MEASUREMENT

Chapter One: Measurement 1.1 Measurements 1.2 Time and Distance 1.3 Converting Measurements 1.4 Working with Measurements

1.1 Measurements A measurement is a determination of the amount of something. A measurement has two parts: a number value and a unit

1.1 Two common systems The English System is used for everyday measurements in the United States. Miles, yards, feet, inches, pounds, pints, quarts, gallons, cups, and teaspoons are all English system units. In 1960, the Metric System was revised and simplified, and a new name was adopted— International System of Units.

1.1 International System of Measurement (SI) The acronym SI comes from the French name Le Système International d’Unités. SI units form a base-10 or decimal system. In the metric system, there are: 10 millimeters in a centimeter, 100 centimeters in a meter, and 1,000 meters in a kilometer.

1.1 The meter stick A meter stick is 1 meter long and is divided into millimeters and centimeters.

1.1 The meter stick Each centimeter is divided into ten smaller units, called millimeters. What is the length in cm?

1.2 Time and Distance Two ways to think about time: What time is it? How much time? A quantity of time is also called a time interval.

1.2 Time Time comes in mixed units. Seconds are very short. For calculations, you may need to convert hours and minutes into seconds. How many seconds is this time interval?

1.2 Distance Distance is the amount of space between two points. Distance is measured in units of length. The meter is a basic SI distance unit. In 1791, a meter was defined as one ten-millionth of the distance from the North Pole to the equator. What standard is used today?

1.2 Metric prefixes Prefixes are added to the names of basic SI units such as meter, liter and gram. Prefixes describe very small or large measurements.

1.3 Converting units To convert 1,565 pennies to the dollar amount, you divide 1,565 by 100 (since there are 100 pennies in a dollar). Converting SI units is just as easy as converting pennies to dollars.

Convert 655 mm to m Looking for: Given: Relationships: Solution: Solving Problems Convert 655 mm to m Looking for: …the distance in meters Given: …distance = 655 millimeters Relationships: Ex. There are 1000 millimeters in 1 meter Solution: 655 mm = .655 meters

Convert 142 km to m Looking for: Given: Relationships: Solution: Solving Problems Convert 142 km to m Looking for: …the distance in meters Given: …distance = 142 kilometers Relationships: Ex. There are ? meters in 1 kilometer? Solution: Use the conversion tool.

Convert 754,000 cm to km Looking for: Given: Relationships: Solution: Solving Problems Convert 754,000 cm to km Looking for: …the distance in kilometers Given: …distance = 754,000 centimeters Relationships: Ex. There are ? cm in 1 m? There are ? m in 1 km? Solution: Use the conversion tool.

1.3 Converting units A conversion factor is a ratio that has the value of one. This method of converting units is called dimensional analysis. To do the conversion you multiply 4.5 feet by a conversion factor.

Convert 4.5 ft to cm Looking for: Given: Relationships: Solution: Solving Problems Convert 4.5 ft to cm Looking for: You are asked for the distance in cm Given: You are given the distance in ft. Relationships: Ex. There are ? cm in 1 ft? 30.48 cm = 1 ft Solution: Make a conversion factor from equivalent

1.3 Converting units Use the correct conversion factor to convert: 175 yds. to m. 2.50 in. to mm.

1.4 Working with Measurements Accuracy is how close a measurement is to the accepted, true value. Precision describes how close together repeated measurements or events are to one another.

1.4 Working with Measurements In the real world it is impossible for everyone to arrive at the exact same true measurement as everyone else. Find the length of the object in centimeters. How many digits does your answer have?

1.4 Working with Measurements Digits that are always significant: Non-zero digits. Zeroes between two significant digits. All final zeroes to the right of a decimal point. Digits that are never significant: Leading zeroes to the right of a decimal point. (0.002 cm has only one significant digit.) Final zeroes in a number that does not have a decimal point.

What is area of 8.5 in. x 11.0 in. paper? Looking for: Given: Solving Problems What is area of 8.5 in. x 11.0 in. paper? Looking for: …area of the paper Given: … width = 8.5 in; length = 11.0 in Relationship: Area = W x L Solution: 8.5 in x 11.0 in = 93.5 in2 # Sig. fig = 94 in2

1.4 Working with Measurements Using the bow and arrow analogy explain how it is possible to be precise but inaccurate with a stopwatch, ruler or other tool.

1.4 Resolution Resolution refers to the smallest interval that can be measured. You can think of resolution as the “sharpness” of a measurement.

1.4 Significant differences In everyday conversation, “same” means two numbers that are the same exactly, like 2.56 and 2.56. When comparing scientific results “same” means “not significantly different”. Significant differences are differences that are MUCH larger than the estimated error in the results.

1.4 Error and significance How can you tell if two results are the same when both contain error (uncertainty)? When we estimate error in a data set, we will assume the average is the exact value. If the difference in the averages is at least three times larger than the average error, we say the difference is “significant”.

1.4 Error How you can you tell if two results are the same when both contain error. Calculate error Average error Compare average error

Is there a significant difference in data? Looking for: Given: Solving Problems Is there a significant difference in data? Looking for: Significant difference between two data sets Given: Table of data Relationships: Estimate error, Average error, 3X average error Solution: Math answer: 93.5 in2 Determine # of significant figures = 94 in2