Multiply 2.7 x 10-4 by 6.3 x 106 and leave your answers in standard form

Question: Multiply 2.7 × 10⁻⁴ by 6.3 × 10⁶ and leave your answer in standard form.

(The question is written as "10-4" and "10 6", which I read as 10⁻⁴ and 10⁶.)

Concept

To multiply numbers in standard form:

1. Multiply the decimal parts together.
2. Add the powers of 10 (using the law aᵐ × aⁿ = aᵐ⁺ⁿ).
3. Make sure the final answer has the form A × 10ⁿ, where 1 ≤ A < 10.

Solution

Step 1: Multiply the decimal parts. 2.7 × 6.3 = 17.01

Check: 2.7 × 6 = 16.2 and 2.7 × 0.3 = 0.81, so 16.2 + 0.81 = 17.01.

Step 2: Add the powers of 10. 10⁻⁴ × 10⁶ = 10⁻⁴⁺⁶ = 10²

Step 3: Combine. 17.01 × 10²

Step 4: Convert to standard form. 17.01 is not between 1 and 10, so write it as 1.701 × 10¹: 1.701 × 10¹ × 10² = 1.701 × 10³

Check: 2.7 × 10⁻⁴ = 0.00027 and 6.3 × 10⁶ = 6,300,000. Their product is 0.00027 × 6,300,000 = 1,701, which equals 1.701 × 10³. ✔

Matching the options

• A. 1.7 × 10³ = 1700, which is not exact.
• B. 1.70 × 10³ = 1700, which is also not exact.
• C. 1.701 × 10³ = 1701, which is correct.
• D. 17.01 × 10³ is not in standard form, since 17.01 is greater than 10.

Tip: In standard form questions, always check that the first number is between 1 and 10. Option D has the right digits but fails this test, and WASSCE often includes this kind of trap. Also, don't round off unless the question asks you to.