Transcript Scientific Notation - Ms. Nigro's Classroom

Scientific Notation
Scientific Notation
Why do we use scientific notation?
Because in science we often deal with numbers which are
ridiculously large or unimaginable small.
For example:
Scientific Notation
How many stars are in an average spiral galaxy?
Answer: At least 200 Billion stars.
or
200,000,000,000,000 stars.
Scientific Notation
What is the distance between the electron and the nucleus of
an atom?
Answer: .0000000001 meters.
Scientific Notation
It is not practical for us to work with numbers written as:
200,000,000,000 or .0000000001
So, we have come up with a way of dealing with these large
and small numbers.
And its called…
Scientific Notation.
Correct Scientific Notation
M x
Mantissa
A number from one
to less than ten.
Ex: 1.3, 3.4, 5.26
n
10
Exponent (Order of Magnitude)
+ Positive for numbers greater than 1
- Negative for numbers less than 1
Scientific Notation
Converting Large numbers to Scientific Notation.
Example:
1,500,000 m
Mantissa = 1.5
Exponent = 6, for 6 decimal places, and positive
1.5 x 106 m
Scientific Notation
Converting Small numbers to Scientific Notation.
Example:
0.000025 A
Mantissa = 2.5
Exponent = -5, 5 for 5 decimal places, and negative
2.5 10-5 A
Scientific Notation
The following two numbers are equal, however only one is
expressed correctly. Which one?
17.5 x 105 m = 1.75 x 106
Answer: 1.75 x 106 m,
the mantissa is a number from 1 - 10
Scientific Notation
Special Case No. 1:
1
1 x 100 = _______
Remember, the exponent tells us how much to move
the decimal.
In this case the exponent is zero. So, the decimal
remains where it is.
Scientific Notation
Special Case No. 2:
10
1 x 101 = _______
101 is like writing a word in shorthand or an abbreviation.
It is implied that there is a “1 x” before the 101.
Scientific Notation
Convert the following to scientific notation.
5.0 x 10-3
0.005 = ______________
2.5 x 10-1
0.25 = _______________
5.050 x 103
5,050 = ______________
2.5 x 10-2
0.025 = ______________
8 x 10-4
0.0008 = _____________
2.5 x 10-3
0.0025 = _____________
1 x 103
1,000 = ______________
500 = _______________
5 x 102
1 x 106
1,000,000 = __________
5,000 = ______________
5 x 103
Scientific Notation
Convert the following to standard notation.
1,500
1.5 x 103 = __________________
.335
3.35 x 10-1 = __________________
.0015
1.5 x 10-3 = ____________
.00012
1.2 x 10-4 = _____________
.0375
3.75 x 10-2 = _________________
10,000
1 x 104 = _______________________
375
3.75 x 102 = ___________________
.1
1 x 10-1 = ________________________
220,000
2.2 x 105 = ____________________
4
4 x 100 = _______________
Homework Answers













Part A
1) 104
2) 10-3
3) 108
4) 3 x 107
5) 4.35 x 1011
6) 1.09 x 108
7) 6.78 x 107
8) 9 x 103
9) 6.02 x 10-1
10) 2.3 x 10-5
11) 5.43 x 101
12) 5.60 x 10-10













Part B
1) 1,000,000
2) .00001
3) 100,000,000,000
4) .0004
5) .0000067
6) 823,000,000
7) .00000001476
8) 7,680
9) .00004356
10) 2.85
11) 9,680,000,000,000
12) .000967