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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