How to Simplify Decimal Numbers Efficiently
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 Made Easy
1. How do you simplify a decimal?
To simplify a decimal, express it in its simplest or most concise form, often converting it to a fraction in lowest terms or rounding it appropriately. For example, 0.75 can be simplified as $\frac{3}{4}$. Simplifying may also involve reducing a repeating or terminating decimal to a fraction with the smallest possible denominator. Vedantu offers live classes on decimal concepts to help students master these skills.
2. How to solve decimal simplification?
To solve decimal simplification problems, follow these steps:
- Identify whether the decimal is repeating, terminating, or non-terminating.
- If required, convert the decimal to a fraction by placing it over the correct power of 10 and then reduce the fraction to the lowest terms. E.g., $0.6 = \frac{6}{10} = \frac{3}{5}$.
- For expressions, combine like terms and perform arithmetic operations as needed.
3. What is 0.99999 to 4 decimal places?
To round 0.99999 to four decimal places, examine the fifth digit (which is 9). Since it is 9, you round the fourth decimal place (also a 9) up by one, resulting in 1.0000. Thus, to 4 decimal places, $0.99999 \approx 1.0000$. Vedantu’s doubt-solving platform covers similar rounding and decimal approximation questions.
4. How to simplify decimal expressions?
To simplify decimal expressions:
- Combine like decimal terms using addition or subtraction.
- Perform operations such as multiplication or division with decimals, making sure to align decimal points correctly.
- Use the order of operations (BODMAS/BIDMAS) where applicable.
For instance, to simplify $0.8 + 0.35$, add: $0.8 + 0.35 = 1.15$. Vedantu provides worksheets and live explanations for mastering these skills.
5. What are some tips for converting decimals to fractions in simplest form?
Tips for converting decimals to fractions:
- Write the decimal over the appropriate power of 10 based on the number of decimal places.
- Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common factor (GCF).
- For repeating decimals, use algebraic methods to set up and solve for the fraction.
6. Why is decimal simplification important in mathematics?
Decimal simplification is important because it helps:
- Make calculations easier and quicker.
- Ensure answers are presented in a clear, concise form.
- Provide accurate results in real-world measurements, finances, and science.
7. How do you round decimals to a specified place value?
To round decimals to a specified place value:
- Identify the digit to be rounded.
- Check the digit immediately to the right.
- If that digit is 5 or greater, increase the rounding digit by one.
- If it is less than 5, leave the rounding digit the same and drop all digits to the right.
8. What is the difference between terminating and non-terminating decimals?
Terminating decimals are decimals that end after a finite number of digits, example: 0.25. Non-terminating decimals continue infinitely and do not end, such as $0.333...$ (repeating) or $\pi$. Vedantu’s conceptual teaching methods clarify these differences through real-life examples and interactive sessions.
9. Can you explain decimal simplification with an example from daily life?
Yes! For instance, if a recipe requires 1.25 liters of water, this decimal can be simplified and expressed as $\frac{5}{4}$ liters. By converting and simplifying decimals, measurements become easier to understand and use. Vedantu teaches students how to apply decimal simplification to practical problems encountered every day.
