# 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.

$$\frac{1}{10}$$ = 0.1

$$\frac{2}{100}$$ = 0.02 → Decimal fractions

$$\frac{3}{1000}$$ = 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

Study the place value chart of the following numerals:

63124, 13642, 36412, 24163, 41263

The place value of 4

in 63124 is  4 ones = 4 × 1 = 4

in 13642 is 4 tens = 4 × 10 = 40

in 36412 is 4 hundreds = 4 × 100 = 400

in 24163 is 4 thousands = 4 × 1000 = 4000

in 41263 is 4 ten thousands = 4 × 10000 = 40000

As the digit moves from right to left

by one place its place value increases 10 times

by two places its place value increases 100 times

by three place its place value increases 1000 times

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.

Again, observe the table below:

 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.

Study the place value chart of the following numerals:

45381,  84351,  38415,  53841,  13584

The place value of 4

in 45381 is  4 ten thousands = 40,000

in 84351 is 4 thousands = 40000 ÷ 10 = 4000

in 38415 is 4 hundreds = 4000 ÷ 10 = 400

in 53841 is 4 tens = 400 ÷ 10 = 40

in 13584 is 4 one = 40 ÷ 10 = 4

As the digit moves from left to right

by one place, its place value becomes one-tenth [$$\frac{1}{10}$$]

by two places its place value becomes one-hundredth [$$\frac{1}{100}$$]

by three place its place value becomes one-thousandth [$$\frac{1}{1000}$$]

A decimal is a fraction whose denominator is 10 or powers of 10.

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 consists of two parts – one whole part and one fractional part.

These two are separated by a point called decimal point.

In a decimal the paces occupied by the digits after the decimal point are called decimal places.

Observe the following table:

 Picture Fractional Numbers(for shaded part) Fractions Decimals       . Read as one-tenth $$\frac{1}{10}$$ 0.1 zero point one two-tenths $$\frac{2}{10}$$ 0.2 zero point two three-tenths $$\frac{3}{10}$$ 0.3 zero point three four-tenths $$\frac{4}{10}$$ 0.4 zero point four five-tenths $$\frac{5}{10}$$ 0.5 zero point five

 Fraction Decimal Read as 2$$\frac{7}{10}$$ 2.7 Two point seven 13$$\frac{5}{10}$$ 13.5 Thirteen point five 4$$\frac{6}{10}$$ 4.6 Four point six 138$$\frac{2}{10}$$ 138.2 One hundred and thirty eight point two

Note:
A number without the whole part can be written omitting the zero of the whole part.

For example:

0.1 = .1          0.4 = .4          0.9 = .9 and so on.

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 $$\frac{20}{100}$$ 0.2 zero point two zero Four hundredths $$\frac{4}{100}$$ 0.04 zero point zero four Four hundred thousandths $$\frac{400}{1000}$$ 0.4 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.

Observe the following place value chart which is extended to tenths, hundredths and thousandths.

When the digit 7 moves one place from the ones place to the right, it is $$\frac{7}{10}$$ and read as 7 tenths.

When the digit 7 moves one place from the tenths place to the right, it is $$\frac{7}{100}$$ and read as 7 hundredths.

When the digit 7 moves one place from the hundredths place to the right, it is $$\frac{7}{1000}$$ and read as 7 thousandths.

Questions and Answers on Concept of Decimals:

I. Write the number names of:

(i) 19.34

(ii) 0.46

(iii) 1.08

(iv) 112.506

(v) 45.245

Answer:

II. Write decimals:

(i) Twenty nine and nine hundredths

(ii) Eighty six and four thousandths

(iii) Five and ninety six hundredths

(iv) One and one thousandth

(v) Seventy five thousandths

III. Write the place value of the underlined digit:

(i) 34.58

(ii) 143.652

(iii) 103.997

(iv) 0.004

(v) 96.829

Answer:

III. (i) 0.5

(ii) 0.002

(iii) 0.007

(iv) 0.004

(v) 0.8

## You might like these

• ### Like Decimal Fractions | Decimal Places | Decimal Fractions|Definition

Like Decimal Fractions are discussed here. Two or more decimal fractions are called like decimals if they have equal number of decimal places. However the number of digits in the integral part does not matter. 0.43, 10.41, 183.42, 1.81, 0.31 are all like fractions

• ### Expanded form of Decimal Fractions |How to Write a Decimal in Expanded

Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is missing either in the integral part or decimal part, substitute with 0.

• ### Multiplication of Decimal Numbers | Multiplying Decimals | Decimals

The rules of multiplying decimals are: (i) Take the two numbers as whole numbers (remove the decimal) and multiply. (ii) In the product, place the decimal point after leaving digits equal to the total number of decimal places in both numbers.

• ### Division of a Decimal by a Whole Number | Rules of Dividing Decimals

To divide a decimal number by a whole number the division is performed in the same way as in the whole numbers. We first divide the two numbers ignoring the decimal point and then place the decimal point in the quotient in the same position as in the dividend.

• ### Multiplication of a Decimal by a Decimal |Multiplying Decimals Example

To multiply a decimal number by a decimal number, we first multiply the two numbers ignoring the decimal points and then place the decimal point in the product in such a way that decimal places in the product is equal to the sum of the decimal places in the given numbers.

• ### Unlike Decimal Fractions | Unlike Decimals | Number of Decimal Places

Unlike decimal fractions are discussed here. Two or more decimal fractions are called unlike decimals if they have unequal numbers of decimal places. Let us consider some of the unlike decimals; (i) 8.4, 8.41, 8.412 In 8.4, 8.41, 8.412 the number of decimal places are 1, 2

• ### Equivalent Decimal Fractions | Like Decimal Fraction | Unlike Decimal

Equivalent decimal fractions are unlike fractions which are equal in value. Numbers obtained by inserting zeros after the extreme right digit in the decimal part of a decimal number are known as equivalent decimals.

• ### Comparison of Decimal Fractions | Comparing Decimals Numbers | Decimal

While comparing natural numbers we first compare total number of digits in both the numbers and if they are equal then we compare the digit at the extreme left. If they also equal then we compare the next digit and so on. We follow the same pattern while comparing the

• ### Addition of Decimal Fractions | Adding with Decimal Fractions|Decimals

Addition of decimal numbers are similar to addition of whole numbers. We convert them to like decimals and place the numbers vertically one below the other in such a way that the decimal point lies exactly on the vertical line. Add as usual as we learnt in the case of whole

• ### Subtraction of Decimal Fractions |Rules of Subtracting Decimal Numbers

The rules of subtracting decimal numbers are: (i) Write the digits of the given numbers one below the other such that the decimal points are in the same vertical line. (ii) Subtract as we subtract whole numbers. Let us consider some of the examples on subtraction

4th Grade Math Activities

From Concept of Decimal to HOME PAGE

### New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

 Share this page: What’s this?