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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. What is a significant figure?. Approximate: weight, height—anything MEASURED. No measurement is perfect.

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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.**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 21.7cm. 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.**How do I know how many Sig Figs?**• Rule: All digits are significant starting with the first non-zero digit on the left.**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**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?**• 2nd Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant.**How do I know how many Sig Figs?**• 3rd Exception to rule: If zeros are at the end of a number that has a decimal, the zeros are significant.**How do I know how many Sig Figs?**• 3rd Exception to rule: These zeros are showing how accurate the measurement or calculation are.**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 How many sig figs here?**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 = ?**The End**Have Fun Measuring and Happy Calculating!

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