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## Significant Figures

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**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 21.700 is the same. 21.700cm 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. 12 - 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.**7**40 0.5 0.00003 7 x 105 7,000,000 1 1 1 1 1 1 How many sig figs?**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 340004 – 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. 23.00 – 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.**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**2000 2100.0 5.00 0.00412 8,000,050,000 4 1 5 3 3 6 How many sig figs here?**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, 0.14 + 1.2243 = 1.3643, 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 325.5 = 107.415, 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 = 5.432 round to 5 cm**A couple of multiplying and dividing examples**• 56.78 cm x 2.45cm = 139.111 cm2 • Round to 139cm2 • 715.8cm / 9.6cm = 74.5625 cm • Round to ? 2 sig. figs • 75 cm**The End**Have Fun Measuring and Happy Calculating!