Significant Figures. Significant Figure Rules 1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant. 1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9)

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1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant. Significant figures are critical when reporting scientific data because they.

Presentation transcript:

Significant Figures

Significant Figure Rules 1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant. 1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant. 2) ALL zeroes between non-zero numbers are ALWAYS significant. 2) ALL zeroes between non-zero numbers are ALWAYS significant. 3) ALL zeroes which are SIMULTANEOUSLY to the right of the decimal point AND at the end of the number are ALWAYS significant. 3) ALL zeroes which are SIMULTANEOUSLY to the right of the decimal point AND at the end of the number are ALWAYS significant. 4) ALL zeroes which are to the left of a written decimal point and are in a number >= 10 are ALWAYS significant. 4) ALL zeroes which are to the left of a written decimal point and are in a number >= 10 are ALWAYS significant.

Examples Number # Significant Figure Rule(s) 48, ,2, (= 4 E-4) 11, , ,2,3,4 3,000,000 (= 3 E+6) ,3,4

ADDITION AND SUBTRACTION: When adding or subtracting numbers, count the NUMBER OF DECIMAL PLACES to determine the number of significant figures. The answer cannot CONTAIN MORE PLACES AFTER THE DECIMAL POINT THAN THE SMALLEST NUMBER OF DECIMAL PLACES in the numbers being added or subtracted.

Example Example: Example: (6 places after the decimal point) (6 places after the decimal point) (4 places after the decimal point) (2 places after the decimal point) (2 places after the decimal point) (on calculator) (on calculator) 24.69(rounded to 2 places in the answer) 24.69(rounded to 2 places in the answer)

MULTIPLICATION AND DIVISION: When multiplying or dividing numbers, count the NUMBER OF SIGNIFICANT FIGURES. The answer cannot CONTAIN MORE SIGNIFICANT FIGURES THAN THE NUMBER BEING MULTIPLIED OR DIVIDED with the LEAST NUMBER OF SIGNIFICANT FIGURES.

Example Example: Example: (8 significant figures) (8 significant figures) x (5 significant figures) (on calculator) (on calculator) (rounded to 5 significant figures) (rounded to 5 significant figures)