Significant Figures.

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Significant Figures Physical Science.

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Presentation transcript:

Significant Figures

Numbers 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. 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 21.700 cm to a scientist means the measurement is accurate to within one thousandth of a cm.

If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.70 cm.

How do I know how many Significant Figures? Rule: All digits are significant starting with the first non-zero digit on the left. 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

How do I know how many Significant Figures? If zeros are sandwiched between non-zero digits, the zeros become significant.

How do I know how many Significant Figures? If zeros are at the end of a number that has a decimal, the zeros are significant. (These zeros are showing how accurate the measurement or calculations are.)

How many sig figs here? 1.2 2100 56.76 4.00 0.0792 7,083,000,000 2 4 3

How many sig figs here? 3401 2100 2100.0 5.00 0.00412 8,000,050,000 4 2 5 3 6

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 off 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 off to  139cm2 75.8cm x 9.6cm = ?

Have Fun Measuring and Happy Calculating! The End Have Fun Measuring and Happy Calculating!