Question

When 52416 is divided by 312, the quotient is 168. What will be the quotient when 52.416 is divided by 0.0168

• A. 312
• B. 3120
• C. 3.12
• D. 2

Hint:

To solve decimal division problems quickly:
Count the decimal places:
- $52.416$ has 3 decimal places.
- $0.0168$ has 4 decimal places.
Multiplying both by $10000$ to clear the decimals:
\[ \frac{52.416 \times 10000}{0.0168 \times 10000} = \frac{524160}{168} = \left(\frac{52416}{168}\right) \times 10 = 312 \times 10 = 3120. \]

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This problem uses the relationship between divisor, dividend, and quotient in division.
If $A \div B = C$, then $A \div C = B$.
When dealing with decimals, we can rewrite the numbers as fractions using powers of ten to simplify the division and avoid errors.
Key Formula or Approach:
Given: \[ \frac{52416}{312} = 168 \implies \frac{52416}{168} = 312 \] We need to evaluate the expression: \[ Q = \frac{52.416}{0.0168} \]

Step 2: Detailed Explanation:
Let us convert the decimals in the expression into fractions:
- Write the numerator as a fraction: \[ 52.416 = \frac{52416}{1000} = 52416 \times 10^{-3} \] - Write the denominator as a fraction: \[ 0.0168 = \frac{168}{10000} = 168 \times 10^{-4} \] Substitute these values back into the expression: \[ Q = \frac{52416 \times 10^{-3}}{168 \times 10^{-4}} \] Group the numerical parts and the powers of ten: \[ Q = \left(\frac{52416}{168}\right) \times \left(\frac{10^{-3}}{10^{-4}}\right) \] Substitute $\frac{52416}{168} = 312$ (derived from the given statement): \[ Q = 312 \times 10^{-3 - (-4)} \] \[ Q = 312 \times 10^{-3 + 4} \] \[ Q = 312 \times 10^1 \] \[ Q = 3120 \] Therefore, the quotient is $3120$.

Step 3: Final Answer:
The quotient when 52.416 is divided by 0.0168 is 3120.
Therefore, the correct option is (B).