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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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Objective 1.To write very large or very small numbers in standard form, in scientific notation, and vice versa. To compare and order numbers in scientific.

Objective 1.To write very large or very small numbers in standard form, in scientific notation, and vice versa. To compare and order numbers in scientific.

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