Decimal is a numerical representation that uses a dot, which we call a decimal point, to separate the whole number part from its fractional part. The decimal numeral system is used as the standard system that is used to distinguish integer and non-integer numbers. In this series of practice questions, we’ll explore the fundamentals of decimals, including their definition, types, and applications.
Decimal in Maths
What are Decimals?
Decimals are numerical representations that extend our understanding of whole numbers by introducing a fractional component. In the decimal system, numbers are expressed in units, tenths, hundredths, and so forth, with each digit’s position indicating a specific decimal place value. This system allows for precise representation of values lying between two whole numbers, facilitating more accurate measurements and calculations in various fields.
For example, in the decimal 3.14, “3” is the whole number part, and “0.14” is the fractional part.
Types of Decimals
There are three basic types of decimals in maths. These are:
-
Recurring Decimals: Recurring decimals are numbers that have a repeating pattern of one or more digits after the decimal point. The repetition is indicated by a bar placed over the repeating part. For example, the recurring decimal representation of 1/3 is 0.333…, denoted as
- Non-Recurring Decimals: Non-recurring decimals are numbers where the decimal expansion does not repeat. The digits after the decimal point do not form a recurring pattern. An example is 0.274, where the digits 2, 7, and 4 do not repeat in a predictable manner.
- Decimal Fractions: Decimal fractions are numbers that fall between two consecutive integers on the number line and are expressed in decimal form. These numbers have a finite number of digits after the decimal point. For example, in the decimal fraction 0.75, the digits 7 and 5 represent the fractional part, and there is no recurring or infinite pattern.
Practice Questions on Decimals
Q1. What is the result of adding 3.25 and 6.75?
Q2. Subtract 2.8 from 5.6.
Q3. Multiply 0.5 by 7.
Q4. Divide 9.6 by 3.
Q5. Calculate 3/4 of 8.
Q6. John has $25.50. He spends $12.75 on a gift and $6.25 on lunch. How much money does he have left?
Q7. A swimming pool is 10.75 meters long and 5.25 meters wide. What is the perimeter of the pool?
Q8. Samantha has 2.5 liters of juice. She pours 0.75 liters into one glass and 0.5 liters into another glass. How much juice is left?
Q9. A bakery sells cakes for $8.25 each. If Sarah buys 3 cakes, how much does she spend in total?
Q10. A train travels at an average speed of 60.5 kilometers per hour for 4.25 hours. How far does it travel?
Q11. A store offers a discount of 20% on a shirt priced at $35. What is the discounted price of the shirt?
Q12. A rectangle has a length of 8.25 meters and an area of 33 square meters. What is the width of the rectangle?
Q13. A bookshelf has 5 shelves, each 1.5 meters wide. What is the total width of the bookshelf?
Q14. A restaurant bill comes to $45.75. If the tip is 15% of the bill, how much is the tip?
Q15. A DVD player is priced at $99.95. If a customer pays with a $100 bill, how much change does the customer receive?
Decimals Practice Questions with Solution
Question 1: Add 2.5 and 3.75
Solution:
To add 2.5 and 3.75,
Align the decimal points and add the numbers as usual:
2.5
+ 3.75
——
6.25So, 2.5 + 3.75 = 6.25
Question 2: Subtract 1.25 from 5.8
Solution:
To subtract 1.25 from 5.8,
Align the decimal points and subtract the numbers as usual:
5.80
– 1.25
—–
4.55So, 5.8 – 1.25 = 4.55
Question 3: Multiply 0.6 by 4
Solution:
To multiple 0.6 by 4,
Align the decimal points and multiple as shown above:
0.6
× 4
—–
2.4So, 0.6 × 4 = 2.4
Question 4: Multiply 1.5 by 2.5.
Solution:
To multiply 1.5 by 2.5, we multiply as usual:
1.5 × 2.5 = 3.75
So, 1.5 multiplied by 2.5 equals 3.75.
Question 5: Divide 4.5 by 1.5.
