SCIENTIFIC NOTATION HANDOUT
SOLVING EQUATIONS - Solve for distance d
V=d
t
SCIENTIFIC NOTATION
Number (Regular Notation) to Scientific Notation – Step a.) Move the decimal point to the left leaving
only one number in front of it. 100 000 = 100 000 Count the number of places you moved the
decimal point. Step b.) Multiply the number from step a. times 10 raised to the + (positive) power of
the number of places you moved the decimal point. 1 x 10
Step a.) Move the decimal point to the right of the first nonzero digit. 0.000 05 = 0.000 05 Count the
number of places you moved the decimal point. Step b.) Multiply the number from step a. times 10
raised to the – (negative) power of the number of places you moved the decimal point. 5 x 10
(Use + if you moved the decimal to the left and - if you moved the decimal to the right)
40 000 000 = 40 000 000 = 4 x 10
99 999 = 99 999 = 9.999 9 x 10
1 900 000 = 1 900 000 = 1.9 x 10
1 800 000 = 1 800 000 = 1.80 x 10
0.000 000 19 = 0.000 000 19 = 1.9 x 10
0.000 060 = 0.000 060 = 6.0 x 10
-
0.900 19 = 0.900 19 = 9.001 9 x 10
-
-
Scientific Notation to Regular Notation - Step a.) If the exponent on the 10 is positive ("+"), move the
decimal to the right the same number of places as the exponent. Add zeros as necessary. Step b.) If the
exponents on 10 is negative ("-"), move the decimal point to the left the same number of places as the
exponent. Add zeros as necessary.
3.2 x 105 =
32 x 105 =
3.2 x 10-5 =
32 x 10-5 =
ADDITION & SUBTRACTION – simply add the numbers but only if the exponents are the same - if
exponents are the same not make them the same.
2.2 x 103 + 3.5 x 103 = ?
5.7 x 103
1.0 x 105 + 2.0 x 104 = ?
1.0 x 105 + 0.20 x 105 = 1.20 x 105
MULTIPLICATION - multiply the numbers and add the exponents
4 x 105 x 5 x 102 = ?
4 x 5 = 20
and 105 x 102 we add the exponents 5+2 = 7 which
gives us 107
putting them together 20 x 107 = 2 x 108
DIVISION - divide the numbers and subtract the exponents
2.0 x 105 / 4 x 107 = ?
10-2
2.0 / 4 = 0.5
putting them together 0.5 x 10-2 = 5 x 10-3
and 105 / 107 we subtract the exponents 5-7 = -2 which give us
Practice Problems – put the following in scientific notation.
1. 190 000 000 =
2. 400 =
3. 1 =
4. 0.000 028 =
5. 10.50 x 106=
6. 3.3 x 102 + 5.1 x 102 =
7. 5.8 x 108 + 5.2 x 108 =
8. 2.8 x 106 + 3.0 x 107 =
9. (2.0 x 106) x (3.1 x 102) =
10. (3.3 x 102) x (5.1 x 102) =
11. (2.3 x 103) x (3.1 x 10-9) =
12. (8.8 x 106) =
(2.2 x 102)
13. (9 x 10-6) =
(3 x 102)