Question 1

1. In the decimal number 405.072, what is the place value of the digit 7?

A) 7 tensB) 7 tenthsC) 7 hundredthsD) 7 thousandths

Answer

✓ Correct Answer: Option C

Explanation: The decimal 405.072 can be expanded as: $$400 + 0 + 5 + \frac{0}{10} + \frac{7}{100} + \frac{2}{1000}$$ The digit 7 is in the second place after the decimal point, which is the hundredths place. Therefore, its value is 7 hundredths or 0.07.

Question 2

2. What is the sum of 12.4, 0.124, and 1.24?

A) 13.664B) 13.764C) 1.3764 137.64

Question 3

3. Express 85 mm in kilometers using decimals.

A) 0.000085 kmB) 0.00085 kmC) 0.0085 kmD) 0.85 km

Answer

✓ Correct Answer: Option A

Explanation: Step 1: Convert mm to cm: $85 mm = \frac{85}{10} = 8.5 cm$ Step 2: Convert cm to m: $8.5 cm = \frac{8.5}{100} = 0.085 m$ Step 3: Convert m to km: $0.085 m = \frac{0.085}{1000} = 0.000085 km$ Alternatively: 1 km = 1,000,000 mm, so $85 mm = \frac{85}{1,000,000} = 0.000085 km$.

Question 4

4. A container holds 4.55 liters of juice. If 1.875 liters are consumed, how much juice is left?

A) 2.685 litersB) 3.675 litersC) 2.625 litersD) 2.675 liters

Answer

✓ Correct Answer: Option D

Explanation: Subtract 1.875 from 4.55 (add a placeholder zero): $4.550 - 1.875 = 2.675$ Thus, 2.675 liters of juice are left.

Question 5

5. What is the result of $0.14 \times 0.6$?

A) 0.84B) 0.084C) 0.0084D) 8.4

Answer

✓ Correct Answer: Option B

Explanation: Step 1: Multiply the whole numbers: $14 \times 6 = 84$. Step 2: Count the total decimal places. 0.14 has 2 places and 0.6 has 1 place. Total = 3 places. Step 3: Place the decimal point in the result to show 3 places: 0.084.

Question 6

6. Solve: $7.75 \div 0.25$

A) 3.1B) 310C) 31D) 0.31

Answer

✓ Correct Answer: Option C

Explanation: To divide by a decimal, move the decimal point in both numbers to make the divisor a whole number: $$7.75 \div 0.25 = \frac{7.75}{0.25} = \frac{775}{25}$$ Dividing 775 by 25: $25 \times 3 = 75$ 77 - 75 = 2, bring down 5 to get 25. $25 \times 1 = 25$. So, $775 \div 25 = 31$.

Question 7

7. Which of the following is the largest?

A) 0.099B) 0.1C) 0.0875D) 0.0099

Answer

✓ Correct Answer: Option B

Explanation: Compare by making the number of decimal places equal: A) 0.0990 B) 0.1000 C) 0.0875 D) 0.0099 Comparing the tenths place: 0.1 has '1' in the tenths place, while others have '0'. Therefore, 0.1 is the largest.

Question 8

8. A rectangular garden is 12.5 m long and 8.4 m wide. Find its area.

A) 10.50 sq. mB) 1050 sq. mC) 10.5 sq. mD) 105 sq. m

Answer

✓ Correct Answer: Option D

Explanation: Area = Length $\times$ Width Area = $12.5 \times 8.4$ $$125 \times 84 = 10500$$ Total decimal places = 1 + 1 = 2. Area = 105.00 = 105 sq. m.

Question 9

9. If 1 kg of apples costs ₹165.50, what is the cost of 0.5 kg?

A) ₹82.75B) ₹82.25C) ₹331.00D) ₹83.75

Answer

✓ Correct Answer: Option A

Explanation: Cost of 0.5 kg = $165.50 \times 0.5$ Since 0.5 is the same as half ($\frac{1}{2}$), we can divide 165.50 by 2: $165.50 \div 2 = 82.75$. The cost is ₹82.75.

Question 10

10. What happens to the decimal point when a number is divided by 1000?

A) It moves 3 places to the right.B) It moves 2 places to the left.C) It moves 3 places to the left.D) It remains at the same position.

Answer

✓ Correct Answer: Option C

Explanation: When dividing by a power of 10, the number becomes smaller. The decimal point moves to the left by the number of zeros in the divisor. Since 1000 has 3 zeros, the point moves 3 places to the left.

Accepted Answer

✓ Correct Answer: Option B

Explanation: Align the decimal points vertically: $\begin{array}{r@{\cdot}l} 12 & 400 \\ 0 & 124 \\ + 1 & 240 \\ \hline 13 & 764 \end{array}$ The sum is 13.764.

Grade 7 : Mathematics (Ganita Prakash) - 3. A Peek Beyond the Point (Set 1)

1. In the decimal number 405.072, what is the place value of the digit 7?

2. What is the sum of 12.4, 0.124, and 1.24?

3. Express 85 mm in kilometers using decimals.

4. A container holds 4.55 liters of juice. If 1.875 liters are consumed, how much juice is left?

5. What is the result of $0.14 \times 0.6$?

6. Solve: $7.75 \div 0.25$

7. Which of the following is the largest?

8. A rectangular garden is 12.5 m long and 8.4 m wide. Find its area.

9. If 1 kg of apples costs ₹165.50, what is the cost of 0.5 kg?

10. What happens to the decimal point when a number is divided by 1000?