Question

Of the following, which is the closest approximation to \( \displaystyle \frac{(1.5)(19.9)(4.012)}{3.02} \)?

• A. 400
• B. 120
• C. 100
• D. 40
• E. 10

Hint:

In approximation problems, look for opportunities to simplify before multiplying everything out. In the expression \( \frac{30 \times 4}{3} \), dividing 30 by 3 first is much easier than calculating \(120 \div 3\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question asks for an approximation of a calculation involving decimals. The key is to round the numbers to simpler values that make the arithmetic easier to perform without a calculator.
Step 2: Key Formula or Approach:
The approach is to round each number in the expression to the nearest integer or a simple fraction that is close to the original value.
Let's round each term:

1.5 is already a simple number. We can also write it as \( \frac{3}{2} \).
19.9 is very close to 20.
4.012 is very close to 4.
3.02 is very close to 3.
Step 3: Detailed Explanation:
Substitute the rounded values into the expression:
\[ \frac{(1.5)(19.9)(4.012)}{3.02} \approx \frac{(1.5)(20)(4)}{3} \] Now, we perform the calculation. Let's multiply the terms in the numerator first.
\[ (1.5) \times 20 = 30 \] So the expression becomes:
\[ \frac{30 \times 4}{3} \] We can simplify this by dividing 30 by 3 first:
\[ \frac{30}{3} \times 4 = 10 \times 4 = 40 \] The approximated value is 40. This matches option (D).
Step 4: Final Answer:
By rounding the numbers to 1.5, 20, 4, and 3, the expression simplifies to approximately 40.