Significant Figures & Rounding Rules

Vocabulary flashcards covering the rules for determining and rounding significant figures, including specific examples.

Non-zero digits

All non-zero numbers (1-9) are always counted as significant figures.

Captive zeros

Zeros between non-zero digits; they are always significant (e.g., 39,004 has 5 sig figs).

Leading zeros

Zeros to the left of the first non-zero digit; they are not significant (e.g., 0.008 has 1 sig fig).

Trailing zeros with decimal point

Zeros to the right of the last non-zero digit in a number that contains a decimal point; they are significant (e.g., 12.000 has 5 sig figs).

Trailing zeros without decimal point

Zeros at the end of a whole number lacking a decimal point; they are generally not significant (e.g., 140 has 2 sig figs).

Significant figures in scientific notation

Only the digits in the coefficient (A) count; the exponent (10^x) does not affect the sig-fig count.

Exact numbers

Values from counting or definitions that have an infinite number of significant figures (e.g., 10 fingers, conversion factors).

Rounding digits 5–9

If the first digit dropped is 5, 6, 7, 8, or 9, increase the last kept digit by one.

Rounding digits 0–4

If the first digit dropped is 0, 1, 2, 3, or 4, leave the last kept digit unchanged.

Step 1: Identify desired sig figs

Count from the first non-zero digit to locate the last significant figure you want to retain.

Step 2: Examine next digit

Look at the digit immediately right of your final desired sig fig to decide whether to round up or down.

Step 3: Placeholding zeros

After rounding a whole number, add zeros to maintain place value; decimals usually need none unless before the point.

Example: 241,529 → 240,000

Rounded to 2 significant figures: 2 and 4 kept; next digit 1 (<5) so number rounds down to 240,000.

Example: 0.037 → 0.04

Rounded to 1 significant figure: 3 kept; next digit 7 (>5) so number rounds up to 0.04.