Solved Examples and Worksheet for Operations on Decimals

Q1Find 50 + 0.3 + 0.003 in standard form.
A. 5.033
B. 50.33
C. 50.033
D. 50.303

Step: 1
50 + 0.3 + 0.003
[Original Expression.]
Step: 2
= 50.303
[Add the terms in the expression.]
Step: 3
50.303 is the standard form.
Q2Find the sum of 0.2 and 5.21.
A. 5.23
B. 5.410
C. 5.01
D. 0.721

Step: 1
0.2 + 5.21
[Original values.]
Step: 2

0.20
+ 5.21
--------
5.410
--------

[Line up decimal points and put zeros to make columns even.]

Step: 3
The sum of 0.2 and 5.21 is 5.410
Q3Find the sum of 6.296 and 5.

A. 11.296
B. 11.196
C. 11.096
D. 11.496

Step: 1
6.296 + 5
[Original values.]
Step: 2

6.296
+ 5.000
---------
11.296
---------

[Line up decimal points and put zeros to make columns even.]

Step: 3
The sum of 6.296 and 5 is 11.296
Q4Find the sum of 0.007 and 0.09.

A. 0.097
B. 0.016
C. 0.16
D. 0.10

Step: 1
0.007  +  0.09
[Original values.]
Step: 2
 0.007 + 0.090 [Line up decimal points and put zero to make columns even.] 0.097 [Add.]
Step: 3
The sum of 0.007 and 0.09 is 0.097
Q5Find the difference between 4.6 and 1.4.
A. 6.0
B. 3.2
C. 4.6
D. 7.8

Step: 1
4.6  -  1.4
[Original values.]
Step: 2

4.6
- 1.4
-----
3.2
-----

[Line up decimal points and make columns even.]

[Subtract.]
Step: 3
The difference between 4.6 and 1.4 is 3.2
Q6Find the difference between 9.12 and 5.1.
A. 14.32
B. 4.12
C. 4.02
D. 14.22

Step: 1
9.12  -  5.1
[Original values.]
Step: 2

9.12
- 5.10
-------
4.02
-------
[Line up decimal points and add trailing zeros to make columns even.]

[Subtract.]
Step: 3
The difference between 9.12 and 5.1 is 4.02
Q7Find the difference between 3.96 and 2.73.

A. 6.69
B. 5.19
C. 3.96
D. 1.23

Step: 1
 3.96 - 2.73
[Line up decimal points.]
Step: 2
 3.96 - 2.73 1.23
[Subtract.]
Step: 3
The difference between 3.96 and 2.73 is 1.23.
Q8Find the missing number in the equation 3.6 + 3.4 = ____ + 9.3.
A. -2.3
B. -7
C. 7
D. 2.3

Step: 1
3.6 + 3.4 = ____ + 9.3
[Original equation.]
Step: 2
Let x be the missing number.
Step: 3
3.6 + 3.4 = x + 9.3
[Modified equation.]
Step: 4
7 = x + 9.3
Step: 5
7 - x = x + 9.3 - x
[Subtract x from both sides.]
Step: 6
7 - x = 9.3
[Simplify.]
Step: 7
- x = 9.3 - 7
[Subtract 7 from both sides.]
Step: 8
- x = 2.3
[Simplify.]
Step: 9
x = -2.3
[Multiply by -1 on both sides.]
Step: 10
The missing number is -2.3.
Q9Find the product of 6.333 and 0.6.
A. 6.4232
B. 4.9232
C. 3.7998
D. 3.2768

Step: 1
6.333 × 0.6
[Original expression.]
Step: 2
 6.333 ×  0.6
................
 3.7998

[3 decimal places.]
[1 decimal place.]

[4 decimal places are required. Place the decimal point so that there are 4 decimal places in the product.]
Step: 3
The product of 6.333 and 0.6 is 3.7998
Q10Solve the equation x ÷ 0.5 = 0.37.

A. 0.185
B. 0.205
C. 0.175
D. 0.195

Step: 1
x ÷ 0.5 = 0.37
[Original expression.]
Step: 2
x = 0.37 x 0.5
[Multiply each side with 0.5.]
Step: 3
 0.37 x 0.5 0.185

[2 decimal places.]
[1 decimal place.]

[3 decimal places are required. Insert zeros and place the decimal point so that there are 3 decimal places in the product.]
Step: 4
The value of x is 0.185.
Q11Find the value of p in the expression p ÷ 3.9 = 0.003.

A. 0.1170
B. 1.1700
C. 0.0117
D. 0.0011

Step: 1
p ÷ 3.9 = 0.003
[Original expression.]
Step: 2
p = 0.003 x 3.9
[Multiply each side with 3.9.]
Step: 3
0.003
x   3.9
_______
0027
+ 0009
_______
0.0117
[Three decimal places.]
[1 decimal plcae.]

[Multiply with 9.]
[Multiply with 3.]

[4 decimal places are required. Insert two zeros and place the decimal point so that there are 4 decimal places in the product.]
Step: 4
The value of p is 0.0117
Q12Find the product of 2.4 and 1.5.

A. 3.50
B. 3.60
C. 3.80
D. 3.70

Step: 1
2.4 × 1.5
[Original expression.]
Step: 2
 2.4 × 1.5 3.60

[1 decimal place.]
[1 decimal place.]

[2 decimal places are required.]
Step: 3
The product of 2.4 and 1.5 is 3.60
Q13Find the quotient of 0.8 ÷ 0.08.

A. 0.1
B. 8
C. 0.01
D. 10

Step: 1
Model the decimal 0.8 as below.
Step: 2
Circle groups of 0.08 as below.
Step: 3
There are 10 groups.
Step: 4
So, the quotient is 10.
[0.08 × 10 = 0.8]
Q14Find the quotient of 1.5 ÷ 0.3.

A. 0.3
B. 3
C. 5
D. 0.5

Step: 1
Model the decimal 1.5 as below
Step: 2
Circle groups of 0.3 as below.
Step: 3
There are 5 groups.
Step: 4
So, the quotient is 5.
Q15Find the quotient of 1.35 ÷ 0.05.

A. 27
B. 17
C. 1.07
D. 1.7

Step: 1
Model the decimal 1.35 as shown.
Step: 2
Circle groups of 0.05 as shown.
Step: 3
There are 27 groups.
Step: 4
So, the quotient is 27.