Practice: a) 27.68 cm –14.369 cm = b) 6.54 m x 0.37 m = c) 40.8 m2 ¸ 5.050 m =

Practice: Raw Math Value Sig. Fig. Value a) 27.68 cm –14.369 cm = 13.311  13.31 b) 6.54 m x 0.37 m = 2.4198  2.4 c) 40.8 m2 ¸ 5.050 m = 8.07921  8.08

Warm-Up Convert 97.0 miles to km. Convert 86 µL to ML. Convert 980 fluid ounces to kL. (Hint: there are 29.6 mL in 1 fl. oz)

1. Convert 97.0 miles to km. 97.0 mi 1.609 km = 156.073  1 mi 156 km

2. Convert 86 µL to ML. 86.0 µL 10-6 ML = 0.0000000000860 106 µL ML

3. Convert 980 fluid ounces to kL. 980 floz 29.6 mL 10-3 kL = 0.029 kL 1 fl oz 103 mL

Monday, August 27th or Tuesday, Aug 28th, 2018 Scientific Notation Monday, August 27th or Tuesday, Aug 28th, 2018

Scientific Notation Scientific notation is way of writing numbers that are too big or too small to be conveniently written in decimal form Think about our last worksheet, measurements and conversions. Wasn’t it exhausting writing all those zeroes? Didn’t some of you lose points because you forgot a zero?

Rules for Scientific Notation To be in proper scientific notation the number must be written with * a number between 1 and 10 * and multiplied by a power of ten 23 X 10 5 is not in proper scientific notation. Why?

1. Move the decimal to the right of the first non-zero number. To write a number in scientific notation: 1. Move the decimal to the right of the first non-zero number. 2. Count how many places the decimal had to be moved.

To write a number in scientific notation: 3. If the you started with was small, the exponent is negative. 4. If the you started with was big, the exponent is positive.

60,000 = 6 x 104 98,000,000 = 9.8 x 107 8657 = 8.657 x 103 250 = 36,700 = 99,000,000,000 = BIG Examples! 10 x 10 x 10 x 10 x 10 x 10 (1 with 6 zeroes) (“move the decimal point 6 over”).

10 x 10 x 10 x 10 x 10 x 10 (1 with 6 zeroes) (“move the decimal point 6 over”).

Convert each from scientific notation into standard/long form or vice versa 4,000 2.48 X 103 6.123 X 106 306,000,000 5.70 x 105 Try These

Convert each from scientific notation into standard/long form or vice versa 4x103 2480 6123000 3.06x108 570000 Answers

0.02 = 2 x 10-2 0.0065 = 6.5 x 10-3 0.0000708 = 7.08 x 10-5 0.25 = 0.0036 = 0.00007001 = small Examples! 10 x 10 x 10 x 10 x 10 x 10 (1 with 6 zeroes) (“move the decimal point 6 over”).

Why does a Negative Exponent give us a small number? 10000 = 10 x 10 x 10 x 10 = 104 1000 = 10 x 10 x 10 = 103 100 = 10 x 10 = 102 10 = 101 1 = 100 Do you see a pattern?

Convert each from scientific notation into standard/long form or vice versa 0.00873 3.48 X 10-4 0.156 0.00000099 5.70 x 10-6 Try These

Convert each from scientific notation into standard/long form or vice versa 8.73x10-3 0.000348 1.56x10-1 9.9x10-7 0.00000570 Answers

Convert each from scientific notation into standard/long form or vice versa 10,003 9.57 x 10-7 1.6 x 103 507,000,000 0.0001 3.301 x 105 6.1 x 1010 1.8 x 10-9 10,000,000,000 0.0045

ANSWERS 1.0003x104 0.000000957 1600 5.07x108 1x10-4 330100 61000000000 0.0000000018 1x1010 4.5x10-3

Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105) Multiplication When multiplying numbers written in scientific notation…..multiply the first factors and add the exponents. Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105) Solution: Multiply 3.2 x 2.1. Add the exponents -3 + 5 Answer: 6.7 x 102

Sample Problem: Divide (6.4 x 106) by (1.7 x 102) Division Divide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator. Sample Problem: Divide (6.4 x 106) by (1.7 x 102) Solution: Divide 6.4 by 1.7. Subtract the exponents 6 - 2 Answer: 3.8 x 104