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Scientific Notation

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**When scientists deal with very large numbers, it’s hard to keep track of place values!**

How far? miles

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**It is hard with very small numbers, too!**

How wide is an atom? meters wide!

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**Scientific notation consists of two parts:**

A number between 1 and 10 A power of 10 N x 10x

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**We use Short hand ! one googol !!! 10 100 = 10 x 10**

1,000 = 10 x 10 x 10 10,000 = 10 x 10 x 10 x 10 100,000 = 10 x 10 x 10 x 10 x 10 1,000,000 = 10 x 10 x 10 x 10 x 10 x 10 one googol !!!

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**Standard Form Scientific Notation**

200 = 2 x 100 4,000 = 4 x 1000 70,000 = 7 x 10,000 500,000 = 5 x 100,000 3,000,000 = 3 x 1,000,000 Scientific Notation

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**A short cut 8 000 000 . . Move the point to get a**

number between 1 and 10 The point moved 6 places . . Add the decimal point Between 1 and 10

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**A short cut 92 000 000 . . Move the point to get a**

number between 1 and 10 The point moved 7 places . . Add the decimal point Between 1 and 10

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**Try for yourself: Turn Standard Form into Scientific Notation**

(1) (2) (3) 5 300 (4) (5)

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**Add 5 zeros, although you probably won’t need them all.**

Changing back The point moves 5 places 3.46 00000 . =346,000 Hint: Add 5 zeros, although you probably won’t need them all. Zeros after the point aren’t needed.

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**Add 7 zeros, although you probably won’t need them all.**

Changing back The point needs to move 7 places 8.6 . =86,000,000 Zeros after the point aren’t needed. Hint: Add 7 zeros, although you probably won’t need them all.

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**Try for Yourself: Change Scientific Notation back to Standard form**

(1) (2) (3) (4) (5) = = 8 000 = = =

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**Standard Form to Scientific Form**

for SMALL numbers Move the point to get a number between 1 and 10 . The point moved 10 places. Negative sign for small numbers.

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**Standard Form to Scientific Notation**

for small numbers Move the point to get a number between 1 and 10 . The point moved 7 places. Negative sign for small numbers.

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**Standard Form to Scientific Notation**

for small numbers Move the point to get a number between 1 and 10 . The point moved 6 places. Negative sign for small numbers.

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**Change Standard Form to Scientific Notation**

Try for Yourself: Change Standard Form to Scientific Notation (1) (2) (3) (4) (5)

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**Changing back small numbers Add 3 zeros to the left of the number.**

Hint: Add 3 zeros to the left of the number. -3 so remember to move point left 3 spaces. 000 . 2 = 0.002 .

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**Changing back small numbers Add 5 zeros to the left of the number.**

-5 so remember to move point left for small numbers. Hint: Add 5 zeros to the left of the number. 00000 . 8.6 =

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**Changing back small numbers Add 6 zeros to the left of the number.**

-6 so remember to move point left for small numbers. Hint: Add 6 zeros to the left of the number. 000000 . 5.16 =

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**Change Scientific Notation to Standard form**

Try for Yourself: Change Scientific Notation to Standard form (1) (2) (3) (4) (5) = = = = =

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