WARM UP!!! 5,783,000,000 0.0000154 1.23 x 107 2.34 x 10-4 Making Scientific Notation By Mr. Mckoy The back and forth of Scientific Notation. What is Scientific Notation? Scientific Notation is a way to write very large or very small numbers
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Presentation Transcript
01
WARM UP!!! 5,783,000,000
0.0000154
1.23 x 107
2.34 x 10-4<br>
02
Making Scientific Notation By Mr. Mckoy
The back and forth of Scientific Notation.<br>
03
What is Scientific Notation? Scientific Notation is a way to write very large or very small numbers into a more readable form.
A number is expressed in scientific notation when it is in the form:
a x 10n
Where a is between 1 and 10 and n is an integer.<br>
04
How to make Scientific Notation? Turning a number from Standard Form to Scientific Notation takes 2 steps.
Move the decimal to the left or right until only one non-zero integer is to the left of the decimal. This will be your number between 1 and 10.
Count the places the decimal moved, this will be the n in 10n. If the original number was bigger then one, n will be positive. If the original number is smaller then one, then n is negative.<br>
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How to go back to Standard Form? Going from Scientific Notation to Standard Form is also a two step process.
Rewrite the number alone, if theres a positive exponent write the number to the left, if a negative exponent write the number to right of your problem.
Move the decimal the same number of places as in the n of 10n. If n is positive move the decimal to the right, if n is negative move the decimal to the left. Add zeros in empty places.<br>
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Examples. 1,230,000 = 1.23 x 106
0.00056 = 5.6 x 10-4
5.7 x 105 = 570,000
4.6 x 10-9 = 0.0000000046<br>
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Tips and Tricks. Remember, if you move the decimal to the left you will increase n in 10n. If you move the decimal to the right you will decrease n in 10n.
This is the same for making scientific notation or remaking standard form numbers.<br>
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Operations with Scientific Notation By Mr. Mckoy
A review and more.<br>
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STANDARD MCC8.EE4:
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.
Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.<br>
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Adding and Subtracting To add or Subtract, the exponent must be the same.
STEPS!!!
Increase the smaller exponent to make it equal to the larger exponent.
Move the decimal point of the number with the smaller exponent to the left the same number of places you increased the exponent.
Add or subtract the numbers, keep the exponent.
Check the answer, make sure its in proper scientific notation.<br>
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Adding and Subtracting Lets make a flow map with the steps.
QUESTION: 1.5 x 105 + 2.2 x 104 STEP 1
2.2 x 104
becomes
2.2 x 105 STEP 2
2.2 x 105
becomes
0.22 x 105 STEP 3
+ 1.52 x 105
+ 0.22 x 105
_;1.72 x 105 STEP 4
1.72 x 105 Increase the smaller exponent Move the decimal by the same amount Add the numbers keep the exponent Check for proper Scientific notation.<br>
12
Multiply and Divide Multiplying and dividing is easy, no converting needed.
STEPS!!!!
Multiply or divide your numbers.
Multiply or divide your exponents.
Check the answer, make sure its in proper scientific notation.
Remember your exponent rules for multiplying and dividing.<br>
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Multiply and Divide Lets make a flow map with the steps.
QUESTION: 4.5 x 105 times 6.1 x 103 STEP 1
4.5 x 6.1
equals
27.45 STEP 2
105 x 103
equals
10(5+3) = 108 STEP 3
27.45 x 108
becomes
2.745 x 109 Multiply or divide the numbers. Multiply or divide the exponents. Change to proper Scientific notation.<br>
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Practice! Makes Perfect! 3.4 x 108 + 5.1 x 106
5.1 x 106 become 5.1 x 108
5.1 x 108 becomes 0.051 x 108
3.4 x 108
)+0.051 x 108
3.451 x 108<br>
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Practice! Makes Perfect! 1.7 x 104 – 2.3 x 105
1.7 x 104 become 1.7 x 105
1.7 x 105 becomes 0.17 x 105
2.30 x 105
)–0.17 x 105
2.13 x 105<br>
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Practice! Makes Perfect! 3.3 x 103 times 1.3 x 105
3.3 x 1.3
3.3 x 1.3 = 4.29
103 x 105
103 x 105 = 10(3 + 5) = 108
Recombine to get 4.29 x 108<br>
17
Practice! Makes Perfect! 4.2 x 106 divided by 2.1 x 104
4.2 / 2.1
4.2 / 2.1 = 2
106 / 104
106 / 104 = 10(6-4) = 102
