In this post we will learn the concept of expansion of numbers with decimals.
After learning the concept we will move to solve questions related to this chapter.
In order to understand the concept of number expansion you should have clear idea of place values of numbers.
Expanded form Math
In number expansion we basically show that any given number is made of sum of individual digits.
In order to expand any given number, we do following steps:
(a) Find the Place value of individual digits of number
(b) Multiply the digits with its factor place value
(c) Adding all the digits to form the number
Let us understand the above steps with the help of example.
First let us start with the simple whole number.
Example 01
write number 1279 in expanded form
Solution
Do the following steps for number expansion
(a) Find Place value of all given numbers
Here we will take help of Place Value chart
From the above table you can note that:
1 ⟹ is in Thousand Place
2 ⟹ is in Hundred Place
7 ⟹ is in Tens Place
9 ⟹ is in Ones Place
(b) Multiply each digit with place value
⟹ 1 x 1000 = 1000
⟹ 2 x 100 = 200
⟹ 7 x 10 = 70
⟹ 9 x 1 = 9
(c) Add all the individual digits
1279 ⟹1000 + 200 + 70 + 9
Hence the expanded form of 1279 is ⟹ 1000 + 200 + 70 + 9
I hope the concept of number expansion is clear till now.
Let us now introduce decimal numbers for number expansion.
Example 02
Write number 32.587 in expanded form
Solution
Follow the below steps
Steps 01
Write the place value of all the individual digits
Below is the place value chart for identification of place value
From the above table we can note that
3 ⟹ is in Tens Place
2 ⟹ is in Ones Place
. ⟹ is decimal point
5 ⟹ is in tenth place
8 ⟹ is in Hundredth Place
7 ⟹ is in Thousandth Place
Step 02
Multiply the digits with place value
⟹ 3 x 10 = 30
⟹ 2 x 1 = 2
⟹ 5 x \frac{1}{10} = \frac{5}{10}\\\ \\
⟹ 8 x \frac{1}{100} = \frac{8}{100} \\\ \\
⟹ 7 x \frac{1}{1000} = \frac{7}{1000} \\\ \\
Step 03
Add all the individual digits
32.587 ⟹ 30 + 2 + \frac{5}{10} + \frac{8}{100} + \frac{7}{1000}\\\ \\
Example 03
Write number 4001.205 in expanded form
Follow the below steps
Step 01
Find the place value of all the digits
We will take the help of Place Value chart
From the above chart, we note that:
4 ⟹ is in Thousands Place
0 ⟹ is in Hundreds Place
0 ⟹ is in Tens Place
1 ⟹ is in Ones Place
. ⟹ is decimal point
2 ⟹ is in tenth place
0 ⟹ is in Hundredth Place
5 ⟹ is in Thousandth Place
Step 02
Multiply the digits with the place values
⟹ 4 x 1000 = 4000
⟹ 0 x 100 = 0
⟹ 0 x 10 = 0
⟹ 1 x 1 = 1
⟹ 2 x \frac{1}{10} = \frac{2}{10}
⟹ 0 x \frac{1}{100} = \frac{0}{100} = 0
⟹ 5 x \frac{1}{1000} = \frac{5}{1000}
Step 03
Add all the individual digits
4001.205 = 4000 + 0 + 0 + 1 + \frac{2}{10} + 0 + \frac{5}{1000}
I hope the concept of number expansion is clear till now.
Let’s move on to solve some practice exercise
Number Expansion Worksheet
In this section we will solve questions related to number expansion of decimal numbers.
All questions are to the standard of Grade 5.
Each questions are provided with detailed solution
Write the numbers in Expanded form
Here decimal numbers are provided in each question.
You have to present the numbers in expanded form.
