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Rounding. We need to round numbers because a calculator often gives an answer with more digits than are justified by the precision of the measurements. Look at the digit to the right of the one to be rounded. If it is Less than 5, # stays the same Greater than or equal to 5, # increases by 1.
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Rounding • We need to round numbers because a calculator often gives an answer with more digits than are justified by the precision of the measurements. • Look at the digit to the right of the one to be rounded. If it is • Less than 5, # stays the same • Greater than or equal to 5, # increases by 1
But how do you determine how many sig digs to round to? • Multiplication and division • The answer can have no more sig digs than the measurement with the least number of sig digs. • EXAMPLE: • 2.4 x 15.82 = 38 • 16.25 / 5.1442 = 3.159
But how do you determine how many sig digs to round to? • Addition and subtraction • The answer has the same number of digits to the right of the decimal point as the measurement having the fewest digits to the right of the decimal point. • EXAMPLE: • 25.1 + 2.03 = 27.1 • 5.44-2.6103 = 2.83
How do you do calculations with scientific notation? • Multiplication • Multiply coefficients • Add exponents • Round EXAMPLES: • (2 x 106)x (3 x 103)= 6 x 109 • (3 x 106)x (3 x 10-3)= 9 x 103
How do you do calculations with scientific notation? • Division • Divide coefficients • Subtract exponents • (numerator-denominator) • Round EXAMPLES: • (6 x 106)/ (3 x 103)= 2 x 103 • (4 x 106)/ (2 x 10-3)= 2 x 109 • (8 x 10-6)/ (2 x 103)= 4 x 10-9 • (6 x 106)/ (3 x 109)= 2 x 10-3
How do you do calculations with scientific notation? • Addition and subtraction • Adjust so exponents are equal • Add or subtract coefficients • Put answer in scientific notation • Round EXAMPLE: (4.2 x 104) + (7.9 x 103) You can do it different ways…
EXAMPLE: • (4.2 x 104) + (7.9 x 103) 4.2 x 104 + 0.79 x 104 4.99 x 104 =5.0 x 104 42 x 103 + 7.9 x 103 49.9 x 103 =50. x 103 =5.0 x 104
Convert from standard notation to scientific notation: • 0.0052 • 6 132 • 0.023 • 0.000 000 120 • 560 000 • 33 400 • 0.000 4120 • 38 000 000 000
Convert from scientific notation to standard notation • 7.050 X 103 • 4.000 05 X 107 • 2.350 X 104 • 1.5 X 10-3 • 2.105 X 10-2 • 7 X 1016 • 4.8 X 10-4 • 6.011 X 10-10
How many significant figures • 804.05 • 0.014 403 0 • 1002 • 10020 • 10020. • 400 • 30 000. • 30 000.0
How many significant figures • 0.000 625 000 • 6.02 x 1023 • 6.00 x 103 • 0.00001 • 0.00123 • 1.23 x 103 • 7430 • 0.006 700 0
Round to 3 significant figures • 0.000 625 500 • 2.7851 • 6.036 x 103 • 0.00001232 • 0.0012499 • 1.23 x 103 • 7435 • 0.006 752
Multiply or divide (how many sigfigs) • 3.20 X 102 m x 1.50 x 103 m • 2.5 x 10-3 m x 1.5 x 104 m • 1.54 X 102 L 2 x 101 min d. 2.0 x 10-2 min
Add or subtract/how many sigfigs • 2.48 X 102 kg + 9.17 X 103 kg = • 7.70 X 10-1 mL- 7.2 X 10-2mL=