Significant Digits Uncertainty of Measurement

Three Rules Non-zero digits are significant Zeros between two significant digits are significant Zeros at the right end of a number, after a decimal point, are significant

Non-zero digits are significant Number Significant Digits

Zero to left of decimal point significant digits The zero to the left of the decimal point is there to communicate that the decimal point is a decimal point - convention

Problems! Numbers like

Zeros between non-zero digits are significant Number Significant Digits

Space Holding zeros on numbers less than one significant digits significant digits

Trailing Zeros 200 is considered to have only one significant digit 38,000 has two significant digits

Problem area 5000 might really have four significant digits - an exact count or measurement write number as Scientific notation used to indicate significant digits

Review ,

Multiplication & Division An answer cannot have more significant digits than the measurement with the least number of significant digits used in the operation. (3.006) X (0.0067) = = only 2 sig. Digits

Addition & Subtraction The answer is rounded to the least number of places in the decimal portion of any number in the operation = 281.6