Decimal Fraction Study Guide for Competitive Exams

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Decimal Fraction

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Decimal Fraction MCQ & Objective Questions

Decimal fractions are a crucial part of mathematics that students encounter in their academic journey. Understanding decimal fractions not only helps in solving mathematical problems but also enhances overall numerical skills. Practicing MCQs and objective questions on decimal fractions is essential for effective exam preparation, as it allows students to familiarize themselves with important questions and improves their chances of scoring better in exams.

What You Will Practise Here

Understanding the definition and representation of decimal fractions
Converting between fractions and decimal fractions
Performing arithmetic operations with decimal fractions
Identifying and comparing decimal fractions
Rounding decimal fractions to a specified number of places
Solving real-life problems involving decimal fractions
Interpreting decimal fractions in graphical representations

Exam Relevance

Decimal fractions are frequently tested in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect questions that require them to convert fractions to decimal form, perform calculations, and apply decimal fractions in word problems. Common question patterns include multiple-choice questions that assess both conceptual understanding and practical application of decimal fractions.

Common Mistakes Students Make

Confusing decimal fractions with whole numbers and improper fractions
Errors in converting fractions to decimal form
Misunderstanding the rules of rounding decimal fractions
Neglecting to align decimal points during addition and subtraction
Overlooking the significance of place value in decimal fractions

FAQs

Question: What are decimal fractions?
Answer: Decimal fractions are fractions where the denominator is a power of ten, and they are expressed using a decimal point.

Question: How can I improve my skills in decimal fractions?
Answer: Regular practice with MCQs and solving objective questions on decimal fractions can significantly enhance your understanding and skills.

Question: Are decimal fractions important for competitive exams?
Answer: Yes, decimal fractions are a key topic in many competitive exams, and mastering them can help you score better.

Start solving Decimal Fraction MCQ questions today to test your understanding and boost your confidence for upcoming exams. Every practice question brings you one step closer to success!

Q. A car travels 120 km in 2 hours. What is its speed in km/h?

A. 50
B. 60
C. 70
D. 80

Solution

Speed = Distance/Time = 120 km / 2 h = 60 km/h

Correct Answer: B — 60

Q. A car travels 60 km in 1 hour. How far will it travel in 0.5 hours?

A. 30 km
B. 20 km
C. 40 km
D. 50 km

Solution

Distance = Speed * Time = 60 * 0.5 = 30 km.

Correct Answer: A — 30 km

Q. A principal of $2500 is invested at a compound interest rate of 3% per annum. What will be the amount after 6 years?

A. $2925.00
B. $3000.00
C. $2800.00
D. $2700.00

Solution

Total Amount = 2500(1 + 0.03)^6 = 2500(1.191016) = 2977.54

Correct Answer: A — $2925.00

Q. A product is sold for $120 after a profit of 20%. What was the cost price?

A. $90
B. $100
C. $110
D. $80

Solution

Let the cost price be x. Then, 120 = x + 0.2x = 1.2x. Therefore, x = 120 / 1.2 = 100.

Correct Answer: A — $90

Q. A shopkeeper bought an article for $80 and sold it for $100. What is the profit percentage?

A. 20%
B. 25%
C. 30%
D. 15%

Solution

Profit = Selling Price - Cost Price = 100 - 80 = 20. Profit Percentage = (20/80) * 100 = 25%.

Correct Answer: B — 25%

Q. A sum of $3000 is invested at a compound interest rate of 7% per annum. What will be the amount after 5 years?

A. $4210.00
B. $4000.00
C. $4500.00
D. $4100.00

Solution

Total Amount = 3000(1 + 0.07)^5 = 3000(1.402552) = 4207.66

Correct Answer: A — $4210.00

Q. A sum of money doubles in 5 years at simple interest. What is the rate of interest?

A. 10%
B. 12%
C. 15%
D. 20%

Solution

If the sum doubles, then the interest earned is equal to the principal. Rate = (Principal/Time) * 100 = (Principal/5) * 100 = 20%

Correct Answer: A — 10%

Q. A sum of money doubles itself in 10 years at compound interest. What is the rate of interest?

A. 7.2%
B. 10%
C. 5%
D. 12%

Solution

Using the Rule of 72, Rate = 72/10 = 7.2%

Correct Answer: A — 7.2%

Q. Convert 0.125 to a fraction.

A. 1/8
B. 1/4
C. 1/2
D. 3/8

Solution

0.125 = 125/1000 = 1/8 after simplification.

Correct Answer: A — 1/8

Q. Convert 0.2 to a fraction.

A. 1/5
B. 1/4
C. 1/2
D. 2/5

Solution

0.2 = 2/10 = 1/5 after simplification.

