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. –Approximate: weight, height—anything MEASURED. No measurement is perfect. –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 21.7cm. To a mathematician 21.70, or is the same cm To a scientist 21.7cm and 21.70cm is NOT the same. It means the measurement is accurate to within one thousandth of a cm.

Our instruments are crude and open to human error. If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7cm or to the nearest 0.1. If you use the balances the best measurement could only be to the nearest 0.01

How do I know how many Sig Figs? Rule #1: All digits are significant starting with the first non-zero digit on the left has 2 significant digits 367 – has 3 sig. digs

How do I know how many Sig Figs? Rule # 2: In whole numbers that end in zero, the zeros at the end are not significant. 300 – has 1 sig. fig. 4,500,000 – has 2 sig figs.

How many sig figs? x ,000,

How do I know how many Sig Figs? Rule #3: If zeros are sandwiched between non-zero digits, the zeros become significant. 201 – has 3 sig figs – has 6 sig figs.

How do I know how many Sig Figs? Rule # 4: If zeros are at the end of a number that has a decimal, the zeros are significant – has 4 sig. figs 10.0 – has 3 sig. figs.

How do I know how many Sig Figs? Rule #4 cont.: These zeros are showing how accurate the measurement or calculation are. The more place values, the more precise the number.

How many sig figs here? ,083,000,

How many sig figs here? ,000,050,

What about calculations with sig figs? Rule # 5: When adding or subtracting, the answer can only show as many decimal places as the measured number having the fewest decimal places. Significant digits aren’t considered. For example, = , but round to 1.36 (two decimal places because 0.14 has only 2 decimal places.)

Rule # 6” Multiplying and Dividing Significant Figures When multiplying or dividing, the answer may only show as many significant digits as the measured number having the fewest significant digits. For example, 0.33 x = , but round to 110 (two significant digits because 0.33 has only two significant digits).

Add/Subtract examples 2.45cm + 1.2cm = 3.65cm, Round off to = 3.7cm 7.432cm - 2cm = round to  5 cm

A couple of multiplying and dividing examples cm x 2.45cm = cm 2 Round to  139cm cm / 9.6cm = cm Round to ? 2 sig. figs 75 cm

The End Have Fun Measuring and Happy Calculating!