Understanding Scientific Notation and Big Numbers in Mathematics
Learn about scientific notation, how to shorten large numbers, positive and negative exponents, converting notation to original form, and multiplying numbers in scientific notation. Discover a simpler way to work with huge numerical values in mathematics.
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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)
