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Bell Ringer • 90 • 4-2 • 3x-3y2 Scientific Notation Mr. Haupt CC.2.2.8.B.1 Why all the big numbers?!?!?! • Speed of light = 299,792,458 meters per second • Distance from sun to earth = 92,960,000 miles • 1 light year = 6,000,000,000 miles • Mass of the sun = 1,989,000,000,000,000,000,000,000,000,000 kg How can we shorten this up? • Scientific Notation • The crazy idea that we don’t have to write huge numbers out over and over. • We turn the number into decimals with only one number to the left of the decimal, and the rest of your significant figures to the right. • Then we multiply that decimal by 10 to whatever power it would take to move the decimal to where it belongs in the original number. For example • Mass of the sun = 1,989,000,000,000,000,000,000,000,000,000 kg • Take the significant figures 1989 and make it a decimal. • 1.989 • Then figure out how many decimal places you moved to get the decimal from its original spot. • In this case, it is 30. • So my answer is 1.989 x 1030 Positive and Negative Exponents • If the original number is a decimal then the power on the ten will be negative. • If the original number is a whole number, the ten will have a positive power. • For example: • 0.00000000456 = 4.56 x 10-9 • 234,000,000 = 2.34 x 108 Turn it back • What if we have the scientific notation and want to change it to its original form? • Write out the significant figures, and then move the decimal as many places, in whatever direction, the ten power tells you. • For example: • 7.56 x 105 2.61 x 10-8 Multiplying Scientific Notation • Multiply the numbers given but ignore the tens and their powers for the moment. • Add the powers on the tens. • Adjust the answer if necessary. • For eexample: • (4.12 x 103)(3.51 x 104) (2.89 x 10-2)(3.02 x 10-5)