.
We're going to look at how fractions and decimals are linked and how we can convert between them.
Before we do this, we'll quickly review place values. These are the ones, the tens, the hundreds
and so on. Separating the whole numbers from the decimal numbers
is a decimal point. Here we have the tenths, the hundredths, the thousandths and so on.
Take this decimal: 0.1 It can also be read as one-tenth, because this is the tenths place.
What does one tenth look like as a fraction? You guessed it: one over ten.
The decimal 0.1 or one-tenth is the same as the fraction one-tenth. They're equivalent.
Here we have two-tenths or 0.2, three-tenths, four-tenths, five-tenths.
Did you notice that we can simplify this fraction? Five-tenths is the same as one-half.
You've probably seen one-half represented as 0.5 many times before.
Six tenths, seven tenths, eight tenths,
nine tenths. After nine tenths we have ten tenths, which we know is just one whole.
Let's move on from tenths look at this decimal:
0.01. This is the hundredths place, so we can also read this decimal number as one-hundredth
As a fraction it would look like this:.
Two hundredths or 0.02, three hundredths, four hundredths and so on.
Now that we're at ten hundredths, what do you notice about the decimal form?
We have moved into the tenths place. Ten hundredths is the same as one tenth.
We can also see that from this model as one tenth is overlaid on the ten hundredths.
Ten hundredths is written as 0.1. The last zero is not needed here. Here we have the
decimal number 0.14. It can be read as fourteen hundredths. We can see that it is made up of one
tenth and four hundredths. One tenth plus four hundredths equals fourteen hundredths.
Here is another: 0.68.
It can be read as sixty eight hundredths. It has six tenths and eight hundredths.
Six tenths plus eight hundredths equals sixty-eight hundredths.
Practice converting between fractions and decimals
as you complete the following table. Pause here while you work.
Let's go through the answers. Number one: two hundredths expressed as a decimal is 0.02.
Number two: 0.47. There are four tenths and seven hundredths. As a fraction it is forty
seven hundredths. Number three: fifty three hundredths as a decimal is 0.53. Number four:
did this 0 throw you off? This decimal number has 8 tenths and so is written as 8 tenths.
You might have written 80 hundredths which is also correct. Let's try a couple more:
three tenths plus six hundredths. Show the answer as a decimal. Pause here.
The answer is thirty-six hundredths. 0.36. One more nine hundredths plus
seven tenths. Show this as a decimal, and be careful with this one. Pause here.
The answer is 79 hundredths. 0.79
Remember, fractions and decimals do the same job:
they both show amounts that are in between whole numbers.
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