In this post we will two different methods to divide decimal numbers.
(a) Long Division Method
(b) Division using Fraction Method
Long Division with decimals
This method can be used when decimal is divided by whole number.
This division involves following steps:
(A) First divide the number before decimal point
(B) Insert the decimal in the quotient and involve digits after decimal.
Let us understand the concept with the help of examples:
Example 01
2.5 divided by 5
Solution
You can observe that:
2.5 (dividend) is a decimal number
5 (divisor) is whole number
Since divisor is whole number, we can use long division method
Long Division Steps
(a) Check division for number before decimal i.e 2
Dividing 2 by 5 results in:
⟹ Quotient = 0
⟹ Remainder = 2
(b) Put decimal in the quotient
(c) Use the next number of dividend (i.e. number 5)
(d) Now divide number 25 by 5
Hence 0.5 is the solution
This method is similar to the whole number division.
Only thing you have to careful is the placing of decimal point in the quotient.
Example 02
Divide 409.4 by 23
Observe that:
Dividend is decimal number (i.e. 409.4)
Divisor is whole number (i.e. 23)
Since Divisor is whole number, we can use long division method
Hence 17.8 is the solution of the division.
Let us understand the division step by step
(a) First divide the number before decimal point (i.e 409)
On dividing 409 by 23 we get:
⟹ 17 as quotient
⟹ 18 as remainder
Its now time to involve number after decimal point.
(b) Do the following Steps
⟹ Put decimal in the quotient
⟹ Involve number after decimal point (i.e. number 4) is the division
Hence, 17.8 is the final solution
Example 03
Divide 1.95 by 13
Notice that:
Divided (1.95) is a decimal number
Divisor (13) is a whole number
Since divisor is a whole number. Its possible to use Long Division Method.
Hence 0.15 is the solution of the division.
Let us understand the division process step by step
(a) First divide the number before decimal point
You can see that we got:
⟹ 0 as a quotient
⟹ 1 as remainder
Now involve the number after decimal point and do the rest of division
(b) Do the following steps
⟹ First put decimal point in the quotient
⟹ Divide rest of the number
From the above division, we found that 0.15 is the solution
Division using Fraction Method
Follow the below steps
Step 01: Write the division in form of fraction
Step 02: Convert decimal into whole number by multiplying with 10, 100, 1000 etc..
Step 03: Divide the whole numbers to get final answer
Let us understand the process with examples
Example 01
18 divided by 0.2
Step 01: Writing in form of fraction
\Longrightarrow \ \frac{18}{0.2}\
Step 02: Convert decimal into whole number
18 ⟹ is already a decimal
0.2 ⟹ decimal with one decimal place value
To convert 0.2 into whole number, we multiply the fraction with 10
(Multiplication of new number is always done both on numerator & denominator)
Step 03: Simply divide the number
From the above division, we found 90 is the solution
Hence, \frac{18}{0.2} \ \Longrightarrow \ 90\
Let us see another example for this method:
Example 02
Divide 9.6 by 0.08
Step 01: Write the division in fraction form
\Longrightarrow \ \frac{9.6}{0.08}\
Step 02: Convert decimals into whole numbers
9.6 ⟹ contains one decimal place value
0.08 ⟹ contains two decimal place value
By Multiplying numerator & denominator by 100, both numbers become whole number
\Longrightarrow \ \frac{9.6\times 100}{0.08\times 100}\\\ \\ \Longrightarrow \ \frac{960}{8}\\\ \\Step 03: Divide the whole numbers
Hence, 120 is the solution of the above division.
i.e. \frac{9.6}{0.08} \ \Longrightarrow \ 120\
Example 03
Divide 5.83 by 0.011
Step 01: Write the division in fraction form
\Longrightarrow \ \frac{5.83}{0.011}\
Step 02: Convert decimals into whole numbers
5.83 ⟹ contains two decimal place value
0.011 ⟹ contains three decimal place value
We multiply numerator and denominator by 1000 so that both numbers become whole numbers
\Longrightarrow \frac{5.83\times 1000}{0.011\times 1000} \\\ \\ \Longrightarrow \ \frac{5830}{11}Step 03: Divide the whole numbers
Hence 530 is the solution of the problem
i.e. \frac{5.83}{0.011} \ \Longrightarrow \ 530\
I hope you have understood both the methods.
It is now time to solve some problems related to division of decimals
Decimal Division Questions
(01) Divide 6.4 by 8
(a) 0.6
(b) 0.8
(c) 0.06
(d) 0.08
⟹ First divide 64 by 8
The equation can be written as :
⟹ Now divide 8 by 10
\Longrightarrow \frac{8}{10} \\\ \\ \Longrightarrow \ 0.8\
Hence 0.8 is the solution
Option (b) is the right answer
(02) Divide 1.2 by 3
(a) 0.08
(b) 0.04
(c) 0.8
(d) 0.4
⟹ First Divide 12 by 3
The equation can be expressed as
⟹ Now divide 4 by 10
\Longrightarrow \frac{4}{10} \\\ \\ \Longrightarrow \ 0.4\
Hence 0.4 is the solution
Option (d) is the right answer
(03) Divide 5.2 by 0.4
(a) 12
(b) 11
(c) 13
(d) 14
On dividing 52 by 4 we get:
Hence 13 is the solution
Option (c) is the right answer
(04) Divide 4.9 by 7
(a) 0.7
(b) 0.8
(c) 0.9
(d) 0.6
Dividing 49 and 7, we get number 7 as quotient
The equation can be written as:
⟹ Now divide 7 by 10
\Longrightarrow \frac{7}{10} \\\ \\ \Longrightarrow \ 0.7\
Hence 0.7 is the solution
Option (a) is the right answer
(05) Divide 2.4 by 0.6
(a) 6
(b) 8
(c) 4
(d) 2
Hence, 4 is the solution of the division
Option (c) is the right answer
(06) Divide 8.64 by 1.8
(a) 4.2
(b) 4.8
(c) 3.6
(d) 3.8
Dividing 864 by 180
Hence, 4.8 is the solution
Option (b) is the right answer
(07) Divide 13.11 by 0.19
(a) 9.6
(b) 6.9
(c) 96
(d) 69
Dividing 1311 by 19, we get:
Hence 69 is the solution
Option (d) is the right answer
(08) Divide 36.75 by 3.5
(a) 10.5
(b) 9.7
(c) 10.8
(d) 9.5
Dividing 3675 by 350, we get:
Hence, 10.5 is the solution
Option (a) is the right answer
(09) Divide 60.2 by 70
(a) 8.6
(b) 0.89
(c) 0.95
(d) 0.86
Dividing 602 by 700 using Long Division Method
0.86 is the solution
Option (d) is the right answer
(10) Divide 3012.54 by 35.4
(a) 85.1
(b) 85.2
(c) 85.3
(d) 85.4
Dividing 301254 by 3540
Hence 85.1 is the solution
option (a) is the right answer