Download 3-1 SCIENTIFIC NOTATION

CHEMISTRY 11
Scientific Notation
Numbers in scientific notation are written such that only one non-zero digit is to the left of the decimal. Ex: 3.81
If the number contains more than one non-zero digit to the left of the decimal, the decimal place moves such as to
make the number or the coefficient only one digit. The exponent is then changed in order to compensate for this. The
exponent goes up by the number of decimal places that the coefficient had to move.
Ex: 381 can be written 381.0 X 100 . It becomes 3.81 X 102 in scientific notation.
If the number is very small and has zeros before the first non-zero digit, the decimal is moved to the right. The
exponent compensates by decreasing.
Ex: 0.00381(written 0.00381 X 100) becomes 3.81 X 10-3 in scientific notation.
If there already is an exponent, but the coefficient is not in scientific notation, the exponent changes in order to
compensate for the moving decimal place.
Ex: 381.00 X 102 can be written as 3.81 X 104 in scientific notation.
Ex: 0.00381 X 10-3 can be written as 3.81 X 10-6 in scientific notation.
1. Change the following into scientific notation.
e.g. 0.003201 = 3.201 x 10-3
a) 0.000582 _______________________________________________
b) 937200 __________________________________________________
c) 279.820 X 10-3____________________________________________
d) 0.00005787 X 10-3_________________________________________
e) 3860.04220 X 103_________________________________________
f) 0.00211 X 102____________________________________________
2. Convert each of the following to its non-exponential form maintaining the proper number of significant digits.
e.g. 1.30 x 10-2= 0.0130 (keep 3 sig digits)
a) 9.447 x 102 =
f) 1.00 x 10-2
=
b) 1.720 x 10
=
g) 4.628 x 10-1 =
c) 5.040 x 10-2 =
h) 6.50 x 10-3
=
-2
d) 3.8 x 10
=
i) 9.08 x 105
=
e) 2.19 x 10-4
=
j) 7.060 x 10-2 =
3. Multiplication & Division of scientific notation: the exponents are added or subtracted.
(keep smallest # of sig digits)
e.g. 2.2 x 10-1 x 5.6 x 102 = 123.2  1.2 x 102 expressed to 2 sig digits
e.g. (1.0 x 10-5)  (9.3 x 10-2)=1.1 x 10-4
a) 1.4 x 10 -3 x 3.4 X 10-1
=
b) (799 X 10-2 )  (8 X 10-4)
=
c) (3.42 X 10-1) x (4.9 X 10-1) =
d) (421 X 1026)  (86 X 1028) =
4. Evaluate each of the following to the correct number of significant digits.
a)
(1.26 x 102)(8.3 x 103)
=
-6
-2
b)
(2.81 x 10 )(3.162 x 10 )
=
c)
(5.25 x 108)(8.9 x 10-3)
=
d)
(5.25 x 108)(8.90 x 10-3)
=
e)
(7.50 x 105) / (2.76 x 102)
=
f)
g)
(7.50 x 10-6 / 2.76 x 10-4)
(9.070 x 102)(2.00 x 105) / (5.67 x 103)
=
=
h)
(9.070 x 105)(2.00 x 10-3) / (5.67 x 104)
=
5. Addition & Subtraction of numbers.
a) 1.39 X 10-2 + 3.39 X 10-1
=
b) 7.99 X 10-2 - 8.32 X 10-4
=
c) 3.42 + 4.89 X 10-1
=
d) 4.21 X 1026 + 8.65 X 1028 =