Significant Figures

• You walk into a hardware store and buy a 3 pack of light bulbs. They cost $5.81. How much does each light bulb cost?

• Does $1.93666666667 make sense?• No, we would say that each bulb costs

$1.94 because we know that in money only 2 digits past the decimal have value to us because that the limit of our currency.

• When making an analogue (non digital) measurement, you will read the scale to the smallest calibrated unit and then estimate 1 smaller decimal place.

• If the measurement seems “exact”, you would use a zero in the last decimal place.

• Digital measurements ( stopwatches) can’t be estimated the same way.

• How do we know which digits in a number are significant?

1. All non-zero digits are significant.• 12.38• 4 sig figs• 4.6666• 5 sig figs• 3.1• 2 sig figs

2. All zeros between non-zero digits are significant. (sandwich rule)

• 12.012• 5 sig figs• 340002• 6 sig figs• 1010101 • 7sig figs

3. Trailing zeros to the right of the decimal point are significant.

• 0.340• 3 sig figs• 0.34000• 5 sig figs• 0.0052000000 • 8 sig figs

Let’s practice• 126.987• 6• 89.023• 5• 0.91• 2• 300,000• 1• 0.0000005• 1

Addition and Subtraction Rules• For every number that is added or

subtracted, count how many decimal places are to the right of the decimal point.• Your answer will have the fewest decimal

places. • 45.987 + 45.93 + 4.5 = • 96.4 (only one place after the decimal

point.)

Let’s practice• 23.56 + 87.1 + 5.6666• 116.3• 9.8455 – 4.555• 5.291• 5 – 4.4• 1

Rules for Multiplication and Division• Your answer can’t have more total sig.

figures than the smallest total of the numbers used to obtain the answer.• 12.3 x 4.7890 = • 58.9 3 sig figs• 45.93 / 2 =• 20 1 sig fig

Let’s practice

• 4.51 x 6.788• 30.6• 6.7 / 3.4• 2.0• 4.5 x 3.67 x 2.311• 38