Ch 2 Flashcards
Scientists make many kinds of measurements
- The determination of the dimensions, capacity, quantity or extent of something
- Length, Mass, Volume, Density
All measurements have 2 parts
- A number
* A unit
Measurements
- are made relative to a standard
* have uncertainty
English System
- Common measurements
* Pints, quarts, gallons, miles, etc.
Metric System
Units in the metric system consist of a base unit plus a prefix.
Exact numbers
- Have no uncertainty associated with them
* They are known exactly because they are defined or counted
Measured numbers
Have some uncertainty associated with them
Accuracy
How closely a measurement comes to the true, accepted value
Precision
How closely measurements of the same quantities come to each other
Significant Figures
Are the digits in any measurement known with certainty, plus one digit that is uncertain.
Measured numbers convey
- Magnitude
- Units
- Precision
Because measurements are never exact, we must include
- The magnitude of the measurement and
* The uncertainty of the measurement
Significant Figures (sig figs)
- The numbers known with certainty plus one extra (uncertain or estimated) digit
- In other words, all digits in a (correctly-made) measurement are significant
Rules for Sig Figs
- All non-zero numbers in a measurement are significant.
- All zeros between sig figs are significant.
- In a number less than 1, zeros used to fix the position of the decimal are not significant.
- When a number has a decimal point, zeros to the right of the last nonzero digit are significant
- When a number without a decimal point explicitly shown ends in one or more zeros, we consider these zeros not to be significant. If some of the zeros are significant, bar notation is used.
Rounding off Numbers
The number of significant figures in measurements affects any calculations done with these measurements
Sometimes, the calculator will show more (or fewer) significant digits than it should
- If the first digit to be deleted is 4 or less, simply drop it and all the following digits
- If the first digit to be deleted is 5 or greater, that digit and all that follow are dropped and the last retained digit is increased by one
Adding Significant Zeros
Sometimes a calculated answer requires more significant digits. Then one or more zeros are added.
When multiplying or dividing, use
- The same number of significant figures in your final answer as the measurement with the fewest significant figures.
- Rounding rules to obtain the correct number of significant figures.
When adding or subtracting, use
- The same number of decimal places in your final answer as the measurement with the fewest decimal places (least precise measurement).
- Use rounding rules to adjust the number of digits in the answer.
If you have both addition/subtraction and multiplication/division in a formula,
- carry out the operations in parenthesis first, and round according to the rules for that type of operation.
- complete the calculation by rounding according to the rules for the final type of operation.
Scientific notation
Is used to write very large or very small numbers
In scientific notation
All digits including zeros in the coefficient are significant
Calculations in Scientific Notation
- The significant figures are those in the coefficient
* Usually, numbers in scientific notation will be multiplied or divided
Conversion factors
A ratio that specifies how one unit of measurement is related to another
Dimensional Analysis
A problem solving method in which the units (associated with numbers) are used as a guide in setting up the calculations.
The Steps of Dimensional Analysis
- Write the unit you have to start out with on the left hand side of the page
- Write the units you want on the right hand side of the page
- Look for a conversion factor that contains both the units you start with and the units you want in the end
- Multiply the number on the left by the conversion factor with the units you want on the top and the units you start with on the bottom.
- Make sure your units cancel out.
What if you don’t have a conversion factor between the units you have and the units you want?
Try to create a chain of conversion factors from the units you have to units you want
Density
A ratio of the mass of an object divided by its volume
Density = Mass/Volume
