Clarify definition of measurement

[Faraz0007]

Homework Statement

A lot of books say definition of measurement as: how many times the standard unit and the standard unit. What how many means here?
Does how many means here numerical value of measurement, for example in measurement 5 m/s, 5 is "how many times" and "standard unit" is meter per second?

Relevant Equations

v=m/s

Please provide solution

 

[renormalize]

Please provide solution

You need to post a much clearer problem statement and also show your own attempt to solve the problem.

 

[haruspex]

Homework Statement: A lot of books say definition of measurement as: how many times the standard unit and the standard unit. What how many means here?
Does how many means here numerical value of measurement, for example in measurement 5 m/s, 5 is "how many times" and "standard unit" is meter per second?
Relevant Equations: v=m/s

Please provide solution

It means what multiple of one of the unit. If the unit is m/s and the multiple is five then we have 5x1m/s=5m/s.

 

[Tom.G]

I also had to read that a few times!

You are close:
yes, "how many times" is the 5
yes, "standard unit" describes the meter
??, "standard unit" also describes the second

I believe that makes "v" a derived value.

Cheers,
Tom

More backgroud:
The "Meter" was originally defined as one ten millionth of the distance from the Equator to the North Pole.
A Google search finds that the modern definition is:
the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.
(http://www.google.com/search?hl=en&q=how+is+meter+defined)

I will let you ask Google to define the Second.

 

[Orodruin]

I also had to read that a few times!

You are close:
yes, "how many times" is the 5
yes, "standard unit" describes the meter
??, "standard unit" also describes the second

No. The “standard unit” of velocity is m/s (in SI). It can actually be any unit of velocity in a measurement as long as it is a well-defined unit of velocity. The meter and the second are base units of the SI.

I believe that makes "v" a derived value.

The unit m/s is a derived unit as opposed to a base unit. The velocity $v$ itself can be measured in this derived unit (or any other unit of velocity), but it is not referred to as a derived value. It is simply a quantity with dimensions L/T, which therefore needs to be measured using a unit of that dimension.

 

[kuruman]

Homework Statement: A lot of books say definition of measurement as: how many times the standard unit and the standard unit. What how many means here?
Does how many means here numerical value of measurement, for example in measurement 5 m/s, 5 is "how many times" and "standard unit" is meter per second?

Suppose you have 48 apples in a basket. If the unit is "1 apple", you have 48×(1 apple). If the unit is "a pair of apples", you have 48×(2 apples) . If the unit is "a dozen apples", you have 4×(12 apples). I used "apple" for the unit but I could just as well have used oranges or bananas.

As @Orodruin pointed out "apple", "orange" and "banana" are derived units and, as such, they don't mix. If you take out of the basket 24 apples and replace them with 12 oranges and 12 bananas, you can only say that you have two dozen apples, one dozen oranges and one dozen bananas. However, you can redefine your unit as "fruit" in which case you have 48×(1 fruit), etc. etc.

 

[Lnewqban]

Welcome, @Faraz0007 !

When “how many times” is a number that becomes too big or too small, prefixes are used.

Please, see:
https://en.m.wikipedia.org/wiki/Metric_prefix