Scaling small decimals with powers of ten Find the power of ten n such that 0.0136 equals 13.6 × 10^n. Choose the correct exponent.

Introduction / Context:
Expressing values as a mantissa times a power of ten lets you shift the decimal point without changing the quantity. This skill is fundamental when converting between unit prefixes (milli, micro, nano) or reformatting numbers for clarity in reports and calculations.

Given Data / Assumptions:

• Decimal value: 0.0136.
• Target form: 13.6 × 10^n with mantissa 13.6 (not normalized scientific notation, but an equivalent scaling).
• We need to find the exponent n that preserves equality.

Concept / Approach:
Moving the decimal point to the right increases the mantissa; to keep the numeric value unchanged, the power of ten must compensate with a negative exponent. Specifically, shifting the decimal point k places to the right requires multiplying by 10^k and simultaneously multiplying by 10^–k to maintain equality when expressing the factor explicitly.

Step-by-Step Solution:

Verification / Alternative check:
Compute 13.6 × 10^–3 = 13.6 / 1000 = 0.0136, confirming equality. Alternatively, write 0.0136 in scientific notation: 1.36 × 10^–2. Multiplying the mantissa by 10 (to 13.6) requires reducing the exponent by 1 (from –2 to –3), consistent with the result.

Why Other Options Are Wrong:

Common Pitfalls:
Confusing the direction of decimal movement with exponent sign; insisting on normalized mantissa unnecessarily when the problem specifies a fixed mantissa of 13.6.

Final Answer:
10^–3