Evaluate 1.25 × 10$^2$ × 0.125 × 10$^3$ × 12.5 × 10$^{-4}$ leaving your answer in standard form

Let me work this out directly.

Step 1: Separate the numbers from the powers of 10

(1.25 × 0.125 × 12.5) × (10² × 10³ × 10⁻⁴)

Step 2: Powers of 10

10^(2+3−4) = 10¹

Step 3: Multiply the decimals

• 1.25 × 0.125 = 0.15625
• 0.15625 × 12.5 = 1.953125

Step 4: Combine

1.953125 × 10¹

This is already in standard form (the number is between 1 and 10). Rounded to 3 significant figures, it is 1.95 × 10¹.

Check: 125 × 125 × 0.00125... let's verify differently: 1.25×10² = 125; 0.125×10³ = 125; 12.5×10⁻⁴ = 0.00125. Then 125 × 125 = 15625, and 15625 × 0.00125 = 19.53125 = 1.953125 × 10¹. ✓

Matching options: Option C (1.95 × 10¹) matches. Option A (1.995 × 10³) is not a correct rounding of the value, and the others have the wrong power of 10.

Tip: In standard form questions, handle the decimals and the powers of 10 separately. Add the indices, then multiply the decimals. Always check that your final number is between 1 and 10. Converting to ordinary numbers, as in the check above, is a quick way to verify your answer.