Download Scientific Notation Calcs 272

Unit 1/Chem 272
- Calculating in Scientific Notation
Rules for calculating are the same as for algebraic expressions.
Multiplication: When multiplying numbers written in scientific notation, multiply the
first factors and add the exponents. Round your final answer to the correct significant
figures.
Ex. (3.2 x 10-3) x (2.1 x 105)= 6.7 x 102
(2.3 x 105)(5.0 x 10-12) = 11.5 x 10-7 = 1.2 x 10-6
(5.1 x 10-6)(2 x 10-3) = 10.2 x 10-9 = 1 x 10-8
(3 x 105)(6 x 103) = 18 x 108 = 2 x 109
Division: When dividing numbers divide factors then subtract the exponent in the
denominator from the exponent in the numerator. Round your final answer to the correct
significant figures.
Ex. 6.4 x 106 divided by 1.7 x 102 = 3.8 x 104
(1.5 x 103) / (5.0 x 10-2) = 0.3 x 105 = 3.0 x 104
Addition and Subtraction:
When adding or subtracting numbers in scientific notation they must be expressed with
the same power of 10. Round your final answer to the correct number of decimal places.
1.8 x 103 + 2.16 x 104 =
4.5 x 10-7 - 3.6 x 10-8 =
Rewrite numbers to make both powers the same –
.18 x 104
+ 2.16 x 104
= 2.34 x 104
4.5 x 10-7
- .36 x 10-7
4.1 x 10-7
Solve the following:
a. (3.7 x 102)(5.1 x 103) =
___________________
b. (7 x 10-3)(1.2 x 109) =
___________________
c. (3.6 x 102) / (4.8 x 108) =
___________________
d. (2.3 x 10-3) / (4.6 x 10-6) =
___________________
e. (9.67 x 102) + (8.5 x 103) = ___________________
f. 2.07 x 10-5 - 8.08 x 10-6 =
___________________
Chem 272/Unit 1
Scientific Notation Calculations
Express the answers to each of the following calculations in scientific
notation using the correct number of significant figures.
1.
(6 000000000000000 m)(7 000 000 000 000 000 000 m)
2.
(0.000 000 000 000 000 800 cm)(3 000 000 000 000 000 000 000 000 000 000 000 cm)
(40 000 000 000 000 000 000 000 000 000 000 cm)
3.
(8.0 x 103 m)(3.00 x 105 m)(2.000 x 104 m)
4.
(3.00 x 104 cm) (4.00 x 10-5 cm)
(1.000 x 10-6 cm)(6.00 x 10-3 s)
5.
(3000 m) (3.0 x 104 m) (0.000 004 m)
(2.0 x 10-1 m)(6 000 000 s)
6.
(2.0 x 104 m) (3.0 x 105 m)
(6.000 x 10-4 m)
7.
(6.0 x 103 cm)(400 000 cm)(2 cm)(0.000 000 002 cm)
(8.0 x 10-7 cm)(2.00 x 10-5 cm)(1000 cm)
8.
(4.0 x 108 m)(2.000 x 108 m)(3.0 x 10-4 m)(2 x 107 m)
(8 x 10-4 m)(6.00000 x 10-5 m)(1.00 x 104 m)
9.
(8.0 x 103 m) + (3.00 x 105 m) + (2.000 x 104 m)
10.
{(2.0 x 104 m) - (3.0 x 105 m)}
(6.000 x 10-4 m)