Decimals are a fundamental aspect of mathematics, representing parts of a whole or fractional quantities. When dealing with decimals, understanding the concepts of like and unlike decimals is important for accurate computations and comparisons.
Like decimals refer to decimal numbers that have the same number of digits after the decimal point whereas Unlike decimals are decimal numbers that have different numbers of digits after the decimal point.
This article provides a complete description of like and unlike decimals, operations on like and unlike decimals along with some solved examples to enhance the understanding of the concept.
Table of Content
- What are Decimals?
- What are Like and Unlike Decimals?
- Converting Unlike Decimals to Like Decimals
- Examples on Converting Unlike decimal to like decimal
- Operations on Like and Unlike Decimals
- Difference between Like and Unlike Decimals
- Why Convert Unlike Decimals to Like Decimals?
- Applications of Like and Unlike Decimals
- Solved Questions on Unlike and Like Decimals
- Practice Questions on Unlike and Like Decimals
What are Decimals?
Decimals are the type of fractions where the denominator is in the power of ten. A decimal number is a number that has two parts: It is a whole number and a fixed fractional part that is written using a decimal point separating the two parts.
For Example, the decimal is 12.345 Here, the whole number is 12 and the fractional part is 345. in Fractions it will be represented by 12345/1000.
Each position to the right of the decimal point represents a power of ten: tenth, hundredth, thousandth, etc. Decimals are applied in real-life situations such as in financial and engineering backgrounds and general measurements because they are accurate in expressing and calculating such portions.
The decimals are further divided into two types namely:
- Like Decimals
- Unlike Decimals
What are Like and Unlike Decimals?
Like decimals are those that have the same number of digits after the decimal point. This means that the fractional parts of the decimals have the same number of decimal places, making it easier to perform arithmetic operations such as addition, subtraction, and comparison.
Like decimals are decimal numbers that have the same number of digits to the right of the decimal point.
Example: These are some like decimals since all of them contain two digits to the right of the decimal point.
- 1.23,
- 34.56
- 7.89
Unlike decimals are decimal numbers that have a different number of digits to the right of the decimal point. This means that their fractional parts are not the same length.
Unlike decimals are decimal numbers that have different lengths of digits after the decimal point.
Example: These are some unlike decimals since the number of digits to the right of the decimal point in each case is different.
- 1.2
- 4.56
- 7.891
Converting Unlike Decimals to Like Decimals
To convert unlike decimals to like decimals, follow these steps:
Step 1: Compare the given decimal numbers and, as a result, find out which decimal number among them contains the maximum number of decimal fraction digits.
Step 2: For an equilibrium of the number of decimal places, add zeros to the other decimals.
Examples on Converting Unlike decimal to like decimal
Let us consider few examples to enhance our understanding:
1: Convert 1.2, 4.56, and 7.891 to like decimals.
Identify the decimal with the most digits after the decimal point: 7.891 (three digits).
Add zeros to match three decimal places:
1.2 becomes 1.200
4.56 becomes 4.560
7.891 remains 7.891
So, 1.2, 4.56, and 7.891 are converted to 1.200, 4.560, and 7.891.
2: Convert 0.5, 2.34, and 0.789 to like decimals.
Identify the decimal with the most digits after the decimal point: 0.789 (three digits).
Add zeros to match three decimal places:
0.5 becomes 0.500
2.34 becomes 2.340
0.789 remains 0.789
Thus, 0.5, 2.34, and 0.789 are converted to 0.500, 2.340, and 0.789.
Operations on Like and Unlike Decimals
Performing arithmetic operations on decimals is more straightforward when they are like decimals. Here are some examples of different operations:
Addition of Like and Unlike Decimals
In case of Like Decimals, adding like decimals is simple because their decimal points are naturally aligned, which simplifies the process.
For Unlike Decimals, we first convert them to like decimals by adding zeros to match the number of decimal places. This ensures accurate addition by aligning the decimal points, making the sum easier to calculate and more precise.
Below are some examples for better understanding:
1: Add 3.45 and 2.78.
Given, 3.45 and 2.78, they are like decimals, Hence
3.45 + 2.78 = 6.23
2: Add 1.2 and 3.456.
Given, 1.2 and 3.456, they are unlike decimals, hence
Converting them to like decimals, we get
1.200 and 3.456.
Add:
1.200 + 3.456 = 4.656
Subtraction of Like and Unlike Decimals
Subtracting like decimals is simple due to the natural alignment of decimal points, which ensures straightforward and accurate subtraction.
For unlike decimals, convert them to like decimals by adding zeros to align the decimal points. This makes it easier to maintain place value integrity and perform accurate subtraction without confusion.
Below are some examples for better understanding:
1: Subtract 5.67 from 8.23
Given 5.67 and 8.23 are like decimals, hence,
8.23 - 5.67 = 2.56
2: Subtract 2.5 from 6.789.
Given, 2.5 and 6.789, they are unlike decimals, hence
First, Convert them to like decimals: 2.500 and 6.789.
Subtract:
6.789 - 2.500 = 4.289
Multiplication of Like and Unlike Decimals
Multiplying decimals is similar for both like and unlike decimals. Both of them are discussed below:
In like decimals, Multiplication involves counting the total number of decimal places in both numbers, performing the multiplication, and placing the decimal point in the product accordingly.
