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 miles

Step 1 93,000,000 = 9.3000000 Move decimal left Leave only one significant number in front of the decimal 93,000,000 = 9.3000000

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

Step 3 7 93,000,000 = 9.3 x 10 Count how many places you moved decimal Make that your power of ten The power of ten is the letter “E” (exponential) for your calculators. 93,000,000 = 9.3 x 10 7

The power of ten is 7 because the decimal moved 7 places. 7 93,000,000 = 9.3 x 10 7

93,000,000 - Standard Form 9.3 x 107 - Scientific Notation 4567 x 10-5 - Scientific Notation .04567 - Standard Form

What if it has a decimal? .000,000,043 --- Standard Form Move the decimal to the right after the first significant (not a zero) number. .000,000,043 --- Standard Form 4.3 x 10-8 - Scientific Notation

Practice Problems Write in scientific notation or standard form. 1.) 9.85 x 10-4? = 2.) 64,100,000,000 = 3.) 2.79 x 10-6 = 4.) 431,200,000 = 5.) .000,0496= .000,985 6.41 x1010 .000,00279 4.31 x 108 4.96 x 10-5

More Practice Problems On these, decide where the decimal will be moved. 734,000,000 = ______ x 108 .000,000,000,870 = ______x 10-10 90,000,000,000 = _____ x 1010 Answers 7.34 x 108 2) 8.70 x 10-10 3) 9.0 x 1010

Complete Practice Problems Write in scientific notation . 50,000 7,200,000 .000,000,802 Answers 1) 5.0 x 104 2) 7.2 x 106 3) 8.02 x 10-7

Scientific Notation to Standard Form Move the decimal to the right 3.4 x 105 in scientific notation 3.40000 --- move the decimal ---> 340,000 in standard form

Move the decimal to the right. Write in Standard Form Move the decimal to the right. 6.27 x 106 9.01 x 104 4.603 x 108 9.94 x 102 6,270,000 90,100 460,300,000 994

Write in Scientific Notation Move the decimal to the left. 3.89 x 10-7 3.872 x 10-6 8.940 x 10-3 4.931 x 10-3 23.8761 x 10-4 .000,000,389 .000,003,872 .00894 .004931 .00238761

Write in Scientific Notation 7.882 × 10-2 2.72338 × 10-6 1.18 × 105 8.72 × 104 2.786 × 10-5 6.64 × 10-7 4.5 × 102 7.41717 × 104 7.7 × 102 8.5 × 10-6 0.07882 = 0.000,00272338 = 118000 = 87200 = 0.000,02786 = 0.000,000664 = 450 = 74171.7 = 770 = 0.000,0085 =

1. What is this number in standard form? 6.73 x 10-6 6,730,000 0.00000673 0.0000673 673,000

2. When the exponent is positive you move the decimal to the: Left Right Top bottom

3. What does your calculator use to designate as a power of ten for scientific notation 10 P G E

4. Why is scientific notation important when dealing with astronomy? They want to They are really big numbers and they are lazy Planets and stars are really far away so using scientific notation makes it easier to record the numbers It helps with Inverse Square Law

5. Which of these numbers shows 1 million in scientific notation? 1 x 103 1 x 104 1 x 107 1 x 106

6. Changer 1204.6 in scientific notation? 1.2 x 103 120 x 10-2 12 x 102 1204 x 100

7. Change 17.8 in scientific notation? 1.78 x 102 1.78 x 101 1.78 x 10-1 1.78 x 10-2

8. Change 567,310 in scientific notation? 567 x 103 56.7 x 105 5.67310 x 105 5 x 106

9. Convert 8.36 x 102 in scientific notation? 83600 8360 836 836000

10. Convert 9.16 x 106 in scientific notation? 0.000000916 0.000916 9,160 9,160,000