Significant Figures

All IB calculations must report answer to correct # of sig fig’s.

All lab measurements must be reported to correct sig fig’s and correct sig fig’s 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, height—anything MEASURED. No measurement is perfect.

When to use Significant figures

• When 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 same

• 21.700cm 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 Fig’s in measurement

• Use 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 Instruments• Use 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 102

• 1.34 x 10 -2

• 4.0012 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 fig’s

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?

• 7• 40• 0.5• 0.00003• 7 x 105

• 7,000,000

• 1• 1• 1• 1• 1• 1

1001

• 2nd 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?

• 1.2• 2100• 56.76• 4.00• 0.0792• 7,083,000,000

• 2• 2• 4• 3• 3• 4

How many sig figs here?

• 3401• 2100• 2100.0• 5.00• 0.00412• 8,000,050,000

• 4• 2• 5• 3• 3• 6

Rounding Rules

• If digit just past last sig fig is 5 or more round up. If we need two sig fig’s,

• 3.67 3.7 5.55 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 examples• 2.45cm + 1.2cm = 3.65cm,

• Round off to = 3.7cm

• 7.432cm + 2cm = 9.432 round to 9cm

Multiplication and Division

• Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

A couple of examples• 56.78 cm x 2.45cm = 139.111 cm2

• Round to 139cm2

• 75.8cm x 9.6cm = ?

730 cm2.

Practice with Sig Figs wksht

• Hwk Kerr pg 9 #2 – 12.