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

The Distance From the Sun to the Earth 93,000,000

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 93,000,000 =

Step 2 Write number without zeros 93,000,000 = 9.3

Step 3 Count how many places you moved decimal Make that numbers your power of ten 93,000,000 = 9.3 X 10 7

If you move the decimal to the right, the exponent (power of ten) will be a negative number. Ex: = 3.45 x If you move the decimal to the left, the exponent (power of ten) will be a positive number. Ex: = 2.8 x 10 8

Practice Problem 1)98,500,000 = 9.85 x 10 ? 2) = 3.08 x 10 ? 3)279,000,000 = 2.79 x 10 ? 4) = 9.3 x 10 ? Write in scientific notation. Decide the power of ten x x x x 10 -7

More Practice Problems 1)734,000,000 = ______ x )870,000,000,000 = ______x ) = _____ x On these, decide where the decimal will be moved. 1)7.34 x ) 8.7 x ) 9.2 x

Complete Practice Problems 1)50,000 2)7,200,000 3)802,000,000,000 Write in scientific notation. 1) 5 x ) 7.2 x ) 8.02 x 10 11

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 x 10 5 = 340, Move the decimal to the right if the exponent is positive, and to the left if the exponent is negative

Write in Standard Form 6.27 x x 10 4 = 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. 2. Any zeros between two significant digits are significant. 3. A final zero or trailing zeros in the decimal portion ONLY are significant has ____ significant figures has ____ significant figures 2.00 x 10 2 has ____ significant figures has ____ significant figures 200 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) b) – – + +

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 x 3.45 Sig figs in 608.3? 4 Sig figs in 3.45? 3 So the answer will have ____ sig figs? x 3.45 = = 2.10 x 10 3

Complete # 6 on your practice sheet.