Scientific Notation
What is Scientific Notation?
Scientific notation is a way of expressing really big numbers or really small numbers.
It is most often used in “scientific” calculations where the analysis must be very precise.
Why use scientific notation?
For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form.
Numbers expressed in scientific notation makes it easier to solve problems with big and small numbers.
Scientific notation consists of two parts:
A number between 1 and 10
A power of 10
N x 10x
Are the following in scientific notation?
Changing standard form to scientific notation.
To change standard form to scientific notation…
Place the decimal point so that there is one non-zero digit to the left of the decimal point.
Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.
Continued…
If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.
When changing from Standard Notation to Scientific Notation:
See if the original number is greater than or less than one.› If the number is greater than one, the
exponent will be positive.
348943 = 3.489 x 105
› If the number is less than one, the exponent will be negative.
.0000000672 = 6.72 x 10-8
When using Scientific Notation, there are two kinds of exponents: positive and negative
Positive Exponent:2.35 x 108
Negative Exponent:3.97 x 10-7
The Distance From the Sun to the Earth
93,000,000
Step 1
Move decimal left Leave only one number in front of
decimal
Step 2
Write number without zeros
Step 3
Count how many places you moved decimal
Make that your power of ten
The power often is 7 becausethe decimalmoved 7 places.
93,000,000 --- Standard Form
9.3 x 107 --- Scientific Notation
Practice Problem
1) 98,500,000 = 9.85 x 10?
2) 64,100,000,000 = 6.41 x 10?
3) 279,000,000 = 2.79 x 10?
4) 4,200,000 = 4.2 x 10?
Write in scientific notation. Decide the power of ten.
9.85 x 107
6.41 x 1010
2.79 x 108
4.2 x 106
More Practice Problems
1) 734,000,000 = ______ x 108
2) 870,000,000,000 = ______x 1011
3) 90,000,000,000 = _____ x 1010
On these, decide where the decimal will be moved.
1) 7.34 x 1082) 8.7 x 1011
3) 9 x 1010
Complete Practice Problems
1) 50,0002) 7,200,0003) 802,000,000,000
Write in scientific notation.
1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011
Example 1
Given: 289,800,000 Use: 2.898 (moved 8 places) Answer: 2.898 x 108
Example 2
Given: 0.000567 Use: 5.67 (moved 4 places) Answer: 5.67 x 10-4
Try Build a Bridge
#1
#2
Try changing these numbers from Standard Notation to Scientific Notation:
1) 9872432
2) .0000345
3) .08376
4) 5673
9.872432 x 106
3.45 x 10-5
8.376 x 102
5.673 x 103
Changing scientific notation to standard form.
To change scientific notation to standard form…
Move the decimal point to the right for positive exponent 10.
Move the decimal point to the left for negative exponent 10.
(Use zeros to fill in places.)
An easy way to remember this is: If an exponent is positive, the
number gets larger, so move the decimal to the right.
If an exponent is negative, the number gets smaller, so move the decimal to the left.
Scientific Notation to Standard Form
Move the decimal to the right
3.4 x 105 in scientific notation
340,000 in standard form
3.40000 --- move the decimal
Example
Given: 5.093 x 106
Answer: 5,093,000 (moved 6 places to the right)
Example
Given: 1.976 x 10-4
Answer: 0.0001976 (moved 4 places to the left)
Write in Standard Form
6.27 x 106
9.01 x 104
6,270,000 90,100
Try changing these numbers from Scientific Notation to Standard Notation:
1) 9.678 x 104
2) 7.4521 x 10-3
3) 8.513904567 x 107
4) 4.09748 x 10-5
96780
.0074521
85139045.67
.0000409748
Try Build a Bridge
#3
#4
Guided PracticeHomework: Practice
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