PEMDAS Rule – Involving Decimals helps you to solve all the decimal operations easily in minutes. Improve your problem-solving skills using PEMDAS Rule while calculating decimal operations. The order of operations is also the same for the calculation of the decimal number using the PEMDAS Rule. The order of operations is Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. Check out different examples and also the order of operation in the below article.
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How to Solve PEMDAS(Order of Operations)?
1. Parenthesis Terms
We have to give the first importance to the parenthesis terms while simplifying an arithmetic expression. For example
0.3 + (0.2 × 0.2).
In the above, expression the parenthesis term is (0.2 × 0.2). By simplifying the term. We will get
0.3 + 0.04.
0.34 (addition).
2. Exponent Terms
After solving the parenthesis terms, we have to give priority to exponent terms in the calculation. For example
0.5 × (0.6 + 0.2) + (0.2)².
First, simplify the parenthesis term. That is
0.5 × 0.8 + (0.2)².
In the above expression, the exponent term is (0.2)². By simplifying the exponent term, we will get
0.5 × 0.8 + 0.04.
0.4 + 0.04 (Multiplication 0.5 × 0.8 = 0.4).
0.44 (addition).
3. Multiplication Terms
While simplifying an arithmetic expression, we need to give the third priority for multiplication terms. For example
0.1 × [(0.2 + 0.5) + (0.8 – 0.4)] + (0.3 + 0.3)².
Simplify the parenthesis terms. That is
0.1×[ 0.7 + 0.4 ] + (0.6)².
0.1×1.1 + (0.6)². (again Parenthesis term simplification).
Next, simplify the Exponent terms. That is
0.1× 1.1 + 0.36.
Now, simplify the Multiplication term 0.1× 1.1. we will get
0.11 + 0.36 = 0.47.
4. Division Simplification.
The next priority while simplification of expression is division terms. For example
0.3 × (0.25 + 0.12) ÷ 0.1 + (0.24)².
First, simplify the parenthesis terms. That is
0.3 × 0.37 ÷ 0.1 + (0.24)².
The second priority for exponent terms. That is
0.3 × 0.37 ÷ 0.1 + 0.0576.
Simplify the Multiplication Terms. That is
0.111 ÷ 0.1 + 0.0576.
Now, Simplify the division terms. We will get
1.11 + 0.0576.
1.1676.
5. Addition Terms Simplification.
The fifth priority while calculating an arithmetic expression is addition terms. For example
0.5 + 0.25 ÷ 0.1 + (0.8)² + (0.2 + 0.6).
Simplify the parenthesis terms. We will get
0.5 + 0.25 ÷ 0.1 + (0.8)² + 0.8.
Exponent terms simplification.
0.5 + 0.25 ÷ 0.1 + 0.64 + 0.8.
Division terms simplification.
0.5 + 2.5 + 0.64 + 0.8.
Now, simplify the additional terms. That is
1.44.
6. Subtraction Terms Simplification.
The last priority while the simplification process is subtraction. For example
0.4 + (0.2)³ × 0.1 ÷ 0.2 – 0.25.
Simplify the exponent terms first. That is
0.4 + 0.008× 0.1 ÷ 0.2 – 0.25.
Multiplication terms simplification.
0.4 + 0.0008 ÷ 0.2 – 0.25.
Simplify the division terms.
0.4 + 0.004 – 0.25.
Addition terms simplification.
0.404 – 0.25.
Subtraction simplification.
0.154.
PEMDAS Rule Involving Decimals Worked Out Problems
1. Simplify the given expressions by using the PEMDAS Rule
(i) 10.5 – 0.5 × 0.25 + (0.5)² + (0.4 + 0.6).
(ii) 12.5 + 0.6 × 0.23 – 0.89 + (1.25 – 0.2).
(iii) 20.25 ÷ 0.5 + 0.26 – 6.45 × (0.3)².
(iv) 50.6 – 25.2 × 0.45 + 0.5 + (0.2 – 0.1)³.
(i) 10.5 – 0.5 × 0.25 + (0.5)² + (0.4 + 0.6).
Solution:
The given expression is 10.5 – 0.5 × 0.25 + (0.5)² + (0.4 + 0.6).
As per the PEMDAS rule, we have to follow the order of operations while simplifying the expression. That is, Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction.
10.5 – 0.5 × 0.25 + (0.5)² + (0.4 + 0.6).
10.5 – 0.5 × 0.25 + (0.5)² + 1.
10.5 – 0.5 × 0.25 + 0.25 + 1.
10.5 –0.125 + 0.25 + 1.
11.75 – 0.125.
11.625.
By simplifying the expression 10.5 – 0.5 × 0.25 + (0.5)² + (0.4 + 0.6), we will get the resultant value as 11.625.
(ii) 12.5 + 0.6 × 0.23 – 0.89 + (1.25 – 0.2).
Solution:
The given expression is 12.5 + 0.6 × 0.23 – 0.89 + (1.25 – 0.2).
As per the PEMDAS rule, we have to follow the order of operations while simplifying the expression. That is Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction.
12.5 + 0.6 × 0.23 – 0.89 + (1.25 – 0.2).
12.5 + 0.6 × 0.23 – 0.89 + 1.05.
12.5 + 0.138 – 0.89 + 1.05.
13.688 – 0.89.
12.798.
By simplifying the expression 12.5 + 0.6 × 0.23 – 0.89 + (1.25 – 0.2)
we will get the resultant value as 12.798.
(iii) 20.25 ÷ 0.5 + 0.26 – 6.45 × (0.3)².
Solution:
The given expression is 20.25 ÷ 0.5 + 0.26 – 6.45 × (0.3)².
As per the PEMDAS rule, we have to follow the order of operations while simplifying the expression. That is, Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction.
20.25 ÷ 0.5 + 0.26 – 6.45 × (0.3)².
20.25 ÷ 0.5 + 0.26 – 6.45 × 0.09.
20.25 ÷ 0.5 + 0.26 – 0.5805.
40.5 + 0.26 – 0.5805.
40.76 – 0.5805.
40.1795.
By simplifying the expression 20.25 ÷ 0.5 + 0.26 – 6.45 × (0.3)²
we will get the resultant value as 40.1795.
(iv) 50.6 – 25.2 × 0.45 + 0.5 + (0.2 – 0.1)³.
Solution:
The given expression is 50.6 – 25.2 × 0.45 + 0.5 + (0.2 – 0.1)³.
As per the PEMDAS rule, we have to follow the order of operations while simplifying the expression. That is, Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction.
50.6 – 25.2 × 0.45 + 0.5 + (0.2 – 0.1)³.
50.6 – 25.2 × 0.45 + 0.5 + (0.1)³.
50.6 – 25.2 × 0.45 + 0.5 + 0.001.
50.6 – 11.34 + 0.5 + 0.001.
51.101 – 11.34.
39.761.
By simplifying the expression 50.6 – 25.2 × 0.45 + 0.5 + (0.2 – 0.1)³ we will get the resultant value as 39.761.