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## Group Activity: Metrics

 Metric Unit Prefixes Prefix Symbol Scientific Notation Number of Base Units These prefixes are what makes the metric system so easy to use. Doing conversions between units with different prefixes is as easy as moving the decimal point. Base units include the meter (m), the gram (g), the liter (L), the second (s), the kelvin (K), and the mole (mol). The SI unit of mass is the kilogram but the base unit for the purposes of this system of prefixes is the gram. The prefix centi- does not follow the pattern of the other prefixes: it is 10x bigger than milli- and 100x smaller than the base unit. All other prefixes are 1,000x bigger or smaller than adjacent prefixes. It is only used for centimeters (cm). The prefixes hecto- (h), deka- (da), and deci- (d) have been left out because they are so seldom used. Giga- G 109 1,000,000,000 Mega- M 106 1,000,000 kilo- k 103 1,000 base unit meter gram Liter 100 1 centi- c 10-2 0.01 milli- m 10-3 0.001 micro- μ 10-6 0.000 001 nano- n 10-9 0.000 000 001 pico- p 10-12 0.000 000 000 001 femto- f 10-15 0.000 000 000 000 001

We will concentrate on using the metric units chart (above) to create conversion factors. Conversion factors can be used as you learned to do for dimensional analysis. For example:

```
There are 1,000 mm (millimeters) in 1 m (meter)
1 m
4,350 mm × --------- = 4.35 m
1,000 mm
```

The old unit cancels out, giving a new unit.

 Unit Abbrev. Measures meter m length gram g mass liter L volume

First, we should review the metric units and how they are put together with the prefixes. See the chart at right for the commonly used units and what they measure. Prefixes are put in front of the names or abbreviations to create new units that measure either larger or smaller amounts. For example, a milliliter (mL) is smaller than a liter (L) and a kilometer (km) is larger than a meter.

To make a conversion factor from the metric units chart is easy. On the chart you will see that the unit prefixes all have a power of ten next to them. By counting the number of powers of ten between a pair of units on the chart you can tell how many of the smaller unit fit in one of the bigger unit. For example:

```There are three powers of ten between the base unit (meter) and milli- (millimeter).
meter: 100           millimeter: 10-3    0 — (-3) = +3
103 = 1,000 so       1 m = 1,000 mm
```

Here’s how you do it, step-by-step:

1. Identify the pair of units you need a conversion factor for and decide which one is the bigger unit. The bigger unit is always the one closer to the top of the chart.
2. Write down the bigger unit’s abbreviation next to the number 1. This is how many of that unit will be in your conversion factor.
3. Figure out how many powers of ten separate the two units.
4. Write down 1 × 10x next to the smaller unit’s abbreviation, where the x is the difference in powers of ten.

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Here are two examples:

```Convert kilograms to milligrams
kg: 10+3    mg: 10-3   kg is the bigger unit  so write: 1 kg = _____ mg
do this: +3 — (-3) = +6   which means 1 × 106 mg
so the conversion factor is 1 kg = 1 × 106 mg (1,000,000 mg)

Convert millimeters to micrometers
mm: 10-3    μm: 10-6   mm is the bigger unit  so write: 1 mm = _____ μm
do this: -3 — (-6) = +3   which means 1 × 103 μm
so the conversion factor is 1 mm = 1 × 103 μm (1,000 μm)
```

The answers should always give you a positive power of ten when you do it this way because you should always expect to have a large number of small units for each big unit.

One thing that is helpful to notice is that most of the prefixes are three powers of ten away from their two nearest neighbors. It becomes as easy as counting by 3s: 3, 6, 9, 12, etc. The only exception in the chart provided here is centi- which is 10-2 and is one power of ten away from milli- and two powers of ten away from the base unit. So skip centi- most of the time (it’s only used for meters, anyway) and count by 3s.

Here is something that will help you decide whether your answers are correct after you do a conversion. If you are changing from a bigger unit to a smaller unit then the numerical answer will be bigger. If you are changing from a smaller unit to a bigger unit then the numerical answer will be smaller. For example:

```         1 × 106 mg
2.9 kg × --------- = 2.9 × 106 mg (or 2,900,000 mg)
1 kg
So the number of mg equivalent to a certain numer of kg is a much larger number.

1 kg
510,000 mg × --------- = 0.51 kg
1 × 106 mg
So the number of kg equivalent to a certain numer of mg is a much smaller number.
```

#### Exercises

Do the following exercises on a separate piece of paper. Number each problem carefully and clearly.

##### How Many Blank in a Blank?

Figure out how many of the first unit there are in the second unit then write a unit equality in the form 1 × 10–2 mentals = 1 centimental or 1012 picolos = 1 los

1. How many g in a kg?
2. How many cm in a m?
3. How many μm in a m?
4. How many mm in a cm?
1. How many nL in a mL?
2. How many L in a GL?
3. How many m in a km?
4. How many nm in a μm?

##### Same Quantity, Many Units

Convert each quantity into the units shown. For each calculation create the correct conversion factor using the metric units chart. Hint: you may have made a few of these conversion factors in the exercise above. Show work for the dimensional analysis calculation.

1. 2.3 m convert to cm and mm
2. 4.89 mm convert to cm and μm
3. 4.35 × 102 mL convert to L and μL
4. 5.23 × 102 μm to mm and nm
5. 47 g to kg and mg
6. 1.0 × 103 mg to g and kg
1. 4.3 × 104 kg to Mg and g
2. 5.30 × 105 g to kg and Mg
3. 4.56 × 103 cm to m and mm
4. 7.82 × 109 mm to cm and m
5. 9.94 mL to nL and μL
6. 3.50 × 102 μL to mL and L
Metrics, Part II
Metrics Homework
Last updated: Jun 18, 2018 Go Back | Home
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