For unlike decimals, convert them to like decimals by adding zeros if necessary. This ensures the correct alignment of decimal places, simplifying the multiplication process and ensuring an accurate result.
Below are some examples for better understanding:
1: Multiply 1.2 by 3.4.
Given, 1.2 and 3.4
Given numbers are like decimals, with 1 decimal place in each, Hence, there solution will have 2 decimal places.
1.2 × 3.4 = 4.08
2: Multiply 1.25 by 2.3.
Given numbers are unlike, hence
First Convert them to like decimals: 1.25 and 2.30.
Multiply:
1.25 × 2.30 = 2.875
Division of Like and Unlike Decimals
Dividing like decimals is straightforward as their decimal points are aligned, allowing for easy division and correct placement of the decimal point in the quotient. When dividing like decimals, first ignore the decimal points temporarily, perform the division as if they were whole numbers, and then place the decimal point in the result (if needed).
For unlike decimals, convert them to like decimals by adding zeros. This simplifies the division process by ensuring proper alignment of decimal points, resulting in an accurate quotient.
Below are some examples for better understanding:
1: Divide 6.42 by 3.21
Given numbers are like, hence we can directly divide them after removing decimal places
642 ÷ 321 = 2
Hence, 6.42 ÷ 3.21 = 2
2: Divide 7.25 by 0.5.
Given numbers are unlike, hence
First Convert them to like decimals: 7.25 and 0.50.
Divide by removing decimal places
725 ÷ 50 = 14.5
Hence, 7.25 ÷ 0.50 = 14.5
Difference between Like and Unlike Decimals
The key difference between like and unlike decimals is given below:
Criteria | Like Decimals | Unlike Decimals |
|---|---|---|
Number of Decimal Places | Same number of decimal places | Different number of decimal places |
Arithmetic operations | Easier to perform | More complex, may require conversion |
Examples | 1.23, 4.56, 7.89 | 1.2, 4.56, 7.891 |
Ease of comparison | Easier to compare | Harder to compare without conversion |
Alignment in calculations | Naturally Aligned | May require adding zeros for alignment |
Why Convert Unlike Decimals to Like Decimals?
Changing, unlike decimals to like decimals is helpful when it comes to comparing and ordering decimals. Where the decimal has the same number of digits after the decimal point, one ought to conveniently deduce which decimal is the largest or the smallest.
This conversion also makes arithmetic computations like addition, subtraction multiplication and even division a lot easier. For example, adding 2. 5 and 3. 75 becomes quite manageable if and when they are written as 2. 50 and 3.75, ensuring all digits align correctly for the calculation.
Applications of Like and Unlike Decimals
The applications of the Like and Unlike Decimals are as follows:
- Data Analysis: In data analysis, converting to like decimals ensures consistency when calculating averages, standard deviations, and other statistical measures.
- Educational Tools: Helping students establish ideas about like and unlike decimals facilitates their ability and accuracy in decimal arithmetic accurately.
- Engineering Calculations: In engineering, precise decimal calculations are crucial for designing structures, circuits, and systems. Converting to like decimals ensures accurate measurements and calculations.
- Inventory Management: Businesses often deal with quantities and prices in decimal form. Converting to like decimals helps in maintaining accurate inventory records and calculating total costs.
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Solved Questions on Unlike and Like Decimals
1: Compare the following pairs of decimals and state if they are like or unlike:
- 3.45 and 2.56
- 4.7 and 3.123
For, 3.45 and 2.56
Both decimals have 2 digits after the decimal point. Hence, they are like decimals.
For, 4.7 and 3.123
4.7 has 1 digit after the decimal point and 3.123 has 3 digits after the decimal point. Hence, they are unlike decimals.
2: Add 4.56 and 3.7
Given, 4.56 and 3.7
Let us convert them into like decimals hence 3.7 = 3.70
Adding 4.56 and 3.70 we get,
4.56 + 3.70 = 8.26
3: Convert the following pair of unlike decimals to like decimals and then add them:
- 5.6 and 3.789
Given, 5.6 and 3.789
Convert 5.6 to 5.600 (3 decimal places)
Now add 5.600 and 3.789,
5.600 + 3.789 = 9.389
Practice Questions on Unlike and Like Decimals
1. A company's profit and loss statement shows that it made a profit of $12.50 in January and a loss of $8.25 in February. If the company wants to calculate its total profit or loss for the first two months, how can it convert these amounts into like decimals to get a clear picture of its financial situation?
2. A meteorologist is tracking the temperature in a city over several days. On Monday, the temperature was 14.5°C, on Tuesday it was 12.8°C, and on Wednesday it was 15.2°C. Compare these temperatures and also find out the mean temperature of the three days.
3. A person has two bank accounts with different interest rates. Account A has an interest rate of 4.25% and Account B has an interest rate of 3.75%. Compare the interest rate of A and B and tell who has greater interest rate and by how much?
Conclusion
Understanding and converting like and unlike decimals is crucial for simplifying mathematical operations and making accurate comparisons. This knowledge can be useful in business management, accounting, computer science and many other fields because the meaning of numbers and operations performed with numbers must be precisely defined. The students and the professionals will, therefore, be in a position to enhance their mathematical knowledge and increase reliability and correctness in their calculations.