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

Question 1

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

A) $7$ tens

B) $7$ tenths

C) $7$ hundredths

D) $7$ thousandths

Answer

Correct Answer: C

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) $13.664$

B) $13.764$

C) $1.3764$

D) $137.64$

Answer

Correct Answer: B

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

Question 3

3. Express $85$ mm in kilometers using decimals.

A) $0.000085$ km

B) $0.00085$ km

C) $0.0085$ km

D) $0.85$ km

Answer

Correct Answer: A

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

Question 4

Question 5

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

A) $0.84$

B) $0.084$

C) $0.0084$

D) $8.4$

Answer

Correct Answer: B

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) $3.1$

B) $310$

C) $31$

D) $0.31$

Answer

Correct Answer: C

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) $0.099$

B) $0.1$

C) $0.0875$

D) $0.0099$

Answer

Correct Answer: B

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. m

B) $1050$ sq. m

C) $10.5$ sq. m

D) $105$ sq. m

Answer

Correct Answer: D

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) ₹ $82.75$

B) ₹ $82.25$

C) ₹ $331.00$

D) ₹ $83.75$

Answer

Correct Answer: A

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: C

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: D

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

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