Correct Answer: A — 1/5

Q. If $1200 is invested at a compound interest rate of 10% per annum, what will be the total amount after 3 years?

A. $1593.00
B. $1500.00
C. $1600.00
D. $1700.00

Solution

Total Amount = 1200(1 + 0.10)^3 = 1200(1.331) = 1597.20

Correct Answer: A — $1593.00

Q. If $1500 is invested at an interest rate of 4% compounded annually, what will be the total amount after 5 years?

A. $1800.00
B. $1820.00
C. $1833.00
D. $1850.00

Solution

Total Amount = P(1 + r/n)^(nt) = 1500(1 + 0.04/1)^(1*5) = 1500(1.2166529) = 1824.98

Correct Answer: C — $1833.00

Q. If 0.2 of a number is 10, what is the number?

A. 40
B. 50
C. 60
D. 70

Solution

Let the number be x. Then, 0.2x = 10. Therefore, x = 10 / 0.2 = 50.

Correct Answer: A — 40

Q. If 0.4 is expressed as a fraction, what is it?

A. 2/5
B. 1/4
C. 3/5
D. 1/2

Solution

0.4 = 4/10 = 2/5 after simplification.

Correct Answer: A — 2/5

Q. If 0.75 of a number is 30, what is the number?

A. 20
B. 25
C. 40
D. 45

Solution

Let the number be x. Then, 0.75x = 30. Therefore, x = 30 / 0.75 = 40.

Correct Answer: B — 25

Q. If a person invests $2000 at a compound interest rate of 5% per annum, what will be the amount after 2 years?

A. $2205
B. $2100
C. $2150
D. $2250

Solution

Amount = Principal * (1 + Rate)^Time = 2000 * (1 + 0.05)^2 = 2000 * 1.1025 = $2205

Correct Answer: A — $2205

Q. If a product costs $120 and is sold at a 15% profit, what is the selling price?

A. $138
B. $130
C. $140
D. $135

Solution

Selling Price = Cost Price + Profit = 120 + (15/100 * 120) = 120 + 18 = 138

Correct Answer: A — $138

Q. If a product costs $120 and is sold for $150, what is the profit percentage?

A. 20%
B. 25%
C. 30%
D. 35%

Solution

Profit = Selling Price - Cost Price = 150 - 120 = 30. Profit Percentage = (30/120) * 100 = 25%

Correct Answer: B — 25%

Q. If a product costs $50 and is sold at a 20% profit, what is the selling price?

A. $60
B. $55
C. $50
D. $65

Solution

Selling Price = Cost Price + Profit = 50 + (20% of 50) = 50 + 10 = $60

Correct Answer: B — $55

Q. If a worker can complete a job in 10 days, how much of the job can he complete in 2.5 days?

A. 1/4
B. 1/2
C. 1/5
D. 1/10

Solution

In 1 day, he completes 1/10 of the job. In 2.5 days, he completes 2.5/10 = 1/4.

Correct Answer: A — 1/4

Q. If a worker can complete a task in 10 hours, how much of the task can he complete in 2.5 hours?

A. 0.2
B. 0.25
C. 0.3
D. 0.5

Solution

In 2.5 hours, the worker completes (2.5/10) = 0.25 of the task.

Correct Answer: B — 0.25

Q. If the price of a shirt is $40 and it is sold at a loss of 10%, what is the selling price?

A. $36
B. $38
C. $40
D. $42

Solution

Selling Price = Cost Price - Loss = 40 - (10% of 40) = 40 - 4 = $36

Correct Answer: A — $36

Q. If you invest $1000 at an interest rate of 8% compounded annually, how much will you have after 2 years?

A. $1166.40
B. $1080.00
C. $1200.00
D. $1150.00

Solution

Total Amount = 1000(1 + 0.08)^2 = 1000(1.1664) = 1166.40

Correct Answer: A — $1166.40

Q. The ratio of boys to girls in a class is 3:2. If there are 30 boys, how many girls are there?

A. 15
B. 20
C. 25
D. 30

Solution

If the ratio is 3:2, then for every 3 boys, there are 2 girls. Therefore, if there are 30 boys, the number of girls = (2/3) * 30 = 20

Correct Answer: B — 20

Q. What is 0.75 as a fraction?

A. 1/2
B. 3/4
C. 2/3
D. 1/4

Solution

0.75 = 75/100 = 3/4 after simplification.

Correct Answer: B — 3/4

Q. What is 0.9 as a fraction?

A. 9/10
B. 1/10
C. 1/5
D. 1/2

Solution

0.9 = 9/10.

Correct Answer: A — 9/10

Q. What is 15% of 0.4?

A. 0.06
B. 0.04
C. 0.05
D. 0.07

Solution

15% of 0.4 = 0.15 * 0.4 = 0.06

Correct Answer: A — 0.06

Q. What is 15% of 0.6?

A. 0.09
B. 0.1
C. 0.08
D. 0.07

Solution

15% of 0.6 = 0.15 * 0.6 = 0.09

Correct Answer: A — 0.09

Q. What is 25% of 0.8?

A. 0.1
B. 0.2
C. 0.25
D. 0.3

Solution

25% of 0.8 = 0.25 * 0.8 = 0.2

Correct Answer: B — 0.2

Q. What is the average of the first five decimal fractions?

A. 0.1
B. 0.2
C. 0.3
D. 0.4

Solution

The first five decimal fractions are 0.1, 0.2, 0.3, 0.4, 0.5. Average = (0.1 + 0.2 + 0.3 + 0.4 + 0.5) / 5 = 0.3.

Correct Answer: B — 0.2

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