SI units are extremely important in the study of science. Without them, a number is just a number without any meaning. The *Système international d’unités* (SI system) is a standard that simplifies international scientific communication. This system comprises seven base quantities and 16 prefixes that designate amounts.

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## SI Units and Prefixes

These reference tables show the different bases and prefixes used to designate metric units with the SI system.

Quantity | Unit | Abbreviation |

Mass | kilogram | kg |

Length | meter | m |

Time | second | s |

Temperature | Kelvin | K |

Amount | mole | mol |

Current | Ampere | A |

Intensity | Candela | Cd |

Prefix | Abbreviation | Meaning | Example |

Giga | G | 10^{9} | 1 gigameter (Gm) = 10^{9 }meters |

Mega | M | 10^{6} | 1 megameter (Mm) = 10^{6 }meters |

Kilo | k | 10^{3} | 1 kilometer (km) = 10^{3 }meters |

Deci | d | 10^{-1} | 1 decimeter (dm) = 10^{-1 }meters |

Centi | c | 10^{-2} | 1 centimeter (cm) = 10^{-2 }meters |

Milli | m | 10^{-3} | 1 millimeter (mm) = 10^{-3 }meters |

Micro | μ | 10^{-6} | 1 micrometer (μm) = 10^{-6 }meters |

Nano | n | 10^{-9} | 1 nanometer (nm) = 10^{-9 }meters |

Pico | p | 10^{-12} | 1 picometer (pm) = 10^{-12 }meters |

Femto | f | 10^{-15} | 1 femtometer (fm) = 10^{-15 }meters |

These base SI units can be combined with any of the prefixes to create units that are most appropriate for what is being measured. For example, you wouldn’t measure the distance from LA to New York in meters, the base unit. Instead, you would use kilometers or even megameters. The different base units can also be combined to form what are called derived units. For example, speed can be measured in meters per second, or in kilometers per nanosecond. The combinations are endless.

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## Scientific Notation

Also note that the SI system uses a lot of scientific notation. This makes it easier to write the numbers without many zeros or decimal places. For instance, if we were to write all the digits, 1 micrometer would be equal to 0.000001 meters. Clearly, it can be challenging to keep track of all those zeros, so scientists like to simplify things as much as possible. If you are a bit rusty with your scientific notation skills, be sure to brush up on them before you try the practice problems below.As a light refresher, remember that the power on the ten refers to the number of decimal places that the decimal point has to move. If the power is positive, move to the right, adding zeros to the number. If the power is negative, move to the left, adding decimal places.

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## Converting SI Units

Converting between the different SI system prefixes is an essential science skill that requires practice. Memorizing the different prefixes and their meanings makes it a lot easier to do these conversions, so try to memorize as many as you can. Of course, you can always refer back to the tables above.

### Conversion Example

Here is an example of a one-step conversion between the SI system prefixes. Let’s try converting 955 kilograms to megagrams. We will need two pieces of information from the table above. Kilogram refers to 10^{3}grams, while megagram refers to 10^{6}grams. Using these two pieces of information, we can set up a dimensional analysis conversion.

955\text {kg}\times \dfrac { { 10 }^{ 3 } }{ 1\text{ kg} } \times \dfrac { 1\text{ Mg} }{ { 10 }^{ 6 } } =0.995\text{ Mg}

Another way to approach these problems is to ask, “How many kilograms fit inside 1 megagram?” To answer this, look at the meaning of the two units: 1 kilogram is 10^{3}grams, while 1 megagram is 10^{6}grams. If we divide megagrams by kilograms, we see that there are 1000 kilograms in 1 megagram. So, we can set up a different factor to solve the conversion:

955\text{ kg}\times \dfrac { 1\text{ Mg} }{ 1000\text{ kg} } =0.995\text{ Mg}

Both methods result in the same answer, but the second method is more straightforward and yields an easier calculation. Use whichever method you are most comfortable with, but try to use the second method for at least a few of the problems.

To check your work, look at the prefix conversion table. As we move up the table, our numbers should be smaller, and as we move down the table, our numbers should be larger. Take the previous problem as an example. The prefix “mega” is above “kilo”, so the number associated with mega, 0.955, was smaller than the number associated with kilo, 955. Larger prefix units always correlate with smaller actual numbers.

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**SI Units Practice Problems**

Try completing these basic SI system conversions. Once you have attempted every problem, view the detailed solutions below. Good luck!

- 1000 meters to decimeters
- 0.206 kilopascals to pascals
- 180 milliliters to liters
- 0.796 grams to nanograms
- 1.65 gigaliters to megaliters
- 96.4 microliters to liters
- 2.29 milliseconds to nanoseconds
- 185 femtometers to millimeters
- 9.8 megagrams to centigrams
- 17.3 centimeters to kilometers

**1. 1000 meters to decimeters**

First, we must know how many meters are in 1 decimeter.

