 # Significant Figures There are two kinds of numbers in the world: Exact

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Significant Figures There are two kinds of numbers in the world: Exact
There are exactly 12 eggs in a dozen Most people have exactly 10 fingers and 10 toes Inexact Any measurement

If I quickly measure the width of a piece of notebook paper, I might get
220 mm 2 significant figures If I am more precise 216 mm 3 significant figures Even more precise 215.6 mm 4 significant figures

Precision vs. Accuracy Accuracy Precision
Refers to how closely a measured value agrees with the correct value Precision Refers to how closely individual measurements agree with each other. Accurate and precise Accurate but not precise Precise not accurate

Significant Figures Significant figures are critical in any measurement. The number of sig. figs. is the number of digits believed to be correct by the person doing the measuring. The measurement always includes one estimated digit.

Significant Figures 4.5 cm
When we measure something, we can (and do) always estimate between the smallest marks 4.5 cm estimate

Sig Figs The better the measuring device the better we can estimate Remember the last number measured is an estimate 4.55 cm estimate

Sig Fig Rules Needed a set of rules to decide which zeros count.
All other numbers do count as significant figs Which zeros count:

Sig Figs Which zeros count Leading zeros are never significant
significant figures Imbedded zeros are always significant sig figs Trailing zeros are significant only if the decimal point is specified. sig fig 3 x 102 sig figs x 102 sig figs x 102

Calculating with Sig Figs
Adding and Subtracting The last sig fig in a measurement is an estimate. Your answer can not be better than your worst estimate. Last digit retained is set by the first doubtful digit.

Rounding Rules Look at the number to the right, or after the one you are rounding. If it is 0 to 4 don’t change it If it is 5 to 9 make the one you are rounding one bigger Round to four sig figs To three sig figs To two sig figs To one sig fig

Multiplication and Division
Rule is simpler Same number of sig figs in the answer as the least in the question 3.6 x 653 2350.8 3.6 has 2 sig figs and 653 has 3 sig figs Answer can only have 2 sig figs 2400

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