JF

Mathematics Skills Overview

Mathematics Skills Overview

This overview covers key mathematics skills:

  • Rounding

  • Significant Figures

  • Dimensional Analysis

Rounding

Rounding rules depend on the digit to be dropped:

  • If > 5, round up (12.6 \to 13)

  • If < 5, round down (12.4 \to 12)

  • If 5 followed by non-zero digits, round up (12.53 \to 13)

  • If ending in .5, round to the nearest even digit (e.g., 11.5 \to 12 (odd rounds up), 12.5 \to 12 (even stays same)).
    These rules are important for scientific accuracy.

Significant Figures

Significant figures (sig figs) indicate a number's precision. Results cannot be more precise than the original measurements.

Rules:

  1. All non-zero digits are significant (123.45 has five).

  2. Zeros between non-zero digits are significant (1,002.05 has six).

  3. Leading zeros are not significant (0.00921 has three).

  4. Trailing zeros in whole numbers without a decimal are not significant (921000 has three).

  5. Trailing zeros to the right of a decimal are significant (0.01230 has four).

  6. All results must include units.

Calculations with Significant Figures

  • Addition/Subtraction: Round the result to the least number of decimal places of any number in the operation (e.g., 11.31 + 33.264 + 4.1 rounds to one decimal place).

Dimensional Analysis

This involves a 13-question worksheet using provided conversion factors, potentially multiple per problem