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“A man with a watch knows what time it is. A man with two watches is never sure” (Unknown)

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A. Uncertainty in Measurement A measurement always has some degree of uncertainty.

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A. Uncertainty in Measurement Different people estimate differently. Record all certain numbers and one estimated number.

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Significant Figures Physical Science

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

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

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When to use Significant figures When a measurement is recorded only those digits that are dependable are written down.

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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.

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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.

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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.

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

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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.

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How many sig figs? 7 40 0.5 0.00003 7 x 10 5 7,000,000 1 1 1 1 1 1

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

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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.

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How do I know how many Sig Figs? 3rd Exception to rule: These zeros are showing how accurate the measurement or calculation are.

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How many sig figs here? 1.2 2100 56.76 4.00 0.0792 7,083,000,000 2 2 4 3 3 4

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How many sig figs here? 3401 2100 2100.0 5.00 0.00412 8,000,050,000 4 2 5 3 3 6

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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.

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Add/Subtract examples 2.45cm + 1.2cm = 3.65cm, Round off to = 3.7cm 7.432cm + 2cm = 9.432 round to 9cm

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Multiplication and Division Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

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A couple of examples 56.78 cm x 2.45cm = 139.111 cm 2 Round to 139cm 2 75.8cm x 9.6cm = ?

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The End Have Fun Measuring and Happy Calculating!

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How wide is our universe? 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

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Scientific Notation A number is expressed in scientific notation when it is in the form a x 10 n where a is between 1 and 10 and n is an integer

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Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

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2. 10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 10 23

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1) Express 0.0000000902 in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10 -8

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Write 28750.9 in scientific notation. 1.2.87509 x 10 -5 2.2.87509 x 10 -4 3.2.87509 x 10 4 4.2.87509 x 10 5

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2) Express 1.8 x 10 -4 in decimal notation. 0.00018 3) Express 4.58 x 10 6 in decimal notation. 4,580,000 On the graphing calculator, scientific notation is done with the button. 4.58 x 10 6 is typed 4.58 6

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