Decimals

1. Define what a decimal is and explain how it relates to fractions.
Answer: A decimal is a way to represent fractions where the denominator is 10, 100, 1000, etc. It uses a point to separate whole and fractional parts.
2. Convert the following fractions to decimals: \( \frac{3}{10}, \frac{7}{100}, \frac{21}{1000} \).
Answer: 0.3, 0.07, 0.021
3. Write 5.4, 0.25, and 13.07 in expanded form.
Answer: 5.4 = 5 + 0.4; 0.25 = 0.2 + 0.05; 13.07 = 10 + 3 + 0.07
4. Place these decimals in ascending order: 3.45, 3.405, 3.5, 3.04.
Answer: 3.04, 3.405, 3.45, 3.5
5. What is the place value of the digit 7 in 45.726?
Answer: The place value of 7 is 0.7 (tenths place).
6. Write the equivalent decimal for:
- 2 rupees 25 paise.
- 7 rupees 4 paise.
Answer: 2.25 and 7.04
7. Explain the relationship between tenths, hundredths, and thousandths.
Answer: Tenths = 1/10, Hundredths = 1/100, Thousandths = 1/1000. Each place is 10 times smaller than the previous one.
8. What happens to the value of a digit when moved one place to the left in a decimal number?
Answer: The value becomes 10 times larger when moved one place to the left.
9. True or False:
- 1.50 and 1.5 are equivalent decimals.
- 2.03 > 2.3.
Answer: True, False
10. What is \( 1000 \) times smaller than \( 1 \) in decimals?
Answer: 0.001
11. Add the following decimals: \( 3.45 + 4.23 + 1.32 \).
Answer: 9.00
12. Subtract \( 17.3 \) from \( 25.7 \).
Answer: 8.4
13. Find the sum of \( 3.08 \), \( 4.7 \), and \( 0.005 \).
Answer: 7.785
14. Subtract \( 9.001 \) from \( 10.5 \).
Answer: 1.499
15. Multiply:
- \( 3.4 \times 10 \), \( 4.07 \times 100 \), \( 0.09 \times 1000 \).
Answer: 34, 407, 90
16. Divide \( 5.6 \) by \( 10 \).
Answer: 0.56
17. Convert \( 1 \frac{2}{5} \) into decimal form.
Answer: 1.4
18. A table is 175 cm long. What is its length in meters?
Answer: 1.75 meters
19. Ramesh saved \( 537.68 \) rupees in March and \( 273.20 \) rupees in April. How much did he save in total?
Answer: 810.88 rupees
20. A milkman sold \( 78.5 \) liters of milk in one colony and \( 32.75 \) liters in another. How much milk did he sell in total?
Answer: 111.25 liters
21. A runner completed \( 8.75 \) km in the first hour and \( 4.5 \) km in the second hour. How much distance did he run in total?
Answer: 13.25 km
22. The weight of a watermelon is \( 5.875 \) kg. If 3 such watermelons are bought, what is their total weight?
Answer: 17.625 kg
23. Convert:
- \( 45 \) cm to meters.
- \( 5 \) kg \( 750 \) g to kilograms.
Answer: 0.45 m; 5.75 kg
24. A bottle contains \( 2.005 \) liters of milk. Express this amount in milliliters.
Answer: 2005 milliliters
25. Write \( 28.52 \) meters in centimeters.
Answer: 2852 cm
26. Convert \( 0.75 \) kg into grams.
Answer: 750 grams
27. The sum of two numbers is \( 35.75 \). One number is \( 12.5 \). Find the other number.
Answer: 23.25
28. A decimal number has two digits after the decimal point. Its digits add up to \( 11 \), and the hundredths place digit is one more than the tenths place. What is the number?
Answer: 5.6
29. Subtract \( 18.926 \) from \( 25.3 \).
Answer: 6.374
30. Arrange the following decimals in descending order: \( 7.77, 7.007, 7.7, 7.77 \).
Answer: 7.77, 7.77, 7.7, 7.007