Download Scientific Notation

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)