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.
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 + \(\frac{1}{10}\) + \(\frac{2}{100}\) + \(\frac{9}{1000}\)
Again,
493.2 = 4 hundreds + 9 tens + 3 ones + 2 tenths
= 400 + 90 + 3 + \(\frac{2}{10}\)
1436.74 = 1 thousands + 4 hundreds + 3 tens + 6 ones + 7 tenths + 4 hundredths
= 1000 + 400 + 30 + 6 + \(\frac{7}{10}\) + \(\frac{4}{100}\)
Note: When a decimal is missing either in the integral part or decimal part, substitute with 0.
1. Write the decimal numbers in expanded
form:
(i) 3479.105
= 3 thousands + 4 hundreds + 7 tens + 9 ones + 1 tenths + 0 hundredths+ 5 thousandths
= 3000 + 400 + 70 + 9 + \(\frac{1}{10}\) + \(\frac{0}{100}\) + \(\frac{5}{1000}\)
(ii) 7833.45
= 7 thousands + 8 hundreds + 3 tens + 3 ones + 4 tenths + 5 hundredths
= 7000 + 800 + 30 + 3 + \(\frac{4}{10}\) + \(\frac{5}{100}\)
(iii) 21.1097
= 2 tens + 1 ones + 1 tenths + 0 hundredths + 9 thousandths + 7 ten thousandths
= 20 + 1 + \(\frac{1}{10}\) + \(\frac{0}{100}\) + \(\frac{9}{1000}\) + \(\frac{7}{10000}\)
(iv) 524.1
= 5 hundreds + 2 tens + 4 ones + 1 tenths
= 500 + 20 + 4 + \(\frac{1}{10}\)
(v) 143.011
= 1 hundreds + 4 tens + 3 ones + 0 tenths + 1 hundredths + 1 thousandths
= 100 + 40 + 3 + \(\frac{0}{10}\) + \(\frac{1}{100}\) + \(\frac{1}{1000}\)
(vi) 840.006
= 8 hundreds + 4 tens + 0 ones + 0 tenths + 0 hundredths + 6 thousandths
= 800 + 40 + 0 + \(\frac{0}{10}\) + \(\frac{0}{100}\) + \(\frac{6}{1000}\)
(vii) 64.21
= 6 tens + 4 ones + 2 tenths + 1 hundredths
= 60 + 4 + \(\frac{2}{10}\) + \(\frac{1}{100}\)
(viii) 4334.334
= 4 thousands + 3 hundreds + 3 tens + 4 ones + 3 tenths + 3 hundredths + 4 thousandths
= 4000 + 300 + 30 + 4 + \(\frac{3}{10}\) + \(\frac{3}{100}\) + \(\frac{4}{1000}\)
2. Write as decimal fractions:
(i) 8 thousands + 8 ones + 3 tenths + 9 hundredths
= 8008.39
(ii) 4000 + 7 + \(\frac{5}{10}\) + \(\frac{6}{100}\)
= 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 + \(\frac{9}{100}\)
= 451.09
(vi) 800 + 70 + 2 + \(\frac{8}{10}\) + \(\frac{5}{1000}\)
= 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.
Expanded form of Decimals:
This is a form in which we add the place value of each digit forming the number.
Practice Problems on Expanded Form of Decimal Fractions:
I. Write each of the following decimals in expanded form:
(i) 38.54
(ii) 83.107
(iii) 627.074
Solution:
(i) 38.54 = 38 + \(\frac{5}{10}\) + \(\frac{4}{100}\) = 30 + 8 + 0.5 + 0.04
(ii) 83.107 = 83 + \(\frac{1}{10}\) + \(\frac{0}{100}\) + \(\frac{7}{1000}\)
= 80 + 3 + 0.1 + 0 + 0.007
= 80 + 3 + 0.1 + 0.007
(ii) 627.074 = 627 + \(\frac{0}{10}\) + \(\frac{7}{100}\) + \(\frac{4}{1000}\)
= 600 + 20 + 7 + 0 + 0.07 + 0.004
= 600 + 20 + 7 + 0.07 + 0.004
II. Write following in short form:
(i) 9 + \(\frac{3}{10}\) + \(\frac{4}{100}\)
(ii) 50 + 7 + \(\frac{6}{10}\) + \(\frac{2}{100}\) + \(\frac{4}{1000}\)
(iii) 100 + 4 + \(\frac{3}{10}\) + \(\frac{6}{1000}\)
Solution:
(i) 9 + \(\frac{3}{10}\) + \(\frac{4}{100}\) = 9.34
(β
±) 50 + 7 + \(\frac{6}{10}\) + \(\frac{2}{100}\) + \(\frac{4}{1000}\) = 57.624
(iii) 100 + 4 + \(\frac{3}{10}\) + \(\frac{6}{1000}\) = 104.306
III. 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 + \(\frac{7}{100}\)
IV. 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
V. 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) 5080.202
VI. Write the following decimals in expanded form:
(i) 31.5
(ii) 37.53
(iii) 307.85
(iv) 752.34
(Ξ½) 882.146
(vi) 41.005
(vii) 345.083
(viii) 435.202
Answer:
VI. (i) 31.5 = 31 + 05
(ii) 37.53 = 30 + 7 + 0.5 + 0.03
(iii) 307.85 = 300 + 7 + 0.8 + 0.05
(iv) 752.34 = 700 + 50 + 2 + 0.3 + 0.04
(Ξ½) 882.146 = 800 + 80 + 2 + 0.1 + 0.04 + 0.006
(vi) 41.005 = 40 + 1 + 0.005
(vii) 345.083 = 300 + 40 + 5 + 0.08 + 0.003
(viii) 435.202 = 400 + 30 + 5 + 0.2 + 0.002
2. Write each of the following in decimal form:
(i) 9 + 4/10 + 6/100 + 2/1000
(ii) 600 + 40 + 5/1000
(iii) 300 + 3 + 5/10 + 2/1000
(iv) 700 + 40 + 7 + 2/100 + 3/1000
Answer:
2. (i) 9.462
(ii) 640.005
(iii) 303. 502
(iv) 747.023
3. Fill in the boxes with correct numbers:
(i) 84.29 = 80 + π² + \(\frac{2}{10}\)+ \(\frac{9}{π²}\)
(ii) 35.265= 30 + 5 + \(\frac{π²}{10}\) + \(\frac{6}{100}\) + \(\frac{5}{π²}\)
(iii) 5672.053= 5000 + 600 + π² + π² + \(\frac{5}{π²}\) + \(\frac{3}{π²}\)
Answer:
3. (i) 84.29 = 80 + 4 + \(\frac{2}{10}\) + \(\frac{9}{\mathbf{{\color{Red}100}}}\)
(ii) 35.265= 30 + 5 + \(\frac{\mathbf{{\color{Red}2}}}{10}\) + \(\frac{6}{100}\) + \(\frac{5}{\mathbf{{\color{Red}1000}}}\)
(iii) 5672.053= 5000 + 600 + 70 + 2 + \(\frac{5}{\mathbf{{\color{Red}100}}}\) + \(\frac{3}{\mathbf{{\color{Red}1000}}}\)
You might like these
Ordering Decimals | Comparing Decimals | Ascending & Descending Order
In ordering decimals we will learn how to compare two or more decimals. (i) Convert each of them as like decimals. (ii) Compare these decimals just as we compare two whole numbers ignoring
