Key Points: Calculator Modes and Significant Figures

Calculator mode: degrees vs radians

  • Set the calculator to the angle unit used in the problem (degrees or radians).

  • If a problem uses degrees, use degrees; if it uses radians, use radians.

  • When unsure, perform checks or convert angles to the unit specified in the problem before evaluating trigonometric expressions.

Scientific notation and significant figures

  • The exponent does not affect the number of significant figures; only the coefficient determines sig figs.

  • In the form c×10nc \times 10^n, the number of significant figures is the same as the sig figs in the coefficient.

  • Examples: 1.23×1041.23 \times 10^4 has 3 sig figs; 1.230×1041.230 \times 10^4 has 4 sig figs.

  • To specify a desired number of sig figs, adjust the coefficient, e.g., 1.0×1041.0 \times 10^4 (2 sig figs) or 1×1041 \times 10^4 (1 sig fig).

  • Ambiguity with expressions like 10−710^{-7}: the number of sig figs depends on the coefficient; write clearly as 1.0×10−71.0 \times 10^{-7} (2 sig figs) or 1×10−71 \times 10^{-7} (1 sig fig).

Ambiguity: 2,400

  • A plain 2,400 is ambiguous because trailing zeros without a decimal point may or may not be significant.

  • Possible interpretations:

    • 2 sig figs: 2.0×1032.0 \times 10^3

    • 3 sig figs: 2.40×1032.40 \times 10^3

    • 4 sig figs: 2.400×1032.400 \times 10^3

  • To convey a specific precision, use scientific notation or include a decimal point, e.g., 2.40×1032.40 \times 10^3 (3 sig figs) or 2.400×1032.400 \times 10^3 (4 sig figs).

Quick recall

  • Always match calculator angle mode to the problem’s unit.

  • Use explicit scientific notation to communicate precision.

  • If precision is not implied, avoid asserting a specific number of sig figs; indicate it explicitly with notation.