Expanded form of Decimal Fractions

We will discuss here about the expanded form of decimal fractions.

In expanded form of decimal fractions we will learn how to read and write the decimal numbers.

Decimal numbers can be expressed in expanded form using the place-value chart. Let us consider the number 561.129. Let us expand each of the digits using the place-value chart.

$Expanded form of Decimal$

So, we can write 561.129 in the expanded form as follows.

561.129 = 500 + 60 + 1 + 0.1 + 0.02 + 0.009

= 5 hundreds + 6 tens + 1 ones + 1 tenths + 2 hundredths + 9 thousandths

= 500 + 60 + 1 + 1/10 + 2/100 + 9/1000

Again,

493.2 = 4 hundreds + 9 tens + 3 ones + 2 tenths

= 400 + 90 + 3 + 2/10

1436.74 = 1 thousands + 4 hundreds + 3 tens + 6 ones + 7 tenths + 4 hundredths

= 1000 + 400 + 30 + 6 + 7/10 + 4/100

Note: When a decimal is missing either in the integral part or decimal part, substitute with 0.

1. Write in expanded form:

(i) 3479.105

= 3 thousands + 4 hundreds + 7 tens + 9 ones + 1 tenths + 0 hundredths+ 5 thousandths

= 3000 + 400 + 70 + 9 + 1/10 + 0/100 + 5/1000

(ii) 7833.45

= 7 thousands + 8 hundreds + 3 tens + 3 ones + 4 tenths + 5 hundredths

= 7000 + 800 + 30 + 3 + 4/10 + 5/100

(iii) 21.1097

= 2 tens + 1 ones + 1 tenths + 0 hundredths + 9 thousandths + 7 ten thousandths

= 20 + 1 + 1/10 + 0/100 + 9/1000 + 7/10000

(iv) 524.1

= 5 hundreds + 2 tens + 4 ones + 1 tenths

= 500 + 20 + 4 + 1/10

(v) 143.011

= 1 hundreds + 4 tens + 3 ones + 0 tenths + 1 hundredths + 1 thousandths

= 100 + 40 + 3 + 0/10 + 1/100 + 1/1000

(vi) 840.006

= 8 hundreds + 4 tens + 0 ones + 0 tenths + 0 hundredths + 6 thousandths

= 800 + 40 + 0 + 0/10 + 0/100 + 6/1000

(vii) 64.21

= 6 tens + 4 ones + 2 tenths + 1 hundredths

= 60 + 4 + 2/10 + 1/100

(viii) 4334.334

= 4 thousands + 3 hundreds + 3 tens + 4 ones + 3 tenths + 3 hundredths + 4 thousandths

= 4000 + 300 + 30 + 4 + 3/10 + 3/100 + 4/1000

2. Write as decimal fractions:

(i) 8 thousands + 8 ones + 3 tenths + 9 hundredths

= 8008.39

(ii) 4000 + 7 + 5/10 + 6/100

= 4007.56

(iii) 6 hundreds + 9 tens + 8 tenths + 4 thousandths

= 690.804

(iv) 3 tens + 7 ones + 6 hundredths + 8 thousandths

= 37.068

(v) 400 + 50 + 1 + 9/100

= 451.09

(vi) 800 + 70 + 2 + 8/10 + 5/1000

= 872.805

(vii) 6 tens + 5 tenths + 8 hundredths

= 60.58

(viii) 9 hundreds + 4 tens + 3 tenths + 4 hundredths

= 940.34

3. Write the following in short form.

(i) 100 + 0.5 + 0.06 + 0.008 (ii) 80 + 1 + 0.02 + 0.005

Solution:

(i) 100 + 0.5 + 0.06 + 0.008

= 100.568

(ii) 80 + 1 + 0.02 + 0.005

= 81.025

4. Write the place-value of the underlined digits.

(i) 2.47 (ii) 11.003 (iii) 5.175

Solution:

(i) 2.47

Place-value of 7 in 2.47 is 7 hundredths or 0.07.

(ii) 11.003

Place-value of 3 in 11.003 is 3 thousandths or 0.003.

(iii) 5.175

Place-value of 1 in 5.175 is 1 tenths or 0.1.

Practice Problems on Expanded Form of Decimal Fractions:

I. Write the given decimals in expanded form by fractional expansion.

One example has been done for you to get the idea how to do decimals in expanded form by fractional expansion.

1.73 = 1 + $\frac{7}{10}$ + $\frac{3}{100}$

(i) 23.8

(ii) 60.27

(iii) 119.05

(iv) 276.207

Answers:

(i) 20 + 3 + $\frac{8}{10}$

(ii) 60 + 0 + $\frac{2}{10}$ + $\frac{7}{100}$

(iii) 100 + 10 + 9 + 0 + $\frac{5}{100}$

(iv) 200 + 70 + 6 + $\frac{2}{10}$ + 0 + $\frac{7}{100}$

II. Write the given decimals in expanded form by decimal expansion.

One example has been done for you to get the idea how to do decimals in expanded form by decimal expansion.

