We have already studied about fractions and now we will discuss here about the concept of decimal.
Fractions can also be expressed as decimal Fractions.
We have already studied about fractions. Fractions can also be expressed as decimal Fractions.
1/10 = 0.1
2/100 = 0.02 → Decimal fractions
3/1000 = 0.003
The dot (.) is 0.1, 0.02, 0.003 is called a decimal point or point.
Before we proceed further, let us understand the concept of decimal.
Concept of Decimal
Observe the place value table shown and note the place value of 1 in each case.
Numerals 8651 →
8615 → 8165 → 1865 → 
Thousands 8 8
8 1 
Hundreds 6 6
1 8 
Tens 5 1
6 6 
Ones 1 5
5 5 
We find that:
Place value of 1 in 8651 = 1 × 1 = 1
Place value of 1 in 8615 = 1 × 10 = 10
Place value of 1 in 8165 = 1 × 100 = 100
Place value of 1 in 1865 = 1 × 1000 = 1000
We observe that the place value of a digit is increasing ten times as it moves one place from right to left i.e. the place value of 1 is 1 at ones place, 10 at tens place, 100 at hundreds place and 1000 at thousands place.
Numerals 1865 →
8165 → 8615 → 8651 → 
Thousands 1 8 8 8

Hundreds 8 1
6 6 
Tens 6 6
1 5 
Ones 5 5
5 1 
Place value of 1 in 1865 = 1000
Place value of 1 in 8165 = 100
Place value of 1 in 8615 = 10
Place value of 1 in 8651 = 1
We observe that the place value of a digit becomes one tenth as it moves one place from left to right i.e. the place value of 1 is 1000 at thousands place, 100 at hundreds place, 10 at tens place and 1 at ones place. We can extend the place value chart further as follows:
0.1, 0.01, 0.001 etc. are known as decimal fractions.
We use fractions to express the numbers smaller than 1. We can also express a number smaller than one by using decimal point. Decimal is derived from ‘decem’ the Latin word which means 10. Remember, 10 is the base of the decimal system.
A decimal number has two parts  A whole number and a decimal fraction. A decimal point separates them. It is denoted by a dot (.). It is also called point.
Observe the table given below.
Number 
Fraction 
Decimal 
Read as 
Four tenths 
\(\frac{4}{10}\) 
0.4 
zero point four 
Six tenths 
\(\frac{6}{10}\) 
0.6 
zero point six 
One and five tenths 
1\(\frac{5}{10}\) 
1.5 
one point five 
Seven hundredths 
\(\frac{7}{100}\) 
0.07 
zero point zero seven 
Twenty hundredths 
\(\frac{20}{100}\) 
0.20 
zero point two zero 
Four hundredths 
\(\frac{4}{100}\) 
0.04 
zero point zero four 
Four hundred thousandths 
\(\frac{400}{1000}\) 
0.400 
zero point four zero zero 
Twentyfive hundredths 
\(\frac{25}{100}\) 
0.25 
zero point two five 
Sixtyseven hundredths 
\(\frac{67}{100}\) 
0.67 
zero point six seven 
Sixtyseven thousandths 
\(\frac{67}{1000}\) 
0.067 
zero point zero six seven 
One and three hundredths 
1\(\frac{3}{100}\) 
1.03 
one point zero three 
One and fortytwo hundredths 
1\(\frac{42}{100}\) 
1.42 
one point four two 
Five and sixtythree hundredths 
5\(\frac{63}{100}\) 
5.63 
five point six three 
Seven and four hundred sixtytwo hundredths 
7\(\frac{462}{1000}\) 
7.462 
seven point four six two 
Five and eightytwo hundredths 
5 \(\frac{82}{1000}\) 
5.082 
five point zero eight two 
Seven hundredths 
\(\frac{7}{1000}\) 
0.007 
zero point zero zero seven 
Remember, the digits after the point are always read separately. For example, 1.345 is read as one point three four five and not as one point three hundred and fortyfive.
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