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When scientists deal with very large numbers, it’s hard to keep track of place values! How far? miles
It is hard with very small numbers, too! How wide is an atom? meters wide!
Scientific notation consists of two parts: A number between 1 and 10 A number between 1 and 10 A power of 10 A power of 10 N x 10 x
We use Short hand ! 100 = 10 x 10 1,000 = 10 x 10 x ,000 = 10 x 10 x 10 x 10 x 10 10,000 = 10 x 10 x 10 x 10 1,000,000 = 10 x 10 x 10 x 10 x 10 x one googol !!!
Standard Form 200 = 2 x 100 4,000 = 4 x ,000 = 5 x 100,000 70,000 = 7 x 10,000 3,000,000 = 3 x 1,000,000 Scientific Notation
Add the decimal point A short cut Between 1 and 10 The point moved 6 places Move the point to get a number between 1 and 10
Add the decimal point Between 1 and 10 The point moved 7 places Move the point to get a number between 1 and 10 A short cut
Try for yourself: Turn Standard Form into Scientific Notation (1) (2) (3) (4) (5)
=346,000 Zeros after the point aren’t needed. The point moves 5 places Hint: Add 5 zeros, although you probably won’t need them all. Changing back
=86,000,000 Zeros after the point aren’t needed. The point needs to move 7 places Hint: Add 7 zeros, although you probably won’t need them all. Changing back
Try for Yourself: Change Scientific Notation back to Standard form (1) (2) (3) (4) (5) = = = = =
The point moved 10 places. Negative sign for small numbers. Move the point to get a number between 1 and 10 Standard Form to Scientific Form for SMALL numbers
The point moved 7 places. Negative sign for small numbers. Move the point to get a number between 1 and 10 Standard Form to Scientific Notation for small numbers
Standard Form to Scientific Notation for small numbers The point moved 6 places. Negative sign for small numbers. Move the point to get a number between 1 and 10
Try for Yourself: Change Standard Form to Scientific Notation (1) (2) (3) (4) (5)
= Hint: Add 3 zeros to the left of the number. -3 so remember to move point left 3 spaces.. Changing back small numbers
= Hint: Add 5 zeros to the left of the number. -5 so remember to move point left for small numbers. Changing back small numbers
= Hint: Add 6 zeros to the left of the number. -6 so remember to move point left for small numbers.
(1) (2) (3) (4) (5) = = = = = Try for Yourself: Change Scientific Notation to Standard form
Very large numbers! BOOM! How far? miles.
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