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What is measurement?
Measurement is the process of comparing a standard unit to some unknown. When you measure your height, you might use a meter stick and compare that to your body.
To have valid comparisons, standardized units must be agreed on. It wouldn't work if your 'meter' was a different length than the one I use. This is just as true if we are measuring volume, or weight or time. Comparisons only work with standard sized units and much of the mathematics in measurement involved changing from one standard unit into another.
For instance, one standard used to measure temperature is degrees Celsius. Another is degrees Fahrenheit. Both are used to measure the same thing, temperature, and with conversion factors (a type of mathematics used in measurement) we can convert from one to the other.
How is measurement used in the real world?
Getting measurements wrong can have dire consequences. In 1999 a mars orbiter was lost because of a mistake in measurement. NASA was using the metric system and a contractor had used the English system (inches, feet, yards) for a key component. The result of the mismatch was that a $125 million orbiter was turned into space junk.
Accuracy is so important that we no longer even rely on a real ruler for the standard. Measurements are now defined with physical constants - for instance the meter is defined as the distance light travels (in a vacuum) in 1/299,792,458 second.
A basic problem in measurement.
How many kilometers is the same as 10 miles?
This is solved by knowing two conversion factors: one mile = 1,609.344 meters and 1000 meters = 1 kilometer. To use these, we multiply 10 miles by 1,609.344 to get 16,093.44 meters and then divide that by 1000 to get 16.09344 kilometers.
This is much more accurate a number than we probably need, so the answer would probably be rounded to 16 kilometers.
Who invented measurement?
The word measurement comes from the Greek word metron which means some part of a whole. This makes sense if you think of cutting up something into countable units, which is what a measurement is. (A 12 inch ruler can be cut up into 12 inch-long pieces.)
Long before the Greeks, Ancient Egyptians had a standard unit of length they called the cubit. A cubit is based on the length of a forearm, but you can see how forearms might vary from person to person. This is similar to how the foot was first defined and can cause confusion.
Because accurate measurement has to have the same standard for everyone, the cubit was standardized by Egyptian rulers. The Egyptian Royal cubit was a unit that was enforced as far back as 5,000 years ago for measurements and is the oldest known standard for length.
An interesting fact about measurement.
A very mysterious fact about measurement was discovered by Einstein. He showed that the length of something changes (and so its measurement changes) depending on how fast it is going.
This is very strange, but it's true. If a meter stick were traveling past you at close to the speed of light, you would measure it to be shorter than a meter as it sped by. If we could take advantage of this property, we might be able to drive a car through a house door by going 186,280 miles per second.