Transcript Week 17 Warm-up - Great Rivers Cooperative

Scientific and standard notation,
conversion
What is Scientific Notation
A number expressed in scientific notation is
expressed as a decimal number between 1 and 10
multiplied by a power of 10 (eg, 7000 = 7 x 103 or
0.0000019 = 1.9 x 10 -6)
Why do we use it?
It’s a shorthand way of writing very large or very
small numbers used in science and math and
anywhere we have to work with very large or very
small numbers.
Scientific and standard notation, conversion
Scientific Notation: expressing a number in the form
n
c x 10 , where 1 < c < 10.
Examples: Are the following numbers written
in scientific notation?
6
3
a. 42 x 10
b. 9.3 x 10
No, 42 is
Yes
greater than 10
Examples: Write in scientific notation:
a.
236,000
b.
0.04325
Move the decimal left or right so that c is between
1 and 10. Count the # of places you moved.
2.36 x 10
c.
0.000725
7.25 x 10
-4
5
4.325 x 10
–2
Example: Write in decimal notation:
–3
a. 2.45 x 10
To change from scientific notation back to
decimal notation, move the decimal n of places,
where n is the power of 10.
0.00245
8
b. 1.38 x 10
138,000,000
Scientific Notation Cornel Notes
Ex. 6800
Changing from Standard
Notation to Scientific Notation
Scientific Notation Cornel Notes
Ex. 6800
6800
3 2 1
Changing from Standard
Notation to Scientific Notation
1. Move decimal to get
a number between 1 &
10 and count places
moved.
Scientific Notation Cornel Notes
Ex. 6800
6800
3 2 1
68 x
3
10
Changing from Standard
Notation to Scientific Notation
1. Move decimal to get
a number between 1 &
10 and count places
moved.
2. Answer is a
number between 1 &
10 times the power of
ten ( places moved).
Ex. 6800
6800
3 2 1
68 x
3
10
Changing from Standard
Notation to Scientific Notation
1. Move decimal to get
a single digit # and
count places moved
2. Answer is a single
digit number times
the power of ten of
places moved.
If the decimal is moved left the power is positive.
If the decimal is moved right the power is negative.
Try This
Ex. 720,000
Changing from Standard
Notation to Scientific Notation
Try This
Ex. 720,000
720000
5 4 3 2 1
Changing from Standard
Notation to Scientific Notation
1. Move decimal to get
a single digit # and
count places moved.
Try This
Ex. 720,000
720000
5 4 3 2 1
72 x
5
10
Changing from Standard
Notation to Scientific Notation
1. Move decimal to get
a single digit # and
count places moved.
2. Answer is a
number between 1 &
10 times the power of
ten (# of places
moved.
Scientific Notation Cornel Notes
Ex. 4.5 x 10-3
Changing from Scientific
Notation to Standard Notation
Ex. 4.5 x
00045
3 2 1
Changing from Scientific
-3
10
Notation to Standard Notation
1. Move decimal the same
number of places as the
exponent of 10.
(Right if Pos. Left if Neg.)
Try This
Ex. 8.9 x 105
Changing from Scientific
Notation to Standard Notation
Try This
Ex. 8.9 x 105
890000
1 2 3 4 5
Changing from Scientific
Notation to Standard Notation
1. Move decimal the same
number of places as the
exponent of 10.
(Right if Pos. Left if Neg.)
2.0 x
102
+ 3.0 x
103
.2 x 103 + 3.0 x 103
= .2+3 x 103
= 3.2 x 103
Addition and subtraction
Scientific Notation
1. Make exponents of 10 the same
2. Add 0.2 + 3 and keep the 103 intact
The key to adding or subtracting numbers
in Scientific Notation is to make sure the
exponents are the same.
2.0 x 107 - 6.3 x 105
2.0 x 107 -.063 x 107
= 2.0-.063 x 107
= 1.937 x 107
1. Make exponents of 10 the same
2. Subtract 2.0 - .063 and
keep the 107 intact
Changing from Standard
Notation to Scientific Notation
Ex. 6800
6800
1. Move decimal to get
a single digit # and
count places moved
3 2 1
68 x 10
2. Answer is a single
digit number times
the power of ten of
places moved.
3
Ex. 4.5 x 10-3
Changing from Scientific
Notation to Standard Notation
00045
1. Move decimal the same
number of places as the
exponent of 10.
3 2 1
(Right if Pos. Left if Neg.)
9.54x107 miles
If the decimal is moved left the power is positive.
If the decimal is moved right the power is negative.
1.86x107 miles
per second
What is Scientific Notation
(3 x 104)(7 x 10–5)
Multiply two numbers
in Scientific Notation
= (3 x 7)(10 4 x 10–5)
1.
= 21 x 10-1
2.
3.
4.
= 2.1 x 10 0
or 2.1
Put #’s in ( )’s Put
base 10’s in ( )’s
Multiply numbers
Add exponents of 10.
Move decimal to put
Answer in Scientific
Notation
A number expressed in scientific notation is
expressed as a decimal number between 1 and 10
multiplied by a power of 10 e( g, 7000 = 7 x 103 or
0.0000019 = 1.9 x 10 -6)
Why do we use it?
It’s a shorthand way of writing very large or very
small numbers used in science and math and
anywhere we have to work with very large or very
small numbers.
2.0 x 10 2 + 3.0 x 103
6.20 x 10–5
8.0 x 103
6.20
8.0
= 0.775 x
10-5
103
10 -8
= 7.75 x 10–9
DIVIDE USING SCIENTIFIC
NOTATION
.2 x 10 3 + 3.0 x 103
= .2+3 x 103
= 3.2 x
1.
2.
Scientific
Notation
Makes
These
Numbers
Easy
Divide the #’s &
Divide the powers of ten
(subtract the exponents)
Put Answer in Scientific
Notation
103
Addition and subtraction
Scientific Notation
1. Make exponents of 10 the same
2. Add 0.2 + 3 and keep the 103 intact
The key to adding or subtracting numbers
in Scientific Notation is to make sure the
exponents are the same.
2.0 x 10 7 - 6.3 x 105
2.0 x 10 7 -.063 x 107
= 2.0-.063 x 10 7
= 1.937 x 10 7
1. Make exponents of 10 the same
2. Subtract 2.0 - .063 and
keep the 107 intact