Worksheet on Decimal Numbers | Decimals Number Concepts | Answers
Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.
Worksheet on Word Problems on Addition and Subtraction of Decimals
Practice the questions given in the worksheet on word problems on addition and subtraction of decimals. Read the questions carefully to add or subtract the decimals as required.
Word Problems on Decimals | Decimal Word Problems | Decimal Home Work
Word problems on decimals are solved here step by step. The product of two numbers is 42.63. If one number is 2.1, find the other. Solution: Product of two numbers = 42.63 One number = 2.1
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
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
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.
Conversion of Unlike Decimals to Like Decimals |Examples of Conversion
In conversion of unlike decimals to like decimals follow the steps of the method. Step I: Find the decimal number having the maximum number of decimal places, say (n). Step II: Now, convert each
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
Like and Unlike Decimals | Concept of Like and Unlike Decimals | Defin
Concept of like and unlike decimals: Decimals having the same number of decimal places are called like decimals i.e. decimals having the same number of digits on the right of the decimal
Converting Fractions to Decimals | Solved Examples | Free Worksheet
In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps:
Converting Decimals to Fractions | Solved Examples | Free Worksheet
In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from the given decimal and take as numerator.
Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths
Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.
Thousandths Place in Decimals | Decimal Place Value | Decimal Numbers
When we write a decimal number with three places, we are representing the thousandths place. Each part in the given figure represents one-thousandth of the whole. It is written as 1/1000. In the decimal form it is written as 0.001. It is read as zero point zero zero one
Hundredths Place in Decimals | Decimal Place Value | Decimal Number
When we write a decimal number with two places, we are representing the hundredths place. Let us take plane sheet which represents one whole. Now, we divide the sheet into 100 equal parts. Each part represents one-hundredths of the whole. It is written as \(\frac{1}{100}\).
β Decimal.
Expanded form of Decimal Fractions.
Changing Unlike to Like Decimal Fractions.
Comparison of Decimal Fractions.
Conversion of a Decimal Fraction into a Fractional Number.
Conversion of Fractions to Decimals Numbers.
Addition of Decimal Fractions.
Problems on Addition of Decimal Fractions
Subtraction of Decimal Fractions.
Problems on Subtraction of Decimal Fractions
Multiplication of a Decimal Numbers.
Multiplication of a Decimal by a Decimal.
Properties of Multiplication of Decimal Numbers.
Problems on Multiplication of Decimal Fractions
Division of a Decimal by a Whole Number.
Division of Decimal Fractions by Multiples.
Division of a Decimal by a Decimal.
Division of a whole number by a Decimal.
Properties of Division of Decimal Numbers
Problems on Division of Decimal Fractions
Conversion of fraction to Decimal Fraction.
From Expanded form of Decimal Fractions to HOME PAGE
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.
Recent Articles
-
5th Grade Highest Common Factor | HCF | GCD|Prime Factorization Method
Mar 24, 25 03:40 PM
The highest common factor (H.C.F.) of two or more numbers is the highest or greatest common number or divisor which divides each given number exactly. Hence, it is also called Greatest Common Divisor… -
5th Grade Factors and Multiples | Definitions | Solved Examples | Math
Mar 23, 25 02:39 PM
Here we will discuss how factors and multiples are related to each other in math. A factor of a number is a divisor which divides the dividend exactly. A factor of a number which is a prime number is… -
Adding 2-Digit Numbers | Add Two Two-Digit Numbers without Carrying
Mar 23, 25 12:43 PM
Here we will learn adding 2-digit numbers without regrouping and start working with easy numbers to get acquainted with the addition of two numbers. -
Worksheet on 12 Times Table | Printable Multiplication Table | Video
Mar 23, 25 10:28 AM
Worksheet on 12 times table can be printed out. Homeschoolers can also use these multiplication table sheets to practice at home. -
Vertical Subtraction | Examples | Word Problems| Video |Column Method
Mar 22, 25 05:20 PM
Vertical subtraction of 1-digit number are done by arranging the numbers column wise i.e., one number under the other number. How to subtract 1-digit number vertically?
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.