Significant Figures Physical Science What is a significant

Significant Figures Physical Science

What is a significant figure? • There are 2 kinds of numbers: –Exact: the amount of money in your account. Known with certainty.

What is a significant figure? –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.

When to use Significant figures –If you measured the width of a paper with your ruler you might record 21. 7 cm. To a mathematician 21. 70, or 21. 700 is the same.

But, to a scientist 21. 7 cm and 21. 70 cm is NOT the same • 21. 700 cm to a scientist means the measurement is accurate to within one thousandth of a cm.

But, to a scientist 21. 7 cm and 21. 70 cm 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. 7 cm.

How do I know how many Sig Figs? • Rule: All digits are significant starting with the first non-zero digit on the left. • 7 76 707 123 5522

How do I know how many Sig Figs? • Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant. • 7 70 700 77700

How many sig figs? • 7 • 40 • 0. 5 • 0. 00003 5 • 7 x 10 • 7, 000 • 1 • 1 • 1

How do I know how many Sig Figs? nd • 2 Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant. • 70 7077 7700

How do I know how many Sig Figs? • 3 rd Exception to rule: • 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 calculation are. • 7. 00 7. 070 7. 007 707. 000

How many sig figs here? • • • 1. 2 2100 56. 76 4. 00 0. 0792 7, 083, 000 • • • 2 2 4 3 3 4

How many sig figs here? • • • 3401 2100. 0 5. 00 0. 00412 8, 000, 050, 000 • • • 4 2 5 3 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 precise of the measured numbers.

Add/Subtract examples • 2. 45 cm + 1. 2 cm = 3. 65 cm, – Round off to 3. 7 cm • 0. 073 cm + 10. 0037 cm = 10. 0767 cm – Round off to 10. 077 cm • 7. 432 cm + 2 cm = 9. 432 – Round off to 9 cm

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. 45 cm = 139. 111 • Round to 139 cm 2 • 75. 8 cm x 9. 6 cm = ? 2 cm

The End Have Fun Measuring and Happy Calculating!