8.461 = 8 + 0.4 + 0.06 + 0.001

(i) 6.08

(ii) 36.505

(iii) 402.613

(iv) 700.037

Answers:

(i) 6 + 0.0 + 0.08

(ii) 30 + 6 + 0.5 + 0.00 + 0.005

(iii) 400 + 0 + 2 + 0.6 + 0.01 + 0.003

(iv) 700 + 0 + 0 + 0.0 + 0.03 + 0.007

III. Write the decimal number for the expansions given below.

(i) 10 + 6 + $\frac{3}{10}$ + $\frac{9}{1000}$

(ii) 600 + 20 + 7 + $\frac{1}{10}$ + $\frac{3}{100}$ + $\frac{7}{1000}$

(iii) 2000 + 8 + $\frac{3}{10}$ + $\frac{9}{100}$

(iv) 400 + 70 + 1 + 0.5 + 0.07 + 0.002

(v) 5000 + 80 + 0 + 0.2 + 0.002

Answers:

(i) 16.309

(ii) 627.137

(iii) 2008.39

(iv) 471.572

(v) 5000 + 80 + 0 + 0.2 + 0.002 5080.202

You might like these

$We will discuss how to express fraction as decimal. Let us consider some of the following examples on expressing a fraction as a decimal. 1. Convert $\frac{4}{5}$ into a decimal.$

Fraction as Decimal | Converting Fractions | Fractions to Decimals Con
We will discuss how to express fraction as decimal. Let us consider some of the following examples on expressing a fraction as a decimal. 1. Convert $\frac{4}{5}$ into a decimal.
$We have already studied about fractions and now we will discuss here about the concept of decimal. Fractions can also be expressed as decimal Fractions.$

Concept of Decimal | Decimal Point | Concept of Decimal System
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.
Uses of Decimals | Decimals In Daily Life | Importance Of Decimals
We will learn uses decimals in every day. In daily life we use decimals while dealing with length, weight, money etc. Use of Decimals whole Dealing with Money: 100 paise = 1 rupee We know that one paise in one hundredth of a rupee.
Addition of Decimals | How to Add Decimals? | Adding Decimals|Addition
We will discuss here about the addition of decimals. Decimals are added in the same way as we add ordinary numbers. We arrange the digits in columns and then add as required. Let us consider some
Subtraction of Decimals | Subtracting Decimals | Decimal Subtraction
We will discuss here about the subtraction of decimals. Decimals are subtracted in the same way as we subtract ordinary numbers. We arrange the digits in columns
$Equivalent decimal fractions are unlike fractions which are equal in value. Numbers obtained by inserting zeros after the extreme right digit in the decimal part of a decimal number are known as equivalent decimals.$

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.
$We will discuss how to express decimal as fraction. Let us consider some of the following examples on expressing a decimal as a fraction. 1. Convert 2.12 into a fraction. Solution: 2.12$

Decimal as Fraction | Convert From a Decimal to a Fraction |Converting
We will discuss how to express decimal as fraction. Let us consider some of the following examples on expressing a decimal as a fraction. 1. Convert 2.12 into a fraction. Solution: 2.12
5th Grade Decimals Worksheet | Operations on Decimals | Comparing |Ans
In 5th Grade Decimals Worksheet contains various types of questions on operations on decimal numbers. The questions are based on formation of decimals, comparing decimals, Converting Fractions to Decimals, Addition of decimals, subtraction of decimals, multiplication of
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
$Division of a decimal number by 10, 100 or 1000 can be performed by moving the decimal point to the left by as many places as the number of zeroes in the divisor. The rules of division of decimal fractions by 10, 100, 1000 etc. are discussed here.$

Division of Decimal Fractions | Decimal Point | Division of Decimal
Division of a decimal number by 10, 100 or 1000 can be performed by moving the decimal point to the left by as many places as the number of zeroes in the divisor. The rules of division of decimal fractions by 10, 100, 1000 etc. are discussed here.
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
Simplification in Decimals |PEMDAS Rule | Examples on Simplification
Simplification in decimals can be done with the help of PEMDAS Rule. From the above chart we can observe that first we have to work on "P or Parentheses" and then on "E or Exponents", then from
Worksheet on Decimal Word Problems |Prob Involving Order of Operations
Solve the questions given in the worksheet on decimal word problems at your own space. This worksheet provides a mixture of questions on decimals involving order of operations
Worksheet on Dividing Decimals | Huge Number of Decimal Division Prob
Practice the math questions given in the worksheet on dividing decimals. Divide the decimals to find the quotient, same like dividing whole numbers. This worksheet would be really good for the students to practice huge number of decimal division problems.
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.