Significant FiguresAll IB calculations must report answer to correct # of sig figs.

All lab measurements must be reported to correct sig figs and correct sig figs with uncertainties must be reported properly.

There are 2 kinds of numbers:Exact: the amount of money in your account. Known with certainty.

Approximate: weight, heightanything MEASURED. No measurement is perfect.

When to use Significant figuresWhen a measurement is recorded only those digits that are dependable are written down.

What is this measurement?1.35 cm

Measure the width of your notebook paper in cm.

When to use Significant figures

If you measured the width of a paper with your ruler you might record 21.7cm.To a mathematician 21.70, or 21.700 is the same.

But, to a scientist 21.7cm and 21.70cm is NOT the same21.700cm to a scientist means the measurement is accurate to within one thousandth of a cm.

But, to a scientist 21.7cm and 21.70cm is NOT the same

If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7cm*.*or 21.75 cm.

Reporting Sig Figs in measurementUse the smallest or half the smallest measure on instrument. That will be the best you can read. There will be situations where the measure will be much less precise than that.Analog Instruments

The smallest measure is 0.1 cm so report 1.3 or 1.35 cm. The last digit is an estimate.

Digital InstrumentsUse the place of the last digit at best.1.00 V1.00

All digits in the prefix before a power of 10 are significant.

2.2 x 1021.34 x 10 -24.0012 x 109.How do I know how many Sig Figs are in a reported number?

How do I know how many Sig Figs not in sci notation?All non-zero digits are signicant.

All digits are significant starting with the first non-zero digit on the left.

0.0022 has 2 sig figs

100 Has 1 sig fig.Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant.

How many sig figs?7400.50.000037 x 1057,000,000111111

10012nd Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant.

3rd Exception to rule: If zeros are at the end of a number that has a decimal, the zeros are significant. They are there to show precision. 3.000

3rd Exception to rule:

These zeros are there to show precision in the measurement or calculation.

How many sig figs here?1.2210056.764.000.07927,083,000,000224334

How many sig figs here?340121002100.05.000.004128,000,050,000425336

Rounding RulesIf digit just past last sig fig is 5 or more round up. If we need two sig figs,3.67 3.75.55 5.6

If digit past last sig fig is 4 or less drop off last numbers:3.322 3.3

What about calculations with sig figs?Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

Add/Subtract examples2.45cm + 1.2cm = 3.65cm, Round off to = 3.7cm

7.432cm + 2cm = 9.432 round to 9cm

Multiplication and DivisionRule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

A couple of examples56.78 cm x 2.45cm = 139.111 cm2Round to 139cm2

75.8cm x 9.6cm = ?730 cm2.

Practice with Sig Figs wkshtHwk Kerr pg 9 #2 12.