Significant Figures

Significant Figures otherwise known as sig figs!

Importance of Sig Figs • Sig Figs let us know how accurate and precise a measurement is. • They give us a clue about the markings for measurement on the instrument used. • Sig Figs are counted by looking at each individual digit within a number

Sig Figs • A measurement can only be as accurate and precise as the instrument that produced it. • A scientist must be able to express the accuracy of a number, not just its numerical value. • We can determine the accuracy of a number by the number of significant figures (or digits) it contains.

Non-zero digits • Non-zero digits ARE ALWAYS significant! Examples: 6.78 3 sig figs 1,234 4 sig figs 456.789 6 sig figs

Zeroes • Three kinds of zeroes within a number • leading zeroes • sandwiched zeroes • trailing zeroes • Each type of zero has its own rule…

Leading Zeroes • Come before all non-zero digits • ARE NEVER significant! Examples: 0.0001 1 sig fig 0.067 2 sig figs 0.234 3 sig figs

Sandwiched Zeroes • zeroes between two non-zero digits • ARE ALWAYS significant. Examples: 101 3 sig figs 40,008 5 sig figs 20.0008 6 sig figs

Trailing Zeroes • Come after the non-zero digits • ARE significant ONLY IF there is a written decimal point somewhere in the number • ARE NOT significant is the decimal is not physically written down Examples: 400. 3 sig figs 400 1 sig fig 80.00 4 sig figs 80 1 sig fig

Scientific Notation All digits written in the coefficient of a number in scientific notation are significant. Example: 1.00 x 105 has 3 sig figs 1 x 10-3 has 1 sig fig

Definitions Some mathematical relationships that are defined are exact numbers and have limitless sig figs. Example: There are 12 inches in 1 foot. Since this is an exact relationship, the numbers 1 and 12 have a limitless number of sig figs and therefore would not affect the rounding of an answer.

Rounding with Sig Figs • Take the needed number of sig figs from the beginning of the number, then look to the digit to the right to see whether to round up or keep same. • If there is a need, substitute zeroes as placeholders (left side of decimal only). • Always check your answer to make sense. Example: 14,863 rounded to 15 doesn’t make sense!

Rounding • 188.93 rounded to 4 sig figs = 188.9 • 188.93 rounded to 3 sig figs = 189 • 188.93 rounded to 2 sig figs = 190 • 188.93 rounded to 1 sig fig = 200 • 112.398 rounded to 5 sig figs = 112.40 • 112.398 rounded to 4 sig figs = 112.4 • 112.398 rounded to 3 sig figs = 112 • 112.398 rounded to 2 sig figs = 110 • 112.398 rounded to 1 sig fig = 100

Multiplying/Dividing with Sig Figs • For multiplying and dividing, the answer should be rounded to the same number of sig figs as the factor with the least number of sig figs. Example: 23.00 cm (432.0 cm) (19 cm) = 188,784 cm3 = 190,000 cm3 or 1.9 x 105cm3 Need 2 sig figs infinal answer

Adding/Subtracting with Sig Figs • For adding and subtracting, the answer should be rounded to the same number of decimalplacesas the measurement with the least number of decimalplaces. Example: 123.25 mL + 46.0 mL + 86.257 mL = 255.507 mL = 255.5 mL Need 1 decimal place in final answer

Multi-Step Problems • If you have a multi-step that is not mixed operations, wait to round to the correct number of sig figs until after the final step. • If you round after each step, you can end up over-rounding your answer.

Mixed Operations • For mixed operations, first add or subtract and apply the decimal place rule, then multiply and divide and apply the sig figs rule. Example: (4.56 + 8.1) (332.1) = 1 decimal place for + (12.7) (332.1) = 3 sig figs for x 4217.67 = 4220 or 4.22 x 103

Significant Figures