Scientific Notation A shorthand way of writing large

Scientific Notation A short-hand way of writing large numbers without writing all of the zeros.

The Distance From the Sun to the Earth 93, 000

Step 1 • Move decimal left for numbers more than one and right for numbers less than one • Leave only one number in front of decimal 93, 000 = 9. 3000000

Step 2 • Write number without zeros 93, 000 = 9. 3

Step 3 • Count how many places you moved decimal • Make that numbers your power of ten 93, 000 = 9. 3 X 7 10

• If you move the decimal to the right, the exponent (power of ten) will be a negative number. Ex: 0. 00000345 = 3. 45 x 10 -6 • If you move the decimal to the left, the exponent (power of ten) will be a positive number. Ex: 280000000 = 2. 8 x 108

Practice Problem Write in scientific notation. Decide the power of ten. 1) 2) 3) 4) 98, 500, 000 = 9. 85 x 10? 0. 0000308 = 3. 08 x 10? 279, 000 = 2. 79 x 10? 0. 00000093 = 9. 3 x 10? 9. 85 x 107 3. 08 x 10 -5 2. 79 x 108 9. 3 x 10 -7

More Practice Problems On these, decide where the decimal will be moved. 1) 734, 000 = ______ x 108 2) 870, 000, 000 = ______x 1011 3) 0. 0000092 = _____ x 10 -10 1) 7. 34 x 108 2) 8. 7 x 1011 3) 9. 2 x 10 -10

Complete Practice Problems Write in scientific notation. 1) 50, 000 2) 7, 200, 000 3) 802, 000, 000 1) 5 x 104 2) 7. 2 x 106 3) 8. 02 x 1011

• Complete # 1 on your practice sheet.

Scientific Notation to Standard Form 1. Add zeros to your number to match the exponents 1) 3. 4 x 105 3. 40000 x 105 2. Move the decimal to the right if the exponent is positive, and to the left if the exponent is negative = 340, 000

Write in Standard Form 6 10 • 6. 27 x 4 • 9. 01 x 10 = 6, 270, 000 = 90, 100

• Complete # 2 on your practice sheet.

Significant Figures • A “significant figure” in a measured value is one that is known with certainty or can be reasonably estimated. How would you report the meter reading? How many significant figures does your answer have?

What time is it? • Someone might say “ 1: 30” or “ 1: 28” or “ 1: 27: 55” • Each is appropriate for a different situation • In science we describe a value as having a certain number of “significant digits”

Sig Fig Rules 1. Non-zero digits are always significant. 523. 7 has ____ significant figures 2. Any zeros between two significant digits are significant. 23. 07 has ____ significant figures 3. A final zero or trailing zeros in the decimal portion ONLY are significant. 3. 200 has ____ significant figures 2. 00 x 102 has ____ significant figures

• Complete # 3 and 4 on your practice sheet.

Adding and Subtracting The number of decimal places in the answers should be the same as in the measured quantity with the smallest number of decimal places. Examples: • a) 13. 64 + 0. 075 + 67 b) 267. 8 – 9. 36 13. 64 + 0. 075 + 67. 81 80. 715 267. 8 – 9. 36 258. 44

• Complete # 5 on your practice sheet.

Multiplication and Division The number of significant figures in the answer should be the same number of significant digits as the value with the fewest number of significant digits. Example 608. 3 x 3. 45 Sig figs in 608. 3? 4 3 Sig figs in 3. 45? 3 sig figs? So the answer will have ____ 608. 3 x 3. 45 = 2098. 635 = 2. 10 x 103

• Complete # 6 on your practice sheet.