How to Simplify Decimals Step by Step with Examples
Have you ever thought about the use of decimal numbers? Decimal numbers are used to denote the numerical quantity that is not the whole but in fractions. For example, 2.35, 1.2, 5.67, etc. all denote decimal numbers. After reading this article, students will be able to understand the simplification of decimal numbers. This is the most basic and interesting topic of Mathematics used in everyday life. Let us now start with the conceptual clarification of the decimals.
What is Decimal Simplification?
Decimal represents a number with decimal points. Simplifying a decimal point means rewriting the like terms of an expression together and solving them by using the BODMAS rule and some decimal simplification tricks.
Decimal Simplification Tricks
Some of the decimal simplification tricks are given below:
Put all the likes terms together and solve them.
Put in the BODMAS rule.
For convenience, convert the decimal point to a fraction and then solve further.
After the solution, convert the fraction back to the decimal point.
Rules of Decimal Simplification
Simplification of decimal numbers involves a series of rules to be followed:
$V \rightarrow V$ stands for Vinculum.
$B \rightarrow B$ stands for Removing Brackets.
Removal of bracket takes place in the $\operatorname{order}(),\{\},[]$.
$O \rightarrow O$ stands for of.
$D \rightarrow$ D stands for Division.
$\mathrm{M} \rightarrow \mathrm{M}$ stands for Multiplication.
$A \rightarrow$ A stands for Addition.
$\mathrm{S} \rightarrow \mathrm{S}$ stands for Subtraction.
Solved Examples
1. Simplify 17.709 + 9.001 - 10.02.
Ans: Simplification of decimals in the expression is given by the following steps:
Write the given decimal expression
17.709 + 9.001 - 10.02
Put in the BODMAS rule to the given expression
26.710 - 10.02
Solving the expression further, we get,
16.69
Hence, the simplification of the decimal expression is 16.69.
Simplification of Decimal Expression
2. Solve $2.8 \times 10+4.2-2.9+4.5 \div 5$.
Ans: Simplification of decimals in the expression is given by the following steps:
Step 1: Write the given decimal expression.
$2.8 \times 10+4.2-2.9+4.5 \div 5$
Step 2: Put in the BODMAS rule to the given expression.
$=2.8 \times 10+4.2-2.9+0.9$
$=28+4.2-2.9+0.9$
Step 3: Solving the expression further, we get,
$=32.2-2.0$
$=30.2$
Hence, the simplification of decimal numbers is $30.2$.
Practice Problems
1. Simplify 17.79 - 19.01 + 11.02.
Ans: 9.80
2. Simplify the given decimal:
$5+2.4 \div (3.1-0.7)$
Ans: $6$
3. Calculate $\left[\frac{(5.39)^2-(2.91)^2}{(5.39)-(2.91)}\right]$.
Ans: 8.3
Decimal Simplification Worksheets
1) $4.25 \times 1.4+9$
2) $92.7 \div 3 \times 25+0.17$
3) $19+6.14 \times 3.5+6$
4) $81-0.96 \div 12$
5) $7.2 \div 0.08+15.2$
6) $2.4 \times 0.3+36-5.6$
7) $42-3.4 \times 7.5-0.18$
8) $213-2.12 \times 8.5$
9) $1.6 \times 9.3-\mathrm{t} 5$
10) $9.9 \div 3 \times 1.5 \div 13.4$
Summary
Finishing up here with the concept of decimal simplification. It is a basic topic of Maths that has wide applications in everyday life. This article has covered decimal simplification tricks, worksheets and solved examples for better clarification of the concepts. The language used in the above article is very simple and to the point. Some practice problems are given above that need to be solved by the students themselves to master the topic deeply. we hope that you enjoyed reading the article.
FAQs on Decimal Simplification Explained with Methods
1. What is decimal simplification?
Decimal simplification is the process of reducing a decimal number to its simplest or most compact form without changing its value. This usually involves:
- Removing unnecessary trailing zeros (e.g., 5.400 = 5.4)
- Converting decimals to fractions in lowest terms
- Rounding decimals when required
2. How do you simplify a decimal number?
You simplify a decimal number by removing unnecessary zeros or converting it into a simpler equivalent form. Follow these steps:
- Step 1: Check for trailing zeros after the decimal point.
- Step 2: Remove zeros that do not change the value (e.g., 3.700 = 3.7).
- Step 3: If required, convert the decimal to a fraction and reduce it.
3. How do you simplify decimals by removing zeros?
You simplify decimals by removing trailing zeros to the right of the last non-zero digit. Trailing zeros do not change the value of a decimal.
- 4.600 → 4.6
- 0.2500 → 0.25
4. How do you convert a decimal to a simplified fraction?
To convert a decimal to a simplified fraction, write it over a power of 10 and reduce to lowest terms. Follow these steps:
- Step 1: Write the decimal as a fraction over 10, 100, 1000, etc.
- Step 2: Remove the decimal point.
- Step 3: Simplify the fraction.
5. What is the simplest form of a terminating decimal?
The simplest form of a terminating decimal is the decimal written without unnecessary trailing zeros. A terminating decimal is one that ends after a finite number of digits.
- Example: 2.500 = 2.5
- Example: 0.80 = 0.8
6. Can you give an example of decimal simplification?
An example of decimal simplification is reducing 0.400 to 0.4 by removing trailing zeros. Here is another example:
- Given: 1.2500
- Remove trailing zeros → 1.25
7. What is the difference between rounding and simplifying decimals?
The difference is that simplifying decimals removes unnecessary zeros, while rounding changes the value to a nearby number.
- Simplifying: 3.400 → 3.4 (value stays the same)
- Rounding: 3.46 rounded to 1 decimal place → 3.5 (value changes slightly)
8. How do you simplify recurring decimals?
Recurring decimals are simplified by converting them into fractions. For example:
- Let x = 0.333...
- Then 10x = 3.333...
- Subtract: 10x − x = 3
- 9x = 3
- x = 1/3
9. Why is decimal simplification important in maths?
Decimal simplification is important because it makes calculations clearer, faster, and easier to understand. It helps in:
- Reducing complexity in arithmetic operations
- Comparing decimal numbers accurately
- Converting between decimals and fractions
10. What are common mistakes when simplifying decimals?
A common mistake in decimal simplification is removing zeros that affect place value. Avoid these errors:
- Incorrect: 4.05 → 4.5 (wrong, value changes)
- Correct: 4.50 → 4.5
- Forgetting to reduce fractions fully after conversion
