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Metrics, Part II

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). |

Giga- | G | 10^{9} |
1,000,000,000 | |

Mega- | M | 10^{6} |
1,000,000 | |

kilo- | k | 10^{3} |
1,000 | |

base
unit |
meter
gram Liter |
10^{0} |
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 |

For this part of the lesson on metric units we will concentrate on using the metric units chart (above) to simply move a decimal or change the power of ten For example:

1,300 mg is 1.3 g and 4.9 × 10^{6}μm is 4.9 × 10^{3}mm is 4.9 m

To figure out how many places to move the decimal (or how much to add or subtract from the exponent) is relatively simple. Each unit prefix in the chart has a power of ten written next to it. By counting the number of powers of ten between two units you can tell how many places to move the decimal. For example:

There are three powers of ten between the base unit (meter) and kilo- (kilometer). meter: 10^{0}kilometer: 10^{3}3 — 0 = +3 so 1.2 km = 1,200 m or 1.45 × 10^{5}m = 1.45 × 10^{2}km

The key to this is remembering which unit is the bigger unit and which unit is the smaller unit. Move the decimal (or change the exponent) so that when you make the unit bigger, the number gets smaller. Or, if you are making the unit smaller, the number should get bigger.

**Here’s how you do it, step-by-step:**

- 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.
- Figure out how many powers of ten separate the two units.
- Move the decimal the required number of places: this matches the number of powers of ten between the two units.
- If the number is in scientific notation then change the exponent by adding or subtracting the number of powers of ten between the units you are converting between.

- Moving to a bigger unit makes the number get smaller
- Moving to a smaller unit makes the number get bigger

One more example: Convert 314 mg to g and μg mg: 10^{-3}(smaller) and g: 10^{0}(bigger) so 3 places --> 314 mg = 0.314 g (smaller because the unit is now bigger) μg: 10^{-6}(smaller) and mg: 10^{-3}(bigger) so 3 places --> 3.14 × 10^{2}mg = 3.14 × 10^{5}μg smaller unit so bigger numerical answer

The whole point of using metric units is that it is no longer a problem to convert between units. Instead of having to remember arcane facts like how many flibbers there are in a flibbertigibbet all you need to know is the chart of metric prefixes. Then you can instantly convert between kilograms and micrograms or from millimeters to nanometers. Units of mass, length, volume and even time (for units smaller than the second) are easily converted just by moving the decimal point.

Well, it’s easy after you have practiced it a bit.

Convert each quantity into the units shown. Simply write both answers after moving the decimal or changing the exponent. Write results in scientific notation if they are bigger than 1 × 10^{2} or smaller than 1 × 10^{-2}. To check your work you may make conversion factors as you learned to do earlier and then set up the dimensional analysis calculation.

- 4.8 m convert to cm and mm
- 108 mm convert to cm and μm
- 5.12 × 10
^{2}mL convert to L and μL - 8.75 × 10
^{2}μm to mm and nm - 925 g to kg and mg
- 3.2 × 10
^{3}mg to g and kg - 5.1 × 10
^{4}kg to Mg and g

- 2.98 × 10
^{6}μg to Gg and ng - 7.74 × 10
^{5}g to kg and Mg - 4.2 × 10
^{3}cm to m and mm - 6.58 × 10
^{9}mm to cm and m - 4.12 mL to nL and μL
- 1.019 × 10
^{2}μL to mL and L - 4.9 × 10
^{2}nL to mL and μL