Understanding units and being able to calculate unit conversions are crucial skills in science where precise measurements are fundamental to scientific research and experimentation. Biological processes often occur on vastly different scales, from molecular interactions at the nanometer level to ecosystem dynamics spanning kilometers. Accurate unit conversions ensure that data from experiments, whether measuring time, mass, length, or volume, can be correctly interpreted, compared, and communicated. Without this foundational knowledge, errors in measurement could lead to incorrect conclusions, affecting everything from drug dosages to ecological assessments. Thus, mastering units and conversions is essential for maintaining the rigor and reliability of scientific research.
One classic and costly example of a unit conversion mishap is the loss of NASA’s Mars Climate Orbiter, which in 1999 made it all the way to Mars only to burn up in the Martian atmosphere because the orbiter software was sending information in units of Newton seconds, but ground control was reading them in pound seconds (1 pound-force is 4.448 Newtons).
Common Units of Measurement
- Length: meters (m), centimeters (cm), millimeters (mm), micrometers (µm), nanometers (nm), Angstrom (Å)
- Mass: kilograms (kg), grams (g), milligrams (mg), micrograms (µg), nanograms (ng), picograms (pg)
- Time: milliseconds (ms), seconds (s), minutes (min), hours (h), days (d)
- Volume: liters (L), milliliters (mL), microliters (µL), cubic centimeters (cm³), and cubic meters (m³)
- Force: Newton (N), Dyne (dyn), pound-force (lbf)
- Radiation: Bequerel (Bq), Gray (Gy), Sievert (Sv), Curie (Ci), Rad, Rem, Roentgen (R), Electronvolt (eV)
Unit Prefixes
Unit prefixes are short symbols or words placed in front of a base unit of measurement to indicate a multiple or fraction of that unit. They make it easier to express very large or very small quantities without using cumbersome numbers. For example, instead of saying “1,000 meters,” we use the prefix “kilo” to say “1 kilometer.” Similarly, instead of “0.001 grams,” we use the prefix “milli” to say “1 milligram.” These prefixes follow the metric system, where each step represents a power of ten, making conversions straightforward and consistent across different units and scientific disciplines. See the tables below for unit prefixes used to describe large and small measurements.
| Prefix | Symbol | Factor | Example Unit |
|---|---|---|---|
| Deca | da | 10¹ | decameter (dam) |
| Hecto | h | 10² | hectogram (hg) |
| Kilo | k | 10³ | kilometer (km) |
| Mega | M | 10⁶ | megabyte (MB) |
| Giga | G | 10⁹ | gigahertz (GHz) |
| Tera | T | 10¹² | terabyte (TB) |
| Peta | P | 10¹⁵ | petawatt (PW) |
| Exa | E | 10¹⁸ | exajoule (EJ) |
| Zetta | Z | 10²¹ | zettabyte (ZB) |
| Yotta | Y | 10²⁴ | yottawatt (YW) |
| Prefix | Symbol | Factor | Example Unit |
|---|---|---|---|
| Yocto | y | 10⁻²⁴ | yoctometer (ym) |
| Zepto | z | 10⁻²¹ | zeptosecond (zs) |
| Atto | a | 10⁻¹⁸ | attogram (ag) |
| Femto | f | 10⁻¹⁵ | femtoliter (fL) |
| Pico | p | 10⁻¹² | picometer (pm) |
| Nano | n | 10⁻⁹ | nanometer (nm) |
| Micro | µ | 10⁻⁶ | microliter (µL) |
| Milli | m | 10⁻³ | milligram (mg) |
| