Decimal numbers


What are decimal numbers?


They're numbers which contain a decimal point.


To better understand decimals consider ...


... place value!


Don't worry about the digits 1 to 7 - they're for illustration purposes only!


In a decimal number, the place or position of a digit affects its value.


For instance, in the above diagram, the digit 7 lies in the thousandths (1/1000s) position - its value is therefore 7 x 1/1000 = 7/1000, i.e. seven thousandths.


Digit 5 lies in the tenths (1/10s) position, making its value 5 x 1/10 = 5/10 (five tenths), while digit 3 lies in the tens (10s) position, giving a value of 3 x 10 = 30 (thirty).


Anything to the left of the decimal point represents a whole number, whereas anything to the right of the decimal point represents part of a number.


Now take a look at the decimal number 0.1


- pronounced zero point one (or naught point one, or point one).


Writing this decimal as 000.100 to compare to the diagram above, you can see that there are no thousands, hundreds, tens or ones (units), there's 1 tenth, but no hundreths or thousandths.


So 0.1 equals 0 + 1/10 - zero and one tenth (or simply, a tenth).


Let's consider some other decimals


For example, one point two

1.2


comprises 1 unit and 2 tenths, i.e. 1.2 is equal to 1 + 2/10 - one and two tenths.


How about

2.13


Here you have 2 units, 1 tenth and 3 hundredths - the decimal number 2.13 equals 2 + 1/10 + 3/100 - two and one tenth and three hundredths.


A few more!


Decimal 13.089 - thirteen point zero eight nine


To the left of the decimal point, 1 ten and 3 units make up the whole number 13.

 

To the right of the decimal point, there are no tenths, 8 hundredths and 9 thousandths.

 

i.e. 13.089 is equal to 13 + 8/100 + 9/1000 – thirteen and eight hundredths and nine thousandths.



Decimal 156.6 – one hundred and fifty six point six

 

1 hundred, 5 tens and 6 units to the left of the decimal point make up the whole number 156. There are 6 tenths to the right of the decimal point.

 

So 156.6 equals 156 + 6/10 – one hundred and fifty six and six tenths.



Decimal 2236.47 – two thousand two hundred and thirty six point four seven

 

Don’t be concerned about the size of this number!

 

Just look to the left of the decimal point – there are 2 thousands, 2 hundreds, 3 tens and 6 units making up the whole number 2236.

 

Now look to the right of the decimal point where you’ll find 4 tenths and 7 hundredths.


 

Therefore 2236.47 is equal to 2236 + 4/10 + 7/100 – two thousand two hundred and thirty six and four tenths and seven hundredths.


Moving on!


Now you've covered the basics of decimals, you're ready to move onto learning more about how to convert decimal to fraction!


For more on decimals click:

Decimal to fraction

Fraction to decimal

Fraction to decimal chart

Decimal to percent

Percent to decimal


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