(a) 7833.39
Find Place Value of Individual digits
From the table you can see that
7 ⟹ is in Thousands Place
8 ⟹ is in Hundreds Place
3 ⟹ is in Tens Place
3 ⟹ is in Ones Place
. ⟹ is decimal point
3 ⟹ is in tenth place
9 ⟹ is in Hundredth Place
5 ⟹ is in Thousandth Place
So the expanded form of number can be written as:
⟹ 7 Thousands + 8 hundred + 3 Tens + 3 Ones + 3 Tenths + 9 Hundredths + 5 Thousandth
⟹ 7000 + 800 + 30 + 3 + (3/10) + (9/100) + (5/1000)
(b) 653.7
Read Solution
The expanded for of 653.7 can be written as:
⟹ 6 hundred + 5 Tens + 3 Ones + 7 Tenth
⟹ 600 + 50 + 3 + (7/10)
(c) 3.602
Read Solution
The number 3.602 can be expanded as
⟹ 3 ones + 6 Tenth + 0 hundredth + 2 Thousandth
⟹ 3 + (6/10) + (0/100) + (2/1000)
⟹ 3 + (6/10) + (2/1000)
(d) 42.71
Read Solution
The number 42.71 can be expressed as:
⟹ 4 Tens + 2 ones + 7 Tenth + 1 hundredth
⟹ 40 + 2 + (7/10) + (1/100)
(e) 1025.253
Read Solution
The number 42.71 can be expressed as:
⟹ 1 Thousands + 0 Hundreds+ 2 Tens + 5 ones + 2 Tenth + 5 hundredth + 1 Thousandth
⟹ 1000 + 0 + 20 + 5 + (2/10) + (5/100) + (1/1000)
(f) 374.69
Read Solution
The number 374.69 can be expressed as:
⟹ 3 Hundreds+ 7 Tens + 4 ones + 6 Tenth + 9 hundredth
⟹ 300 + 70 + 4 + (6/10) + (9/100)
(g) 1.735
Read Solution
The number 1.735 can be expressed as:
⟹ 1 ones + 7 Tenth + 3 hundredth + 5 Thousandth
⟹ 1 + (7/10) + (3/100) + (1/1000)
(h) 0.2
Read Solution
The number 0.2 can be expressed as:
⟹ 0 ones + 2 Tenth
⟹ 0 + (2/10)
(i) 63.251
Read Solution
The number 63.251 can be expressed as:
⟹ 6 Tens + 3 ones + 2 Tenth + 5 hundredth + 1 Thousandth
⟹ 60 + 3 + (2/10) + (5/100) + (1/1000)
(j) 0.301
Read Solution
The number 0.301 can be expressed as:
⟹ 0 ones + 3 Tenth + 0 hundredth + 1 Thousandth
⟹ 0 + (3/10) + (0/100) + (1/1000)
⟹ (3/10) + (1/1000)
Write the decimals for given expanded numbers
Here expanded numbers are provided in the question.
You have to understand the number and write in decimal form
(1) 7 Hundreds + 4 Tens + 2 Ones + 5 Tenths
(a) 763.2
(b) 845.3
(c) 740.2
(d) 742.5
Read Solution
The expanded numbers can be written as:
⟹ 700 + 40 + 2 + (5/10)
⟹742 + 0.5
⟹ 742.5
Hence 742.5 is the solution
Option (d) is the right answer
(02) 1 Thousands + 1 Tens + 3 Ones + 6 Tenths + 2 Hundredths
(a) 1013.4
(b) 1013.62
(c) 1013.6
(d) 1013.63
⟹ 1000 + 10 + 3 + (6/10) + (2/100)
⟹ 1013 + 0.6 + 0.02
⟹ 1013.62
Option (b) is the right answer
(03) 2 Tens + 4 Ones + 8 Tenths + 6 Hundredths + 9 Thousandth
(a) 24.869
(b) 24.991
(c) 24.842
(d) 24.356
⟹ 20 + 4 + (8/10) + (6/100) + (9/1000)
⟹ 24 + 0.8 + 0.06 + 0.009
⟹ 24.869
Option (a) is the right answer
(04) 1 Hundreds + 5 Tenths + 2 Hundredths
(a) 100.55
(b) 101.55
(c) 101.52
(d) 100.52
⟹ 100 + (5/10) + (2/100)
⟹ 100 + 0.5 + 0.02
⟹ 100.52
Option (d) is the right answer
(05) 2 Hundreds+ 2 Tens + 2 ones + 2 Tenth + 2 hundredth + 2 Thousandth
(a) 333.222
(b) 222.333
(c) 222.222
(d) 222.232
⟹ 200 + 20 + 2 + (2/10) + (2/100) + (2/1000)
⟹ 222 + 0.2 + 0.02 + 0.002
⟹ 222.222
Option (c) is the right answer
(06) 2 Tens + 4 ones + 3 Tenth + 6 Thousandth
(a) 24.306
(b) 24.97
(c) 24.303
(d) 24.31
⟹ 20 + 4 + (3/10) + (6/1000)
⟹ 24 + 0.3 + 0.006
⟹ 24.306
Option (a) is the right answer
(07) 8 thousands + 5 Tens + 2 ones + 3 Tenth + 7 hundredth + 1 Thousandth
(a) 8051.220
(b) 8052.120
(c) 8052.371
(d) 8051.330
⟹ 8000 + 50 + 2 + (3/10) + (7/100) + (1/1000)
⟹ 8052 + 0.3 + 0.07 + 0.001
⟹ 8052.371
Option (c) is the right answer
(08) 1 Tenth + 9 Thousandth
(a) 0.109
(b) 0.207
(c) 0.110
(d) 0.190
⟹ (1/10) + (9/1000)
⟹ 0.1 + 0.009
⟹ 0.109
Option (a) is the right answer
(09) 9 Tens + 9 ones + 6 Tenth + 1 hundredth
(a) 99.66
(b) 99.61
(c) 99.16
(d) 99.69
⟹ 90 + 9 + (6/10) + (1/100)
⟹ 99 + 0.6 + 0.01
⟹ 99.61
Option (b) is the right answer
(10) 4 Tenth + 5 Hundredth + 2 Thousandth
(a) 0.456
(b) 0.472
(c) 0.551
(d) 0.452
⟹ (4/10) + (5/100) + (2/1000)
⟹ 0.4 + 0.05 + 0.002
⟹ 0.452
Option (d) is the right answer