Chapter 1. Section 3 Measurement. A. Scientific Notation a. A way of expressing a value as the product of a number between 1 and 10 and a power of 10. b. The goal of scientific notation is to make very large or very small numbers easier to work with.
A. Scientific Notation
a. A way of expressing a value as the product of a number between 1 and 10 and a power of 10.
b. The goal of scientific notation is to make very large or very small numbers easier to work with.
Ex. 3,000,000,000 = 3.0 X 109
Ex. 0.00086 = 8.6 X 10-4
c. To multiply numbers in scientific notation you multiply the numbers that appear before the multiplication sign and add the exponents.
Ex. (3.0 X 108m/s) X (5.0 X 102m)
= 15 X 1010 m = 1.5 X 1011m
d. To divide numbers written in scientific notation, you divide the numbers that appear before the exponential terms and subtract the exponents.
Ex. (1.5 X 1011m) / (3.0 X108m/s)
= (1.5/3.0) X1011-8s = .50 X 103s
=5.0 X 102s
B. SI Units of Measuring
a. A set of measuring units that scientists use
b. Stands for International System of Units
c. Base units are units that the SI system is built upon, there are seven of them.
d. Derived units are made from combinations of base units
e. SI Prefixes
f. Conversion Factors are a ratio of equivalent measurements that are used to convert a quantity expressed in one unit to another unit.
i. Mt. Everest = 8,848 m convert this to kilometers
1km/1000m x 8848 m = 8.848 km
k h d m d c m
C. Significant Figures
a. All the digits that are known in a measurement, plus the last digit that is estimated.
i. The precision of a calculated answer is limited by the least precise measurement used in the calculation.
ii. Ex. Mass = 34.73 g, Volume = 4.42 cm^3 find the density.
Density = mass / volume
= 34.73 g/ 4.42 cm^3
= 7.857466 g/cm^3
iii. The answer should only have three sig figs in it due to the volume only having three sig figs in it.
Therefore, the answer is 7.86 g/cm^3.
D. Measuring Temperature
a. A thermometer is an instrument that measures temperature.
b. Fahrenheit scale
i. Water freezes at 32 degrees f and boils at 212 degrees f
c. Celsius scale
i. Water freezes at 0 degrees c and boils at 100 degrees c.
i. 0 k refers to the lowest possible temperature that can be reached. This is currently -273.15 degrees c.
i. c = 5/9 (f – 32) f = 9/5 ( c ) + 32 k = c + 273