Sig Figs

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Sig Figs

Precision and Significant Figures

Unit #1

Topic 2b

Using Significant Figures

(1.02b)


Uncertainty and Significant Figures

Cartoon courtesy of Lab-initio.com


Numbers that end at a Place

Smaller than the ones

The precision is whatever place the rightmost digit

is in.

10.030 cm __________

2.12 mL __________

0.0020 g __________

23.226 s ___________

0.100 mg ___________

23.000 cm ___________


Numbers larger than 1:

The precision is either where the integers run

out, or where there is a line over a zero, or at

a decimal point.

134000 pm ______________

12000 µL ______________

12000 ppm ______________

12000 L ______________

12000. cm ______________


Significant Figures

Significant figures (sig figs) are digits

that were actually measured ending

with the last place that was estimated.

(all known digits and one estimated

digit)


Rules for Counting Sig Figs

Nonzero integers always count as

significant figures.

3456 has 4 sig figs


Rules for Counting Sig Figs

Zeros

Imbedded zeros always count as sig figs.

16.07 has 4 sig figs


Rules for Counting Sig Figs

Zeros

Leading zeros do not count as sig figs.

0.0486 has 3 sig figs


Rules for Counting Sig Figs

Zeros

Trailing zeros are significant only if the

number contains a decimal point.

9.300 has 4 sig figs


Rules for Counting Sig Figs

Zeros

Trailing zeros in numbers larger than 1

are significant only if they are followed by a

decimal or have a line over them.

104,000 has 3 sig figs

104,000. has 6 sig figs

104,000 has 5 sig figs


Sig Fig Practice #1

How many significant figures in each of the following

1.0070 m à 5 sig figs

17.10 kg à 4 sig figs

100,890 L à 5 sig figs

3.29 x 10 3 s à 3 sig figs

0.0054 cm à 2 sig figs

3,200,000 à

500,000 à

2 sig figs

5 sig figs


Number that are smaller

than one.

Practice:

0.12 mL __________

0.0020 g ___________

0.226 s ___________

0.100 mg ___________

0.00033cm ___________

0.0500 L ___________

0.00005 m ___________


If your measurement is larger than

one:

Start with the digit on the leftward side and count to the

last integer, or a line over a zero, or a decimal point.

13400 pm _______ 12000 L __________

12000 µg _______ 12000. cm __________

12000 ppm_______ 9500 g __________

9500. km _______


Bigger than one with a decimal

point– theyre all sig figs

28.0 cm __________

320.04 mL __________

90.000 g __________

32.92 s __________

42.010 mg __________


Sample Problems:

How many significant figures are in each of the

following measurements

a.) 28.6 g d.) 0.046 04 L

b.) 3440. cm

e.) 0.006 700 0 kg

c.) 910 m

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