\dfrac { \text{decimeter} }{ \text{meter} } =\dfrac { { 10 }^{ -1 } }{ 1 } =\text{0.1 \text{ meters per decimeter}}

1000 \text{ meters}\times \dfrac { 1\text{ decimeter} }{ 0.1\text{ meters} } =10000\text{ decimeters}={ 10 }^{ 4 }\text{ decimeters}

**2. 0.206 kilopascals to pascals**

Looking at the conversion table, we can see that there are 10^{3}pascals (base unit) in one kilopascal.

0.206 \text{ kilopascals}\times \dfrac { 1000\text{ pascals} }{ 1\text{ kilopascal} } =206\text{ pascals}

**3. 180 milliliters to liters**

Milli refers to 10^{-3} so there are 1000 milliliters in one liter.

180 \text{ mL}\times \dfrac { 1\text{ liter} }{ 1000\text{ mL} } =0.18\text{ liter}

**4. 0.796 grams to nanograms**

Nanograms refer to 10^{-9}grams, so there are 100,000,000 nanograms in one gram.

0.796\text{ gram}\times \dfrac { 1\text{ gram} }{ { 10 }^{ -9 }\text{ nanograms} } =796000000\text{ nanograms}={ 7.96\times 10 }^{ -8 }\text{ nanograms}

This problem brings up a particularly interesting property of SI unit conversions. As we look at the table of conversions, notice that all the conversion factors are in scientific notation. That is, they are in the form 10^{x}. So, yet another way to solve these problems is to just consider how many places the decimal point has to move over to successfully complete the conversion. 7.98 x 10^{-8} is the same as 0.796 x 10^{-9}, just with an adjustment to comply with standard scientific notation. Also notice that nanograms refers to 10^{-9}. So, for the following problems, the solution will be given using this shortcut method.

**5. 1.65 gigaliters to megaliters**

“Giga” refers to 10^{9} while “mega” refers to 10^{6}, so the difference between these values is 10^{3}. Remember, the exponent must be positive, because as we convert downwards on the conversion table, the numbers must get larger.

1.65\text{ gigaliters}={ 1.65\times 10 }^{ 3 }\text{ megaliters}=1650\text{ megaliters}

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**6. 96.4 microliters to liters**

“Micro” refers to 10^{-6}, and liters are the base unit. We need the number to get smaller because we are moving up the table, so we can keep the negative exponent.

96.4\text{ microliters}={ 96.4\times 10 }^{ -6 }\text{ liters}={ 9.64\times 10 }^{ -5 }\text{ liters}

**7. 2.29 milliseconds to nanoseconds**

“Milli” refers to 10^{-3}, while “nano” refers to 10^{-9}. The difference between these is 10^{6}, and since we are going down the table, the exponent should be positive.

2.29\text{ milliseconds}={ 2.29\times 10 }^{ 6 }\text{ nanoseconds}

**8. 185 femtometers to millimeters**

Femto is equivalent to 10^{-15}, and milli, as noted in the problem above, is equivalent to 10^{-3}. Thus, since we are going up the table, the difference here is 10^{-12}.

185\text{ femtometers}={ 185\times 10 }^{ -12 }\text{ millimeters}={ 1.85\times 10 }^{ -10 }\text{ millimeters}

**9. 9.8 megagrams to centigrams**

“Mega” refers to 10^{6} and “centi” refers to 10^{-2}. Therefore, the difference is 10^{8}, which is positive since we are going down the table.

9.8\text{ megagrams}={ 9.8\times 10 }^{ 8 }\text{ centigrams}

**10. 17.3 centimeters to kilometers**

“Centi” refers to 10^{-2} and “kilo” refers to 10^{3}. Therefore, the difference is 10^{-5}, negative because we are moving up the conversion table.

17.3\text{ centimeters}={ 17.3\times 10 }^{ -5 }\text{ kilometers}={ 1.73\times 10 }^{ -4 }\text{ kilometers}

If you got at least half of those, you are doing a great job! With a bit more practice and you will be converting SI units with ease.

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## Conclusion

By this point, you will have hopefully learned how to quickly and easily convert between the various SI units. If not, remember that practice makes perfect. Keep trying, and soon it will seem simple. Remember two key points: It is beneficial to memorize the table of prefixes, and the best way to approach the problems is to ask, “How many of the first unit are in one of the second unit?” You can use that information to set up a dimensional analysis problem that will get you to your answer quickly.