Download Scientific Notation – Rewriting Exponents

Scientific Notation – Rewriting Exponents
A number in scientific notation sometimes needs to be written from one exponent into
another.
Example:
4x1010 * 6x1010 = 24x1020 But… this should not be our final answer. It does not fit our
general format for scientific notation because the coefficient of 24 is not from 1<10.
We need to slide the decimal back 1 place to 2.4 and that means we need to change the
exponent, because 24x1020 is not the same as 2.4x1020.
24x1020 = 2400000000000000000000… = 24and 20 zeros
2.4x1020= 240000000000000000000… = 24 and 19 zeros
Therefore, we have to add one to the exponent to represent the correct standard number.
24x1020 = 2.4x1021 (Count out the decimal places and compare and you’ll see that they
represent the same standard number.)
If you are asked to rewrite from one exponent into a new specific exponent, there is a rule
that you can follow. It goes like this.
“Old exponent – New exponent = What to do with the decimal”
Example 1:
Rewrite 24x1020 into _______________ x1021
(Old exponent -New exponent) 20 – 21 = -1 (What to do with the decimal)
The decimal moves 1 place to the left (+ right, - left) in the coefficient of the new exponent.
24 x 1020 = 2.4 x 1021
Example 2:
Rewrite 3.88 x 1022 = _____________ x 1019
3.88 x 1022 = 3880 x 1019
22-19 = 3 Move the decimal 3 to the right.
Rewrite each of the following into the new exponent.
4.045x109
= __4045_____________ x106
3.4x10-7
= __.34_____________ x10-6
.098x10-5
= ___9.8____________ x10-7
500x104
= ___5____________ x106
1.234x1011
= ____1234___________ x108
Here is a nice worksheet with background of scientific notation and calculations
http://www.ieer.org/clssroom/scinote.html
Here is a site with some nice drill problems
http://science.widener.edu/svb/tutorial/scinot.html
Scientific Notation - Calculations
When multiplying numbers in scientific notation, you multiply the coefficients and ADD
the exponents.
Example:
2x10 4 multiplied by 4x10 5
Multiply the coefficients to get your new coefficient
Add exponents
2x4=8
4+5=9
Your answer is 8x10 9
When dividing numbers in scientific notation, you divide the coefficients and
SUBTRACT the exponents in the order of the problem.
Example:
9x10 9 divided by 3x10 4
Divide the coefficients to get your new coefficient
Subtract exponents in order
9/3 = 3
9–4=5
Your answer is 3x10 5
Important! If you subtract a negative, it becomes a positive. 10 - 4 / 10 – 6 = 10 2
- 4 – (-6) is the same as - 4 +6 and they both = 2)
Do the following scientific notation calculations. * means multiply, / means divide
2.3x1012 * 3x1013
= _____6.9x1025_________________________
4.44x1020 / 2x1010
= ____2.22x1010__________________________
4.44x1020 * 2x1010
= ______8.88x1030________________________
4x1030 * 5x10 12
= _______20x1042_______________________
1.8x1040 / 9x1010
= ________.2x1030______________________
4.44x1020 / 2x10-10
= ________2.22x10-2______________________
2.3x10-12 * 3x1013
= ________6.9x10-156______________________
1.8x1040 / 9x10-10
= ________.2x10-4______________________
6.42x10-28 / 2x1012
= 3.21x10-2.3 repeating______________________