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Significant Figures. What is a significant figure?. The precision of measurements are indicated based on the number of digits reported. Significant figures are the digits that are reported Approximate: weight, height—anything MEASURED; no measurement is perfect.

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## Significant Figures

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**What is a significant figure?**• The precision of measurements are indicated based on the number of digits reported. • Significant figures are the digits that are reported • 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. • Example: If you measured the width of a piece of paper with your ruler you might record 21.7cm. -To a mathematician 21.70, or 21.700 is the same.**When To Use Significant Figures**• 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 21.7cm.**How do I know how many Significant Figures?**Rules: 1. All digits are significant starting with the first non-zero digit on the left. (1, 2, 3, 4, 5, 6, 7, 8, 9) **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?**Rules continued… 2.If zeros are sandwiched between non- zero digits, the zeros become significant. Ex. (103) (12.06) 3. If zeros are at the end of a number that has a decimal, the zeros are significant. Ex. (8.20); 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 significant figures?**Rule: • When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers. OR, in other words, the smallest number of sig figs in the problem are how many sig figs you should record in your answer. • Exponents MUST be equal before you add or subtract!**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. OR, in other words, the smallest number of sig figs in the problem are how many sig figs you should record in your answer. • When multiplying, add exponents • When dividing, subtract exponents**A couple of examples**• 56.78 cm x 2.45cm = 139.111 cm2 • Round to 139cm2 • 75.8cm x 9.6cm = ?**The End**Happy Calculating!

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