Decimals - The Decimal System

 The word 'Decimal' is derived from the Latin word 'decem', meaning ten. The system has its roots in India at around 300BC although this system was also evident in China at around the same time. The system was further developed in Persia and Egypt with the familiar Hindu-Arabic numerals similar to what we use today being introduced to Europe around the 12th century.

The Decimal system is based on ten symbols 0,1,2,3,4,5,6,7,8, and 9. The position of these symbols, ie their place, in a number determines the value of the number. This is why Place Value is such an important concept to understand.

I would recommend reviewing Place Value before moving on.

Each place is ten times the value of the place to it's right, and consequently each place is ten times smaller than the place to it's left.

TTh
Th
H
T
U
  
1/10
  
1/100
Ten Thousands
Thousands
Hundreds
Tens
Units
.
Tenths
Hundredths

0

0

1

1

1

.

0

0

 

The number 1 placed in the Hundreds column is worth 100, its value is 100, which is ten times greater than the 1 in the Tens column whose value is 10, which is in turn ten times greater than the 1 in the units column whose value is 1.

So far we have only looked at whole numbers, but the decimal system can also be used to represent numbers that are less than a whole number, less than one. The whole numbers and parts of whole numbers are separated by the decimal point. Any number placed to the left of the decimal point is a whole number and the value of any number placed to the right of the decimal point is less than a whole and each column to the right of the decimal point decreases by ten or is a tenth of the column to its left. These numbers to the left of the decimal point can be thought of as Decimal Fractions.

TTh
Th
H
T
U
  
1/10
  
1/100
Ten Thousands
Thousands
Hundreds
Tens
Units
.
Tenths
Hundredths

0

0

0

0

1

.

1

1

 

The number 1 placed in the tenths column to the right of the decimal point has a value ten time smaller than the 1 placed in the Units column - one tenth. The number 1 placed in the Hundredths column to the right of the decimal point has a value ten time smaller than the 1 placed in the Tenths column - one hundredth.

It is important that children understand that the numbers placed to right of the decimal point are parts of a whole number - ensure that for 1.11 they say "One point one one" and not "One point Eleven" because the .11 does not mean eleven, This is a common misconception and you need to make sure that they fully understand this.

Write out some decimal numbers and have your child say them out loud to you.

2.63 is 'two point six three' not 'two point sixty three'

Decimal numbers can be thought of in terms of fractions - any number to the left of the decimal point is the whole number and anything to the right of the decimal point is the fraction - But the fraction of what?

Lets look at the first column to the right of the decimal point, any number placed here has a value of that number of tenths - so 0.1 is 1/10, 0.2 is 2/10, 0.5 is 5/10 and so on.

Any number placed in the second column to the right of the decimal point has a value of that number of hundredths - so 0.01 is 1/100, 0.02 is 2/100, 0.5 is 5/100 and so on.

Ask your child to say different decimal numbers as fractions.

What is 1.1? ...... One and one tenth
What is 2.3? ... Two and three tenths
What is 5.04? .... Five and four hundredths

What is 25.16? - Twenty five and one tenth and six hundredths
(or Twenty Five and sixteen hundredths, but be careful not to confuse them with this -
It's the concept that is important here)

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Try these worksheets from Maths is Fun

Units and Tenths /Answers       Hundredths / Answers      Units and Hundredths / Answers

Units and Tenths 2 /Answers     Units and Hundredths / Answers

 

Maths Index - 11 Plus for Parents  Decimals - Adding and Subtracting title=















CAT4 / 12 Pus papers