Transcript Scientific Notation Shorthand method of writing very large

Opener:
• When you’re taking notes, if you have to write
the same big word or words over and over
again….do you write it out every time? How
do you make it quicker?
• If some random person looked at your notes
would they be able to read them? Why or
why not?
Scientific Notation
Shorthand method of writing very large and very
small numbers based on powers of 10
For example:
432600000000 = 4.326 x 1011
0.00000000134 = 1.34 x 10-9
The decimal goes after the first whole number
The superscript tells you how many decimal places
to move, and in what direction.
7.3x104 = 7.3 x 10,000 = 73,000
• (to write the number out longhand, the
decimal point moved 4 places to the right)
•
9.4x10 -3 = 9.4 x 0.001 = 0.0094
• ( to write the number out longhand, the
decimal point moved 3 places to the left)
• Practice
• Write the following numbers in scientific notation;
94,320,000,000
469,000,000,000,000,000,000
0.000000000948 (9 zeros after the decimal)
0.0000643
• Write the following numbers out the long way;
7.14 x 106
8.96 x 10 -4
3.41 x 10 3
1.81 x 10 -5
Math with exponents
When adding and subtracting numbers with
exponents, you must first convert all numbers
to have the same exponent.
1)
2.81x107 + 4.32x108 =
0.281x108 + 4.32x108 =
4.601x108
2)
9.32x1021 - 1.54x1020 =
2)
9.32x1021 - 1.54x1020 =
9.32x1021 - 0.154x1021 =
2)
9.32x1021 - 1.54x1020 =
9.32x1021 - 0.154x1021 =
9.166x1021
When multiplying numbers with exponents, you
simply multiply the coefficients and add the
exponents.
3)
(1.21x1014 )(3.42x1012) =
(1.21 x 3.42) x10(14+12) =
4.14x1026
When dividing numbers with exponents, you
divide the coefficients and subtract the
exponents.
4)
7
(4.19x10 )
/
3
(2.16x10 )
(4.19/2.16) x10(7-3) =
1.94x104
=
Now you try a few…
8.46x109 +
1.23x1011 =
14
9.84x10
15
6.18x10
-
6
4
(2.91x10 )(4.33x10 )
=
7.94x1010 ∕ 3.24x103 =
=
Closer:
• List the steps involved in
multiplying two numbers that
have exponents.
• How would those steps change
if you were dividing the
numbers instead?