Scientific Notation with positive powers of 10 Lesson 2.2 Mrs. Carley.
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Transcript of Scientific Notation with positive powers of 10 Lesson 2.2 Mrs. Carley.
![Page 1: Scientific Notation with positive powers of 10 Lesson 2.2 Mrs. Carley.](https://reader035.fdocuments.us/reader035/viewer/2022081418/5697bfed1a28abf838cb8e41/html5/thumbnails/1.jpg)
Scientific Notation
with positive powers of 10Lesson 2.2Mrs. Carley
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Definition of Scientific Notation
• Scientific notation is a method of expressing very large and very small numbers as a product of a number greater than or equal to 1 and less than 10 and a power of 10.
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Scientific Notation
A number is expressed in scientific notation when it is in
the form
a x 10n
where a is between 1 and 9
and n is an integer
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Example IWrite 4,776 in scientific notation
Place the decimal immediately to the right of the left-most non-zero number. This should give you a number between
one and ten.
4.776Count the number of digits between the old and the new
decimal point, this gives the power, n of 10 (10n).
4 776 X 103
Since the decimal is shifted to the left, the exponent is positive.
4.776 x 103
3 Digits
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Writing a number in Standard Notation
Example #2 Video
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Example #2Write 4.953 x 104 in standard form
Write the decimal number.
4.953Move the decimal the number of places specified by the powers of ten: to the right since it is positive.
X 104 4 9530Rewrite the number in integer/standard form.
49,530
4 Places
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Scientific notation with Negative Powers of 10
Lesson 2.3
Mrs. Carley
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RULES• Writing numbers in Scientific Notation
– When I move the decimal to the right the exponent is negative.
– When I move the decimal to the left the exponent is positive.
• Writing numbers in Standard Notation– When I move the decimal to the right, the
number is positive– When I move the decimal to the left, the
number is negative.– HINT: Think about the number line
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Example #1
• The average size of an atom is about 0.00000003 centimeters across. Write the average size of an atom in scientific notation.– Step 1: Place the decimal point– Step 2: Count the number of places you
moved the decimal point.– Step 3: Any time you move the decimal point
to the right….the exponent to the power of 10 is negative.
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Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
9.02The decimal was moved how many
places?8
When the original number is less than 1, the exponent is negative.
9.02 x 10-8
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Write 28750.9 in scientific notation.
1. 2.87509 x 10-5
2. 2.87509 x 10-4
3. 2.87509 x 104
4. 2.87509 x 105
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Write 531.42 x 105 in scientific notation.
1. .53142 x 102
2. 5.3142 x 103
3. 53.142 x 104
4. 531.42 x 105
5. 53.142 x 106
6. 5.3142 x 107
7. .53142 x 108
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Writing a Number in Standard Notation
Example #2
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Example #2Platelets are one component of human blood. A typical platelet has a diameter of approximately 2.33 x 10-6 in standard notation.
– Step1: Use the exponent to the power of 10 to see how many places to move the decimal point.
– Step 2: Place the decimal point. Since you are going to write a number less than 2.33, move the decimal point to the left. Add place holder zeros if necessary.
Answer: 0.00000233
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Another ExampleWrite 8.397 x 10-1 in standard form
Write the decimal number.
8.397Move the decimal the number of places specified by
the powers of ten: to the left since it is negative.
X 10-1 0 8 397Rewrite the number in integer/standard form.
0.8397
1 Place
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Express 1.8 x 10-4 in decimal notation.0.00018
Express 4.58 x 106 in decimal notation.
4,580,000
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Operations with Scientific Notation
Lesson 2.4
Mrs. Carley
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Adding/Subtracting Numbers
• Look at Example#1:– Step1: Write each number in standard
notation– Step2: Complete the operation – add/ subtract– Step3: Write the answer in scientific notation
• Complete #1 “Your Turn” on page 52.
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Multiplying Numbers in Scientific Notation
• Multiply: (5.1 * 104) x (2.3 * 106)1. Multiply the coefficients: 5.1 * 2.3 = 11.73
2. Add the powers of 10: 4+6 =10
3. Check to be sure the product is in scientific notation. (5.1 * 104) x (2.3 * 106) = 11.73 * 1010
• 1.173 * 1011
• Therefore, (5.1 * 104) x (2.3 * 106) = 1.173 * 1011
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Write (2.8 x 103)(5.1 x 10-7) in scientific notation.
1. 14.28 x 10-4
2. 1.428 x 10-3
3. 14.28 x 1010
4. 1.428 x 1011
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Dividing Numbers in Scientific Notation
• Divide (3.9 * 108)
(6.5 * 10-4)1. Divide the coefficients: 3.9 / 6.5 = 0.6
2. Subtract the powers of 10: 8 – (-4) = 12
3. Check to be sure the quotient is in scientific notation.
• (3.9 * 108) = 0.6 * 1012)
(6.5 * 10-4)
• 6.0 * 1011
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Example #2 Page 52
• Complete #2-3 “your Turn”