Put lab sheet on corner of your desk for me to pick up “Significant Figures” Do these in composition book: 104.21 + 12.15 219.100 – 101 3.25 X 25 21.894 / 7.11

Accuracy vs. Precision and Significant Figures

Accuracy versus Precision Accuracy refers to the proximity of a measurement to the true value of a quantity. Precision refers to the proximity of several measurements to each other.

Significant Figures The term significant figures refers to digits that were measured. The more significant figures, the greater the certainty implied for the measurement. When rounding calculated numbers, we pay attention to significant figures so we do not overstate the accuracy of our answers.

Need your ws out to go over from yesterday How do you feel about sig fig’s?

Rules: Significant Figures All nonzero digits are significant. 528.3 Zeroes between two significant figures are themselves significant. 1005 or 40.6 Zeroes at the beginning of a number are never significant. 0.0032 Zeroes at the end of a number are significant if a decimal point is written in the number. 50.600 Zeroes at the end of a number are not significant if a decimal point is absent. 20300

Rules: Significant Figures The USA trick sums up all the rules for you… Pacific Ocean Atlantic Ocean Decimal is Present Decimal is Absent Start counting significant figures in the direction the arrow points The first non-zero number you come to is the first significant figure, and then everything after is also significant

Significant Figures: Examples How many significant figures? a) 3.774 km b) 0.0012060 s c) 303020 L d) 40 pm e) 3500. kg f) 5.130 x 102 ms

Significant Figures: Examples How many significant figures? a) 3.774 km b) 0.0012060 s c) 303020 L d) 40 pm e) 3500. kg f) 5.130 x 102 ms 4 5 5 1 4 4

Controlling Number of Significant Figures If rounding is necessary, look at the leftmost digit to be dropped off. If it is… 5 or greater, round the digit to its left up 457.3 expressed as 2 SF becomes 460 NOTE: 457.3 expressed as 2 SF is NOT 46! DO NOT move the decimal place when you are rounding! 4 or less, leave the digit to its left as it is 454.1 expressed as 2 SF becomes 450 If more significant figures are required, add zero(s) to the end 320 expressed as 4 SF becomes 320.0 Scientific notation can always be used to express the correct number of significant figures. 54039 expressed as 3 SF becomes 5.40 x 104

2) Add X10 to the power you moved the decimal Examples: Significant Figures Steps: 1) identify significant figures & keep that many in the coefficient 2) Add X10 to the power you moved the decimal Express each as scientific notation: a) 3.774 km b) 0.0012060 s c) 303020 L d) 40 pm e) 3500. kg f) 5.130 x 102 ms

Examples: Significant Figures Express each as three significant figures: a) 3.774 km b) 0.0012060 s c) 303020 L d) 40 pm e) 3500. kg f) 5.130 x 102 ms 3.77 km or 3.77 x 100 km 0.00121 s or 1.21 x 10-3 s 303000 L or 3.03 x 105 L 40.0 pm or 4.00 x 101 pm 3.50 x 103 kg 513 ms or 5.13 x 102 ms

Significant Figures in Calculations When carrying measured quantities through calculations, the least certain measurement limits the certainty of the calculated quantity, and thereby determines the number of significant figures in the final answer.

Significant Figures in Calculations When multiplication or division is performed, The result contains the same number of SIGNIFICANT FIGURES as the measurement with the FEWEST significant figures. 134.7 x 43.100 ÷ 1.9 = The answer is 3100 or 3.1 x 103 because 1.9 has only two significant figures. 3055.563159 four significant figures five significant figures two significant figures Round the answer to two significant figures (3100 or 3.1 x 103)

Significant Figures in Calculations When addition or subtraction is performed, The result has the same number of DECIMAL PLACES as the measurement with the FEWEST decimal places. 50.62 5.343 + 381.1 437.063 The answer is 437.1 because 381.1 has only one decimal place. two decimal places three decimal places one decimal place Round off to one decimal place (437.1)

Significant Figures in Calculations When rounding: Do NOT round until the final step of a multiplication/division problem Do NOT round until the final step of an addition/subtraction problem Exact numbers have an infinite number of significant figures (so don’t use them to determine significant figures)

Examples: Significant Figures in Calculations b) 64.1 * 50500 = c) (512.13561 – 512.1256) ÷ 354.1 =

Examples: Significant Figures in Calculations 68.42 68.4 a) 56.32 + 12.1 = b) 64.1 * 50500 = c) (512.13561 – 512.1256) ÷ 354.1 = 3,237,050 3,240,000 or 3.24 x 106 0.000028269 2.827 x 10-5