Introduction
Decimals are numbers that fall between integers on a number line. In mathematics, they are just another method to express fractions. We may write more accurate values of quantifiable things such as length, weight, distance, money, and so on using decimals.
Define Decimals
Decimals is the exact value of the fraction which contains both whole numbers as well as fraction parts in them. The decimal number can be identified by the “.” Or a decimal sign in between the digits in the number. The numbers towards the left of the decimal sign are integers or whole numbers, while the numbers to the right are decimal fractions. . If we proceed directly from one place, the following place will be ( \[\frac{1}{{10}}\] ) times smaller, resulting in a ( \[\frac{1}{{10}}\] )th or tenth place value. Take a look at the decimal place value chart for the number 12.45, for example.
Place Value Chart Of Decimal Number
Addition And Subtraction Of Decimals
The standard addition and subtraction rules apply when adding and subtracting decimals. The only details to consider are the decimal places following the decimal point. The numbers must be put in columns based on where they fall before and after the decimal point. According to the decimal place value chart, place values before the decimal point begin with ones, tens, hundreds, and so on, but place values following the decimal point begin with tenths, followed by hundredths, and so on.
Example Of Addition Word Problems Of Decimals
Sample problem: you brought two erasers of 2.25 and 3.89 bucks each. How much money did you spend on the erasers?
Ans:
Step one: write the decimal number under their columns of their own place values.
Step two: add the digits present in the same column.
Money spent on first eraser = 2.25
Money spent on second eraser= 3.89
Total money spent on the erasers = 6.14
Example Of Subtraction Of Decimal Number
Sample problem: Ritu had 500 gm of flour with her. She used 250.78gm of flour to bake a cake. How much flour is left with her?
Ans:
Step one: write the digits in their place value columns.
Step two: Subtract the digits placed in the same column.
Total amount of flour = 500gm
Amount of flour used for baking cake = 250.78gm
Amount of flour left= 249.22gm
Conclusion
Decimals can be added, subtracted, multiplied and divided. Putting a zero after the decimal digits has no effect on the value of a decimal. For instance, 5 can be written as 5.00. Despite the fact that the time and angle measurements are in decimal format, those cannot be subtracted or added together as decimals.
Decimal Word Problems With Solutions
1. Kavita travelled 267.97km and Sheena travelled 862.73km using their own cars. Who travelled the most and by how much?
a. 590.74, Kavita
b. 594.76, Sheena
c. 549.67, Sheena
d. 509.47, Kavita
Ans: 594.76, Sheena
Explanation: the approximate distance covered by Kavita is 200km and Sheena is 800km. As the distance travelled by Sheena is the longest so we will subtract 862.73 from 267.97 which will give us the answer as 594.76.
2. Annie spent 29.89 bucks on fruits and 62.45 bucks on vegetables. How much money did she spend in total?
a. 92.34
b. 92.35
c. 93.72
d. 90.45
Ans: 92.34
Explanation: the amount of money spent on vegetables and fruits can be calculated by adding the amount spent on each item. So, the digits would be placed in their columns and would be added together to get the result.
3. The cost of mangoes is 85.345 and the cost of apples is two times that of mangoes then what is the cost of apples?
a. 170.69
b. 170.89
c. 170.79
d. 170.99
Ans: 170.69
Explanation: in this question, we need to do multiplication to find the original cost of the apples. For that, you need to multiply 85.345 by 2.
FAQs on Word Problems On Decimals
1. What are decimals and why are they important for solving real-world word problems?
Decimals represent parts of a whole number, just like fractions. They are crucial for real-world problems because they allow us to work with precise quantities that are not whole numbers. For example, they are used for:
- Money: Calculating costs like ₹125.50
- Measurements: Expressing weight like 2.5 kg or distance like 3.7 km
- Scores: Recording scores or times in sports, like a 9.8-second sprint
2. What is the first step to take when you read a word problem with decimals?
The first and most important step is to read the entire problem carefully to understand the situation. Before calculating, you must:
- Identify the key information given (the numbers).
- Determine what the question is asking you to find.
- Look for keywords that suggest the correct mathematical operation, such as 'total' or 'altogether' for addition, 'how much is left' for subtraction, or 'cost of each' for division.
3. How do you solve a word problem that requires adding decimals?
To solve an addition word problem with decimals, you must line up the numbers vertically, ensuring the decimal points are aligned. Add each column from right to left, just like with whole numbers. Place the decimal point in your answer directly below the decimal points in the numbers you added. For example, if you buy items for ₹20.25 and ₹15.50, you align the decimal points to get a total of ₹35.75.
4. What is a common mistake when subtracting decimals in word problems and how can it be avoided?
A common mistake is forgetting to align the decimal points, especially when the numbers have a different number of decimal places. To avoid this, always write the numbers with their decimal points lined up. If one number has fewer decimal places, you can add placeholder zeros to the right. For example, to subtract 5.25 from 10, you should write it as 10.00 - 5.25 to ensure correct alignment and borrowing.
5. How do you approach a word problem involving the multiplication of a decimal by a whole number?
First, ignore the decimal point and multiply the numbers as if they were both whole numbers. After you get the product, count the number of decimal places in the original decimal number. Finally, place the decimal point in your answer so that it has the same number of decimal places you counted. For instance, to find the cost of 3 pens at ₹10.50 each, you multiply 1050 by 3 to get 3150, then place the decimal two places from the right to get ₹31.50.
6. Why is aligning the decimal points so crucial when adding or subtracting decimals?
Aligning decimal points is crucial because it ensures that you are combining digits with the same place value. The decimal point separates the whole number part from the fractional part. By aligning them, you make sure you are adding tenths to tenths, hundredths to hundredths, and so on. Misaligning them is like incorrectly adding tens to ones, which would give a fundamentally wrong answer.
7. How are word problems involving money different from those involving measurements like length or weight?
The main difference lies in the context and standard conventions for rounding.
- Money Problems: Answers are almost always expressed with exactly two decimal places to represent currency (e.g., ₹50.75). You might need to round your answer to the nearest hundredth.
- Measurement Problems: The required precision can vary. A problem might involve weight to three decimal places (e.g., 2.125 kg) or length to one (e.g., 4.5 m). The context of the problem dictates how many decimal places are significant.
8. How do you determine the correct operation (addition, subtraction, multiplication, or division) in a decimal word problem?
You can determine the operation by looking for specific keywords and understanding the scenario:
- Addition: Look for 'total', 'sum', 'altogether', 'in all'.
- Subtraction: Look for 'difference', 'how much more', 'left', 'remaining'.
- Multiplication: Look for 'of', 'product', or when finding the total value for multiple items of the same price.
- Division: Look for 'each', 'per', 'average', or when sharing/distributing a quantity equally.
