You have had this since 5th or sixth grade... but check out the links at the bottom of these notes
Powers of ten provide a convenient way to write very large numbers. You restate very big numbers or very small numbers using powers of ten in exponential form. Numbers that are expressed as products of two factors
(1) a number greater than or equal to 1, but less than 10,
AND
(2) a power of ten
are said to be written in scientific notation.
We can write 'a number greater than or equal to 1, but less than 10' as an mathematical inequality 1 ≤ n < 10 To write a number in scientific notation we move the decimal point to the left until the resulting number is between 1 and 10. We then multiply this number by the power of 10, whose exponent is equal to the number of places we moved the decimal point. 4,592,000,000 in scientific notation First move the decimal point to the left to get a number between 1 and 10 4,592,000,000 the first factor in scientific notation becomes 4.592 Since the decimal point was moved 9 places, we multiply 4.592 by 109 to express the number in scientific notation
4.592 x 109 (Yes, you get to use the × symbol for multiplication .. but only for this!!
5,900,000,000 was given as the population of the world in 1998. I wonder what it is now? Anyone find out?
Anyway to write that large number in scientific notation it would be the product of two factors 5.9 and a power of ten
5.9 X 109
It is a way to write very large numbers AND very small numbers
Numbers expressed as products of a number greater than or equal to 1 BUT less than 10, AND a power of ten are called Scientific Notation.
Two Factors
91) 1≤ n < 10 (2) Power of 10 4,592,000,000 becomes 4.592 X 109
moved the decimal 9 places so we must multiply our number by a power of 109
98,000,000 = 9.8 X 107
320,000 = 3.2 X 105
What if I give you 7.04 X 108 and ask you to put it back into STANDARD NOTATION:
704,000,000.
0.0000207
0.0031 = 3.1 X 10-3
It isn't a negative number its just a very tiny number
1≤ n < 10 0.16 becomes 1.6 x 10 -1
0.0000207 becomes 2.07 X 10 -5
0.000345 becomes 3.45 X 10 -4
We also changed scientific notation back into standard notation ( the regular number)
9.32 X 10 -2 becomes 0.0932
we practiced some more
14,500 first we changed the number into something that fit the first factor 1 ≤ n < 10
so that becomes 1.45
Then we need to figure out how many places we moved the decimal
1.45 X 104
that works!
73,000,000 = 7.3 X 107
63,500 = 6.35 X 104
Write 3.45 X 104 into standard notation
34, 500
What happens if you are given 1/8000 this is a fraction and we need to change it to a decimal BEFORE we can write it in scientific notation
1/8000 = 0.000125
so it is
1.25 X 10-4
suppose you are multiplying two scientific notation numbers-- you do NOT need to change them into standard notation
(2.5 X 103 )(4.4 X10-5).
We found that it was
11 X 10-2
But 11 isn't 1 ≤ n < 10 so we need to change 11 into scientific notation
that alone is 1.1 X 101
Now we have 1.1 X 101 X 10-2
so 1.1 X 10-1 interesting
(6.2 X102 )( 8 X103) = (6.2)(8) X 102 X103 and
49.6 X 105 but 49.6 isn't in scientific notation
so
49.6 becomes 4.96 X101
4.96 X 101 X105 is
4.96 X 106
So
Try
(9.1 X 10-1 ) ( 5.4 X107)
(9.1)(5.4) X 10-1 X 107
So
49.14 X 106 and again 49.14 isn't in scientific notation
changing just 49.14 into scientific notation we get 4.914 X 101
so we have
4.914 X101 X 106
which
is
4.914 X 107
List from least to greatest
3.4 X 10-4 3.4 X 10-5 and 3.4 X 10-6
We noticed that the -6 exponent would be a smaller number-- when we wrote it in standard form so
3.4 X 10-6 < 3.4 X 10-5 < 3.4 X 10-4 would be the listing
Check out the following links:
this one takes you from huge numbers to teeny tiny ones
this one lets you practice scientific notation
this one lets you practice multiplying scientific notation
this one lets you practice dividing sn
this one lets you practice even harder ones!
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