Download Scientific Notation 9. 26 11. 7.3 x 10 12. 8.1 X 10 13

Scientific Notation
Please convert the following to scientific notation. (Please show your work!)
1. 34,000
2.0.000058
3.5,798
4.854,231
5.0.936421
6. 1,200,000
7. 0.285438563
8. 0.000000092
9. 26
Please convert the following to standard notation.
10.3.6x109
11. 7.3 x 10-3
12. 8.1 X 10-7
13. 4.9 x 1021
14. 9.4 x 102
15. 1.0 x 10-10
16. 5.5 x 10-8
17. 9.9 x 106
18. 2.8 x 10-27
Not only does scientific notation give us a way of\vriting very large and very
small numbers, it allows LIS to easily do calculations as \vell. Calculators are vel}' helpful
tools. but unless you can do these calculations without them, you can never check to see
if your answers make sense. Any calculation should be checked using your logic, so
don't just assume an answer IS correct. This page will ex.plain the rules for calculating
with scientific notation.
Rule for Multiplication :When you multiply numbers with scientific notation, multiply the
coefficients together and add the exponents. The base will remain 10.
Ex 1. Multiply (3.45 x 107) x (6.25 x 105)
first rewrite the problem as: (3.45 x 6.25) x (107 x 105)
Then multiply the coefficients and add the exponents: 21.5625 x 1012
Then change to correct scientific notation and round to correct significant digits:
2.16x1013
NOTE - we add one to the exponent because we moved the decimal one place
to the left.
Remember that correct scientific notation has a coefficient that is less than 10,
but greater than or equal to one.
Ex. 2. Multiply (2.33 x 10-6) x (8.19 x 103)
rewrite the problem as: (2.33 x 8.19) x (10-6 x 103)
Then multiply the coefficients and add the exponents: 19.0827 x 10-3
Then change to .~9rrect scientific notation and round to correct significant
digits: 1.91 x 10-2
Remember that -3 + 1 =: -2
,
I
Rule for Division - When dividing with scientific notation, divide the coefficients
and subtract the exponents. The base will rernain10.
Ex. 1 Divide 3.5 x 108 by 6.6 x 104
rewrite the problem as: 3.5 X 108
6.6 X 104
Divide the coefficients and subtract the exponents to get: 0.530303 x 104
Change to correct scientific notation and round to correct significant digits to
get: 5.3 x 103
Note - We subtract one from the exponent because we moved the decimal one
place to the right.
Show all work in the spaces provided. Leave your answer in proper scientific
notation, and round to the correct number of significant digits.
Calculate the following;
1) (6.8 X 103) x (4.54 X 106)
2) (2.0 X 10-1) x (8.5 X 105)
3) (4.42 X 10-3) x (4 X 10-2)
4) (3 x 106) x (7 x 10-7)
5) (9.2 X 10-3) / (6.3 X 106)
6) (2.4 x 106) / (5.49 x 10-9)
Rule for Addition and Subtraction- when adding or subtracting in scientific
notation, you must express the numbers as the same power of 10. This will often
involve changing the decimal place of the coefficient.
Ex. 1 Add 3.76 x 104 and 5.5 x 102
move the decimal to change 5.5 x 102 to 0.055 x 104
add the coefficients and leave the base and exponent the same: 3.76 + 0.055 =
3.815 x 104
following the rules for rounding, our final answer is 3.815 x 104
Rounding is a little bit different because each digit shown in the original problem
must be considered significant, regardless of where it ends up in the answer.
Ex. 2 Subtract (4.8 x 105) - (9.7 X 104)
move the decimal to change 9.7 x 104 to 0.97 x 105
subtract the coefficients and leave the base and exponent the same: 4.8 - 0.97 =
3.83x105
round to correct number of significant digits: 3.83 x 105,,'
Addition and Subtraction Examples
Show all work in the spaces provided. Leave your answer in proper scientific
notation, and round to the correct number of significant digits
Calculate the following;
1) (5.9 X 108) + (5.9 X 109)
2) (2.69 x 100) + (3.65 X 101)
3) (9.81 X 10-6) + (3.91 X 10-7)
4) (5.9 x 108) - (5.9 x 109)
5) (2.69 x 100) - (3.65 x 101)
6) (9.8 X 10-6) - (3.9 X 10-7)