Transcript Scientific Notation

Scientific Notation
with positive powers of 10
Lesson 2.2
Mrs. Carley
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.
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
Example I
Write 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.
4.776
Count the number of digits between the old and the new
decimal point, this gives the power, n of 10 (10n).
4 776
3 Digits
X 103
Since the decimal is shifted to the left, the exponent is positive.
4.776 x
3
10
Writing a number in
Standard Notation
Example #2 Video
Example #2
Write 4.953 x 104 in standard form
Write the decimal number.
4.953
Move the decimal the number of places specified by the
powers of ten: to the right since it is positive.
X
4
10
4 Places
4 9530
Rewrite the number in integer/standard form.
49,530
Scientific notation with
Negative Powers of 10
Lesson 2.3
Mrs. Carley
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
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.
Express 0.0000000902 in
scientific notation.
Where would the decimal go to make the
number be between 1 and 10?
9.02
The decimal was moved how many
places?
8
When the original number is less than 1,
the exponent is negative.
9.02 x 10-8
Write 28750.9 in scientific
notation.
1.
2.
3.
4.
2.87509 x 10-5
2.87509 x 10-4
2.87509 x 104
2.87509 x 105
Write 531.42 x 105 in scientific
notation.
1.
2.
3.
4.
5.
6.
7.
.53142 x 102
5.3142 x 103
53.142 x 104
531.42 x 105
53.142 x 106
5.3142 x 107
.53142 x 108
Writing a Number in
Standard Notation
Example #2
Example #2
Platelets 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
Another Example
Write 8.397 x 10-1 in standard form
Write the decimal number.
8.397
Move the decimal the number of places specified by the
powers of ten: to the left since it is negative.
X
-1
10
1 Place
0 8 397
Rewrite the number in integer/standard form.
0.8397
-4
10
Express 1.8 x
in decimal
notation.
0.00018
Express 4.58 x 106 in decimal
notation.
4,580,000
Operations with Scientific
Notation
Lesson 2.4
Mrs. Carley
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.
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
Write (2.8 x 103)(5.1 x 10-7) in
scientific notation.
1.
2.
3.
4.
14.28 x 10-4
1.428 x 10-3
14.28 x 1010
1.428 x 1011
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)
(6.5 * 10-4)
• 6.0 * 1011
= 0.6 * 1012)
Example #2 Page 52
• Complete #2-3 “your Turn”