Tutorial 1.4: Part 1

SI Units

SI Units

Scientific work is done using SI (metric) units.

Larger or smaller units are made by adding prefixes to base units.

Larger and smaller units differ from base units by some power of ten.

Base unit for length: meter

To answer questions of length we need a reference standard.

The standard used in scientific work is the meter.

It is somewhat longer than a yard. ( 1 m = 1.09 yds)

How would you find the length of the line shown?

To answer we need a reference standard.

The gold ruler shown has a length of 1 meter.

We measure a length of 7.0 m.

This line we would measure as 6.6 m.

We recognize that the last digit representing 0.6 m is a reasonable but uncertain guess.

This line we would measure as 0.6 m, and again note that our measure is reasonable but uncertain.

To measure shorter lengths it is convenient to use a smaller standard. By dividing the meter into 10 equal parts we can define a new unit, the decimeter. It is one power of ten smaller than the base unit and has a length of 1/10 or 0.1 m. It is written as 1 dm.

To measure even shorter lengths we can use a smaller standard yet. By dividing the decimeter into 10 equal parts we can define a new unit, the centimeter. It is written as 1 cm.

The decimeter is one power of ten smaller than the base unit, the meter, and has a length of 1/10 or 0.1 m. The centimeter is two powers of ten smaller than the base unit, the meter, and has a length of 1/100 or 0.01 m.

Two prefixes used thus far to make smaller units than the base (meter).

Factor Number Name Symbol
10-1 0.1 deci d
10-2 0.01 centi c

If we break a cm into ten equal parts we get the mm.

Factor Number Name Symbol
10-1 0.1 deci d
10-2 0.01 centi c
10-3 0.001 milli m

To work with very small objects we break the mm into 1000 equal parts to get the µm.

Factor Number Name Symbol
10-1 0.1 deci d
10-2 0.01 centi c
10-3 0.001 milli m
10-6 0.000 001 micro µ

To work at the atomic level we break the µm into 1000 equal parts to get the nm, and the nm into 1000 parts to get the pm.

Factor Number Name Symbol
10-1 0.1 deci d
10-2 0.01 centi c
10-3 0.001 milli m
10-6 0.000 001 micro µ
10-9 0.000 000 001 nano n
10-12 0.000 000 000 001 pico p

Just as we used prefixes to define units smaller than a base unit, we can use them to define larger units.

The dekameter is one power of ten larger than the base unit, the meter, and has a length of 10 m. The hectometer is two powers of ten larger than the base unit, the meter, and has a length of 100 m.

These two prefixes make larger units than the base (meter).

Factor Number Name Symbol
102 100 hecto h
101 10 deka da

To work with longer distances or objects we make a unit ten times larger than the hectometer (hm) called the kilometer (km).

Factor Number Name Symbol
103 1000 kilo k
102 100 hecto h
101 10 deka da

To work with longer distances yet we define a unit 1000 times larger than the kilometer (km) called the megameter (Mm).

Factor Number Name Symbol
106 1 000 000 mega M
103 1000 kilo k
102 100 hecto h
101 10 deka da

To work with longer distances yet we define a giga and a terameter.

Factor Number Name Symbol
1012 1 000 000 000 000 tera T
109 1 000 000 000 giga G
106 1 000 000 mega M
103 1000 kilo k
102 100 hecto h
101 10 deka da

Base Units

The base unit standard for measuring length is the meter. Other base units and what they measure is shown above. They can be combined with the same prefixes we explored with the meter. For example, the way 1 km means 1000 meters, 1 kg means 1000 grams, and 1 kmol means 1000 moles.

Base Units

To keep our languange and logic consistent, we will treat the gram, g, as the base unit for mass, not the kilogram, kg. While technically incorrect, it is far less confusing.

Factor Number Name Symbol
1012 1 000 000 000 000 tera T
109 1 000 000 000 giga G
106 1 000 000 mega M
103 1000 kilo k
102 100 hecto h
101 10 deka da

Factor Number Name Symbol
10-1 0.1 deci d
10-2 0.01 centi c
10-3 0.001 milli m
10-6 0.000 001 micro µ
10-9 0.000 000 001 nano n
10-12 0.000 000 000 001 pico p

Factor Number Name Symbol
1012 1 000 000 000 000 tera T
109 1 000 000 000 giga G
106 1 000 000 mega M
103 1000 kilo k
102 100 hecto h
101 10 deka da

Factor Number Name Symbol
10-1 0.1 deci d
10-2 0.01 centi c
10-3 0.001 milli m
10-6 0.000 001 micro µ
10-9 0.000 000 001 nano n
10-12 0.000 000 000 001 pico p