Concept of Decimal
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 |
|
Twenty-five hundredths |
\(\frac{25}{100}\) |
0.25 |
zero point two five |
|
Sixty-seven hundredths |
\(\frac{67}{100}\) |
0.67 |
zero point six seven |
|
Sixty-seven 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 forty-two hundredths |
1\(\frac{42}{100}\) |
1.42 |
one point four two |
|
Five and sixty-three hundredths |
5\(\frac{63}{100}\) |
5.63 |
five point six three |
|
Seven and four hundred sixty-two hundredths |
7\(\frac{462}{1000}\) |
7.462 |
seven point four six two |
|
Five and eighty-two 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 forty-five.
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