Solution:
To divide 4.5 by 1.5, we divide as usual:
4.5 ÷ 1.5 = 3
So, 4.5 divided by 1.5 equals 3.
Question 6: Calculate 2/5 of 3.2.
Solution:
2/5 × 3.2 = 1.28.
So, 2/5 of 3.2 equals 1.28.
Question 7: Find the average of 1.8, 2.4, and 3.6.
Solution:
To find the average, we add the numbers and divide by the count:
1.8 + 2.4 + 3.6 = 7.8
Dividing 7.8 by 3 (the count of numbers), we get 2.6.
So, the average is 2.6.
Question 8: Convert 0.75 to a fraction.
Solution:
0.75 as a fraction is 3/4.
Question 9: Find 20% of 120.
Solution:
20% of 120 = 0.20 × 120 = 24
So, 20% of 120 is 24.
Question 10: Round 3.267 to the nearest hundredth.
Solution:
3.267 rounded to the nearest hundredth is 3.27.
Question 11: Express 0.125 as a percentage.
Solution:
0.125 as a percentage is
0.125 × 100 = 12.5%
So, 0.125 as a percentage is 12.5%.
Word Problems on Decimals
Problem 1: Sarah bought 3.5 kilograms of apples and 2.75 kilograms of oranges. How many kilograms of fruit did she buy in total?
Solution:
To find the total kilograms of fruit, we add the weights of apples and oranges:
3.5 kg + 2.75 kg = 6.25 kg.
So, Sarah bought 6.25 kilograms of fruit in total.
Problem 2: A car travels at an average speed of 65.5 kilometers per hour for 3.25 hours. How far does it travel?
Solution:
To find the total distance traveled, we multiply the speed by the time:
65.5 km/h × 3.25 h = 212.375 km.
So, the car travels 212.375 kilometers.
Problem 3: Tom has $15.75. He spends $8.50 on a book and $3.25 on snacks. How much money does he have left?
Solution:
To find the remaining money, we subtract the total spent from the initial amount:
$15.75 – ($8.50 + $3.25) = $15.75 – $11.75 = $4.00.
So, Tom has $4.00 left.
Problem 4: A rectangular field measures 12.5 meters in length and 6.75 meters in width. What is the area of the field?
Solution:
To find the area of the field, we multiply the length by the width:
12.5 m × 6.75 m = 84.375 square meters.
So, the area of the field is 84.375 square meters.
Problem 5: During a sale, a store offers a discount of 15% on a TV priced at $450. How much does the TV cost after the discount?
Solution:
To find the discounted price, we calculate 15% of $450 and subtract it from the original price:
15% of $450 = $450 × 0.15 = $67.50.
So, the discounted price is $450 – $67.50 = $382.50.
FAQs on Decimals
What are decimals?
Decimals are a way of expressing parts of a whole or numbers that fall between two whole numbers. They consist of a whole number part and a fractional part separated by a decimal point.
How do you read decimals?
Decimals are read by stating the whole number part, followed by the word “point,” and then reading the fractional part as individual digits. For example, the decimal 3.25 is read as “three point two five.”
What are terminating and recurring decimals?
Terminating decimals are decimals that end after a finite number of digits, while recurring decimals have a repeating pattern of digits after the decimal point.
How do you compare decimals?
Decimals can be compared by looking at the digits to the left of the decimal point first. If they are the same, then compare the digits to the right of the decimal point. Start from the leftmost digit and move to the right until you find digits that are different.
How do you add and subtract decimals?
To add or subtract decimals, align the decimal points and perform the addition or subtraction as you would with whole numbers. Remember to carry over any digits if necessary.
How do you multiply and divide decimals?
To multiply or divide decimals, ignore the decimal points and perform the multiplication or division as you would with whole numbers. Count the total number of digits to the right of the decimal points in the original numbers and place the decimal point in the result accordingly.
What are the applications of decimals?
Decimals are used in various real-life situations such as measurements (length, weight, volume), financial calculations (money, percentages), and scientific calculations. They provide a precise way of representing fractional parts of numbers, making them essential in many fields.