Notes

Precision and accuracy, while related, are actually different.
Notice that these arrows are all over the target. There is not much consistency between them. They have low precision.
These arrows however, are grouped together. Even though they are not directly in the center of the target, there is not much change between each arrow so the precision would be high.
Accuracy
These arrows are all grouped together in a bunch, but they are far from the center of the target. They have low accuracy.
These arrows are grouped around the center of the target. They may not be very precise, but the accuracy is much higher.
What would the target look like if the arrows had high precision and high accuracy?
The amount of rounding can affect the accuracy of a number. For example, the distance between railroad rails on the Transcontinental Railroad was set at 4.70833 feet. What would happen if the distance between rails was rounded?
•4.7083 feet
•4.708 feet
•4.71 feet
•4.7 feet
•5 feet
The acceptable amount of rounding will depend on your situation. The Transcontinental Railroad probably found it acceptable to round to the tenth or hundredth place as those numbers are still very accurate.
Sienna is measuring a rectangular canvas on which she wants to paint. One side of the canvas is 11.4 inches long, and the shorter side is 8.3 inches. What is the area of the canvas, rounded appropriately?
Knowing that the canvas is a rectangle and the two different measurements makes this calculation very straightforward.
A = l • w
A = (11.4 inches)(8.3 inches)
A = 94.62 square inches
Look at all those numbers after the decimal point. More than we started with. Some of them can be rounded off.
Sienna had two measurements: 11.4 inches has three digits and 8.3 inches has two digits. These are referred to as significant figures (Significant digits can be used interchangeably.) Because the least number of significant figures in one of the measurements is two, the answer can have only two significant figures. This means it would be appropriate to round the answer to 95 square inches.
The numbers beyond the significant digits, namely the .62 are rounded off because we cannot be certain of their accuracy. We do not know how accurate Sienna was when measuring and her 8.4 inches could have actually been 8.44 inches or even 8.35 inches. Had she said the measurement was 8.40 inches, then it would have three significant digits.Charlie measured the sides of his math textbook and found that it was 12.4 inches by 10.50 inches by 1.75 inches. What is the volume of Charlie's textbook?
The volume of the textbook can be found by multiplying the three measurements together.
V = l • w • h
V = (12.4)(10.50)(1.75)
V = 227.85 cubic inches
The measurements 12.4 inches, 10.50 inches, and 1.75 inches have three, four, and three significant figures respectively. Therefore, the answer can only have three significant figures. It will be rounded to 228 cubic inches.
A rate is when one unit of measure changes in terms of another. The telltale sign you are dealing with a rate is the word “per”.
•Gallons per minute
•Assignments per week
•Calories per serving
There is some hidden structure to the name of the rate. The first unit of measure listed is the dependent variable. The second unit of measure is the independent variable. At times, these quantities are graphed on a coordinate grid.
The independent variable is graphed on the x-axis, while the dependent variable is graphed on the y-axis.Precision versus Accuracy
•High precision means that the data is grouped close together.
•High accuracy means that the data is near the expected value.
Example: If 200 soda bottles are tested for their sugar contents, and they vary on all sides of the listed amount but are close to the listed amount, then they would have high accuracy but low precision.
Rounding
Check the significant figures in the measurements given to choose the appropriate accuracy in answers.
Units of Measure
•When using descriptive modeling, make sure that the units of measure accommodate the situation. If a car is traveling across the United States, you would not want to measure distance in centimeters, but a larger distance measure such as miles would fit.
Rates of Measure
•Rates of measure involve two units of measure and typically the word “per”.
•One unit will be the dependent variable and will be graphed on the y-axis.
•The other unit will be the independent variable and wil be graphed on the x-axis. This is typically the unit after the word “per.”