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SIGNIFICANT FIGURES

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ACCURACY VS. PRECISION In labs, we are concerned by how “correct” our measurements are They can be accurate and precise Accurate: How close a measured value is to the actual measurement Precise: How close a series of measurements are to each other

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EXAMPLE The true value of a measurement is 23.255 mL Below are a 2 sets of data. Which one is precise and which is accurate? 1. 23.300, 23.275, 23.235 2. 22.986, 22.987, 22.987

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SCIENTIFIC INSTRUMENTS In lab, we want our measurements to be as precise and accurate as possible For precision, we make sure we calibrate equipment and take careful measurements For accuracy, we need a way to determine how close our instrument can get to the actual value

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SIGNFICANT FIGURES We need significant figures to tell us how accurate our measurements are The more accurate, the closer to the actual value Look at this data. Which is more accurate? Why? 25 cm 25.2 cm 25.22 cm

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ANSWER 25.22cm The more numbers past the decimal (the more significant figures ), the closer you get to the true value. How do we determine how many significant figures are in different pieces of lab equipment?

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SIGNIFICANT FIGURES Significant figure – any digit in a measurement that is known for sure plus one final digit, which is an estimate Example: 4.12 cm This number has 3 significant figures The 4 and 1 are known for certain The 2 is an estimate

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SIGNIFICANT FIGURES In general: the more significant figures you have, the more accurate the measurement Determining significant figures with instrumentation Find the mark for the known measurements Estimate the last number between marks

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SIGNIFICANT FIGURES Try these: Graduated cylinder Triple Beam balance Ruler

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RULES FOR SIGNIFICANT FIGURES Rule 1: Nonzero digits are always significant Rule 2: Zeros between nonzero digits are significant 40.7 (3 sig figs.) 87009 (5 sig figs.) Rule 3: Zeros in front of nonzero digits are not significant 0.009587 (4 sig figs.) 0.0009 (1 sig figs.)

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RULES FOR SIGNIFICANT FIGURES Rule 4: Zeros at the end of a number and to the right of the decimal point are significant 85.00 (4 sig figs.) 9.070000000 (10 sig figs.) Rule 5: Zeros at the end of a number are not significant if there is no decimal 40,000,000 (1 sig fig)

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RULES FOR SIGNIFICANT FIGURES Rule 6: When looking at numbers in scientific notation, only look at the number part (not the exponent part) 3.33 x 10 -5 (3 sig fig) 4 x 10 8 (1 sig fig) Rule 7: When converting from one unit to the next keep the same number of sig. figs. 3.5 km (2 sig figs.) = 3.5 x 10 3 m (2 sig figs.)

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HOW MANY SIGNIFICANT FIGURES? 1. 35.02 2. 0.0900 3. 20.00 4. 3.02 X 10 4 5. 4000

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ANSWERS 1. 4 2. 3 3. 4 4. 3 5. 1

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ROUNDING TO THE CORRECT NUMBER OF SIG FIGS. Many times, you need to put a number into the correct number of sig figs. This means you will have to round the number EXAMPLE: You start with 998,567,000 Give this number in 3 sig figs.

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ANSWER Step 1: Get the first 3 numbers (3 sig figs.) 998 Step 2: Check to see if you have to round up or keep the number the same You need to look at the 4 th number 998 5 If the next number is 5 or higher, round up If the next number is 4 or less, stays the same Therefore = 999

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ANSWER Step 3: Take your numbers and put the decimal after the first digit 9.99 Step 4: Count the number of places you have to move to get to the end of the number and put it in scientific notation. 9.99 x 10 8 NOTE: If the number is BIG it will be a positive exponent. If the number is a DECIMAL, it will be a negative exponent.

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OTHER POSSIBILITY Example: 999,999,999 (3 sig. figs.) When you take the first three numbers, you get 999 But when you round, it is going to round from 999 1000 Therefore, the number becomes: 1.00 x 10 8

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TRY THESE 1. 10,000 (3 sig. figs.) 2. 0.00003231 (2 sig. figs.) 3. 347,504,221 (3 sig. figs.) 4. 0.000003 (2 sig. figs.) 5. 89,165,987 (3 sig. figs.)

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