Name: SCIENTIFIC NOTATION
Uploaded: 2022-02-11
Duration: 9 min 11 s
Description: SCIENTIFIC NOTATION. A QUICK WAY TO WRITE REALLY, REALLY BIG OR REALLY, REALLY SMALL NUMBERS..

SCIENTIFIC NOTATION. A QUICK WAY TO WRITE REALLY, REALLY BIG OR REALLY, REALLY SMALL NUMBERS.. 

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A QUICK WAY TO WRITE  REALLY, REALLY  BIG  OR   REALLY, REALLY  SMALL   NUMBERS.

Mathematicians are Lazy!!!. They decided that by using powers of 10, they can create short versions of long numbers.. 

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They decided that by using powers of 10, they can create short versions of long numbers.

Rules for Scientific Notation. To be in proper scientific notation the number must be written with * a number between 1 and 10 * and multiplied by a power of ten 23 X 10 5 is not in proper scientific notation. Why?. 

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To be in proper scientific notation the number must be written with 	* a number between 1 and 10 	* and multiplied by a power of      ten       23 X 10 5   is not in proper scientific notation.  Why?

The number 4,500 is written in scientific notation as ________________.. 

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The number 4,500 is written in scientific notation as ________________.

The coefficient must be a number  greater than or equal to 1 and smaller than 10.

The power of 10 or exponent in this example is ______.

The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4,500.

If a number is greater than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation.. 

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If a number is greater than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation.

If a number is less than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation.. 

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If a number is less than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation.

1. Move the decimal to the right of the first non-zero number.. 

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1.  Move the decimal to the right of the first non-zero number.

2.  Count how many places the decimal had to be moved.

3.  If the decimal had to be moved to the right, the exponent is negative.

4.  If the decimal  had to be moved to the left, the exponent is positive.

To write a number in scientific notation:

So......... 137,000,000 can be rewritten as 1.37 X 10 8. 

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137,000,000 can be rewritten as  1.37 X 10 8

Using scientific notation, rewrite the following numbers.. 

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Using scientific notation, rewrite the following numbers.

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4,000. 4 X 103. Try These. 2.48 X 103. 2,480. 

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In the United States, 15,000,000 households use private wells for their water supply. Write this number in scientific notation.. 

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In the United States, 15,000,000 households use private wells for their water supply.  Write this number in scientific notation.

The U.S. has a total of 1.2916 X 107 acres of land reserved for state parks. Write this in standard form.. 

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The U.S. has a total of 1.2916 X 107 acres of land reserved for state parks.  Write this in standard form.

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Why does a Negative Exponent give us a small number ?. 

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Why does a Negative Exponent give us a small number ?

10000 =   10 x 10 x 10 x 10 =  10 4      1000   =   10 x 10 x 10 =  10 3   100     =   10 x 10 =  10 2 	10      =    10 1            1    =    10 0   Do you see a pattern?

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Using Scientific Notation,. Your Turn. rewrite the following numbers.. 

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1) 0.0004. 4 X 10-4. More Examples. 2) 1.248 X 10-6. 

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A ribosome, another part of a cell, is about 0.000000003 of a meter in diameter. Write the length in scientific notation.. 

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A ribosome, another part of a cell, is about 0.000000003 of a meter in diameter.  Write the length in scientific notation.

Scientists must be able to use very large and very small numbers in mathematical calculations. As a student in this class, you will have to be able to multiply, divide, add and subtract numbers that are written in scientific notation. Here are the rules.. 

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Using  Scientific Notation in Multiplication, Division, Addition and Subtraction

Scientists must be able to use very large and very small numbers in mathematical calculations.  As a student in this class, you will have to be able to multiply, divide, add and subtract numbers that are written in scientific notation.  Here are the rules.

When multiplying numbers written in scientific notation….. multiply the first factors and add the exponents.. 

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When multiplying numbers written in scientific notation….. multiply the first factors and add the exponents.

Sample Problem:  Multiply (3.2 x 10 -3 ) (2.1 x 10 5 )

Solution:  Multiply 3.2 x 2.1.    Add the exponents -3 + 5

Divide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator.. 

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Divide the numerator by the denominator.  Subtract the exponent in the denominator from the exponent in the numerator.

Sample Problem:  Divide (6.4 x 10 6 ) by (1.7 x 10 2 )

Solution:  Divide 6.4 by 1.7.    Subtract the exponents 6 - 2

To add or subtract numbers written in scientific notation, you must…. express them with the same power of ten.. 

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To add or subtract numbers written in scientific notation, you must…. express them with the same power of ten.

Sample Problem:  Add (5.8 x 10 3 ) and (2.16 x 10 4 )

Solution:  Since the two numbers are not expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other. 5.8 x 10 3  =  .58 x 10 4       so .58 x 10 4  + 2.16 x 10 4  =?