Simplify 0.000215 x 0.000028 and express your answer in standard form

Analyze the question: We need to multiply two very small decimals and write the result in standard form (A × 10ⁿ, where 1 ≤ A < 10).

Concept: Write each number in standard form first, then multiply the numbers and add the powers of 10.

Solution:

1. Convert each number: • 0.000215 = 2.15 × 10⁻⁴ • 0.000028 = 2.8 × 10⁻⁵

2. Multiply: • (2.15 × 2.8) × 10⁻⁴ × 10⁻⁵ • 2.15 × 2.8 = 6.02 • 10⁻⁴ × 10⁻⁵ = 10⁻⁹

3. Result: 6.02 × 10⁻⁹

Check: 215 × 28 = 6020, and the decimal places are 6 + 6 = 12, giving 6020 × 10⁻¹² = 6.02 × 10⁻⁹. ✔

Answer: The options are printed as "109" and "10-9", which are formatting losses of 10⁹ and 10⁻⁹. Since the product of two numbers much less than 1 must be tiny, the exponent has to be negative. So the answer is option D, 6.02 × 10⁻⁹.

Tip: For tiny decimals, count the places moved to get each exponent, then multiply the front numbers and add the exponents. Always sanity-check the sign of the exponent: small × small = very small, so the power is negative.