Significant FiguresSignificant Figures

But their friends call them sig But their friends call them sig figs…figs…

““Only those who have the patience to Only those who have the patience to do simple things perfectly will do simple things perfectly will acquire the skill to do difficult things acquire the skill to do difficult things easily.”easily.”• Johann von ShillerJohann von Shiller

MeasurementsMeasurements

Numbers in science class are Numbers in science class are measurements, and have a meaning.measurements, and have a meaning.

In the measurement, .0045 cm, the In the measurement, .0045 cm, the zeros are just place holders for the zeros are just place holders for the measurement digits of 4 and 5.measurement digits of 4 and 5.

We could rewrite this as 4.5x10We could rewrite this as 4.5x10-3-3 without losing any accuracy, so these without losing any accuracy, so these zeros don’t matter as much as the 4 zeros don’t matter as much as the 4 and five.and five.

Sig FigsSig Figs

Numbers that are important in a Numbers that are important in a measurement are called measurement are called significant significant figuresfigures..

There are four simple rules we can There are four simple rules we can follow to determine which numbers follow to determine which numbers are are sig figssig figs in a measurement. in a measurement.

Rule 1Rule 1

Every nonzero number is a sig fig.Every nonzero number is a sig fig.• 2300 has two sig figs, the 2 and the 32300 has two sig figs, the 2 and the 3• 12.43 has four sig figs12.43 has four sig figs

• How about 724000?How about 724000?

• Three sig figs!Three sig figs!

Rule 2Rule 2

Zeroes trapped are sig figs.Zeroes trapped are sig figs.• 203 has three sig figs203 has three sig figs

The two and three because of rule 1The two and three because of rule 1 The zero is trapped, so it’s a sig figThe zero is trapped, so it’s a sig fig

• 1.024 has four sig figs1.024 has four sig figs

• How many sig figs are in 609,000?How many sig figs are in 609,000?• Three!Three!

Rule 3Rule 3

Zeros on the left are not sig figs.Zeros on the left are not sig figs.• .0045 has two sig figs.0045 has two sig figs• .0203 has three sig figs.0203 has three sig figs

• How many sig figs are in .004903?How many sig figs are in .004903?

• Four sig figs!Four sig figs!

Rule 4Rule 4

Final zeros to the right of the decimal Final zeros to the right of the decimal are sig figs.are sig figs.• .04900 has four sig figs.04900 has four sig figs• 1.0030 has five sig figs1.0030 has five sig figs

• How many sig figs are in 3.00?How many sig figs are in 3.00?• 3 sig figs!3 sig figs!

How many sig figs are in each How many sig figs are in each measurement?measurement?

7.507.50

4.3044.304

.0070.0070

4.200 x 104.200 x 1022

33

44

22

4 4

(the 10 factor doesn’t (the 10 factor doesn’t count)count)

Why does this matter?Why does this matter?

When we use measurements to do math, When we use measurements to do math, we often end up with more digits than we we often end up with more digits than we started with.started with.

Ex. Ex. • Find the area of a triangle with a base of .3 cm Find the area of a triangle with a base of .3 cm

and height of 1.5 cm.and height of 1.5 cm.• Area = .225 cmArea = .225 cm22

• Problem, we have an answer that is accurate Problem, we have an answer that is accurate to the thousandths place, but the to the thousandths place, but the measurements were only accurate to the measurements were only accurate to the tenth.tenth.

Old Man! I’m Confused!Old Man! I’m Confused!

I will show you a trick.I will show you a trick.

Remember: tricks are useful, but Remember: tricks are useful, but don’t confuse them with don’t confuse them with understanding…understanding…

If there is a decimal…If there is a decimal…

If there is a decimal, we bring an arrow If there is a decimal, we bring an arrow from the left…from the left…

.0004560.0004560

The arrow goes through any zeros. The arrow goes through any zeros. It stops when it hits a number.It stops when it hits a number. Everything left is a sig fig…Everything left is a sig fig…

If there is If there is no no decimal…decimal…

If there is no decimal, we bring an arrow If there is no decimal, we bring an arrow from the right…from the right…

780000780000

The arrow goes through any zeros. The arrow goes through any zeros. It stops when it hits a number.It stops when it hits a number. Everything left is a sig fig…Everything left is a sig fig…

AssignmentAssignment

Page 51Page 51• 83 and 8483 and 84

Add this to previous book workAdd this to previous book work Need help? More info on sig figs can Need help? More info on sig figs can

be found on pages 38-39, including be found on pages 38-39, including some samples.some samples.