Table of Content

• What are Decimals?
• Decimal Simplification Tricks
• Decimals Simplification Rules
• Solved Examples on Simplification of Decimals

VBODMAS Rule	Description
V	V means vinculum.
B	B means brackets.
O	O means of.
D	D means division.
M	M means multiplication.
A	A means addition.
S	S means subtraction.

Methods to Simplify Decimals

Some of the common methods related to decimal simplification are:

• Converting Decimals to Fractions
• Rounding Decimals
• Truncating Decimals

Converting Decimals to Fractions

• Step 1: Write the decimal as a fraction with the appropriate power of 10 in the denominator.
• Step 2: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Example: Convert 0.75 into fraction and simplify.

Solution:

0.75 → 75/100​

Find the GCD of 75 and 100, which is 25.

Simplify: (75 ÷ 25)/(100 ÷ 25) = 3/4​

Rounding Decimals

Another method to simplify the decimals is rounding decimals, which can be performed using the following steps:

• Step 1: Identify the place value to which you want to round (e.g., tenths, hundredths).
• Step 2: Look at the digit immediately to the right of your rounding place.
• Step 3: If that digit is 5 or greater, round up. If it is less than 5, round down.

Example: Round 3.14159 to the nearest hundredth.

Solution:

Look at the thousandth place (1 in this case).

Since 1 is less than 5, round down: 3.14159 ≈ 3.14.

Truncating Decimals

• Step 1: Decide on the number of decimal places to keep.
• Step 2: Simply cut off the decimal after the desired place without rounding.

Example: Truncate 3.14159 to three decimal places.

Solution:

The truncated value is 3.141.

Decimal Simplification Tricks

The steps to simplify the decimals are given below.

• Arrange all like terms and solve them.
• Apply BODMAS rule.
• If required, convert decimals into fractions and solve them.
• Convert the fraction obtained again into decimals to get the simplification of decimals.

Conclusion

From the above discussion we can conclude that decimals can be simplified by converting it to fractions and the expressions of decimals can be simplified by the VBODMAS rule. In the given decimal expression, we apply VBODMAS rule and solve it to get the simplified form.

Read More,

• Arithmetic Operations
• What is Arithmetic?
• Hex to Decimal Converter
• Number System

Solved Examples on Simplification of Decimals

Example 1: Simplify the decimal expressions: 5.91 + 2.02 – 3.6

Solution:

Let x = 5.91 + 2.02 – 3.6 [Applying BODMAS rule]

x = 7.93 – 3.6

x = 4.33

Example 2: Solve: 7.5 × 10 + 5.3 – 1.5 ÷ 3

Solution:

Let p = 7.5 × 10 + 5.3 – 1.5 ÷ 3

Applying BODMAS rule

p = 75 + 5.3 – 1.5 ÷ 3

p = 75 + 5.3 – 0.5

p = 69.7 – 0.5

p = 69.2

Example 3: Simplify x = 10.2 ÷ 3 + 1.7

Solution:

x = 10.2 ÷ 3 + 1.7 [Applying BODMAS rule]

x = 3.4 + 1.7

x = 5.1

Example 4: Solve 4.36 × 1.1 + 3.5 – 9 ÷ 4

Solution:

Let y = 4.36 × 1.1 + 3.5 – 9 ÷ 4

Applying BODMAS rule

y = 4.796 + 3.5 – 9 ÷ 4

y = 4.796 + 3.5 – 2.25

y = 8.296 – 2.25

y = 6.046

Example 5: Solve (6.2 – 4.3) × 2.1 + (9.3 ÷ 3.1)

Solution:

Let a = (6.2 – 4.3) × 2.1 + (9.3 ÷ 3.1)

Applying BODMAS rule

a = 1.9 × 2.1 + 3

a = 3.99 + 3

a = 6.99

Practice Questions on Simplification of Decimals

Q1: Simplify 2.59 + 3.2 – 8.65

Q2: Solve 1.26 × 3.2 + 1.87 – 2.1

Q3: Simplify 8.3 ÷ (4.1 × 6.3) + 2.1 – 1

Q4: Solve (2.5 + 3) ÷ 5.1 + 1.2 – 1.8

Q5: Simplify 4.5 ÷ 3 × (1.2 – 0.36) + 4

FAQs on Simplification of Decimals

How to Simplify Decimal Numbers?

To simplify the decimals by converting it to its fraction form.

Can a Decimal be Simplified?

Decimals can be simplified using two methods i.e., either by converting it to fractions or by rounding it to specific decimal places.

How to Simplify Expressions with Decimals?

To simplify expressions with decimals, we use the BODMAS rule.