The History of Measurement

Measurement One of the steps of the scientific methods involves making observations. An observation is information gathered by our five senses.

Types of Observations There are two types of observations: Qualitative Observations Quantitative Observations

Qualitative Observations involve describing the properties of an object using words.

Examples of Qualitative Observations The fire engine is red. The fire engine is big. The fire engine is shiny. The fire engine has silver doors on the side.

Your Qualitative Observations Make and record five Qualitative Observations about yourself.

Quantitative Observations Quantitative Observations involve measurements. A measurement includes a number and a unit.

Physical Properties The following physical properties can be measured: Length Width Height Mass Temperature Viscosity Density Etc.

History of Measurement Objects were measured to aid commerce. Many early measurements were based on body parts.

The Cubit A cubit is the distance from your elbow to the tip of your middle finger.

Span A span is the distance between the thumb and the little finger while the hand is outstretched.

Palm A palm is the width of the closed hand.

A digit is the distance across the index finger.

Body Part Measurement Practice Measure the following using the unit indicated: Length of the room in: Cubits Spans Length of the textbook in: Digits Palms

Problems with Body Part Measurments Body part measurements are not accurate when dealing with fractions of body parts. People have different sized body parts. The ratio of cubit to span may be different for different people.

Standard Systems of Measurement Standard Systems are based on some standard to measure against. Early standard systems often used body parts of the king or ruler as the standard distance. When the king died, a new measurement system would be created.

Imperial System of Measurement 1 foot = average length of a man’s foot 1 yard = average length of a legionaire’s stride 1 inch = width of a thumb

Imperial System Conversions 12 inches = 1 foot 3 feet = 1 yard 1760 yards = 1 mile 1 league = 3 miles 6 feet = 1 fathom 22 yards = 1 chain

How many inches in 2.5 leagues? 2.5 x 3 x 1760 x 3 x 12 =

The Metric System In 1799, Napoleon commissioned a survey to find the length from the equator to the North Pole. One ten-millionth of this distance was defined as a metre. Conversions from one unit to another were all done by factors of 10.

SI Units of Measurement: The Seven Base Units Name Symbol Unit of metre m length kilogram kg mass second s time ampere A electric current kelvin K thermodynamic temperature mole mol amount of substance candela cd luminous intensity

Your Quantitative Observations Make and record 5 metric quantitative observations about yourself.

Accuracy and Precision There are a number of ways that errors can be made during measurements. The Accuracy of a measurement is how close the measurement is to the “true value.” The Precision of a measurement is the number of digits in the measurement. i.e. 1.78 m versus 1.781232243 m The first is precise to three “Significant Digits” while the second is precise to 10 “Significant Digits.” The smallest digit is 3 billionths of a metre, almost a thousand times smaller than width of a human hair.

Significant Digits The significant digits in a number must indicate the precision of a measurement. 250 kg has two significant digits as the zero may only be a placeholder. 0.0250 kg has three significant digits. If we didn’t write down the zero on the right, the value would be the same. We must have written it down for a reason. 205 kg has three significant digits. Zeros with other non-zero numbers on both sides must be part of the precision of the measurement. Any time a zero is used as a placeholder, it is assumed not to be part of the accuracy. 2.50 kg has three significant digits.

Scientific Notation Scientific notation has a number been 1.0 and 9.999999999 that is multiplied by an exponent of 10. 2.50× 10 4 kg has 3 significant digits.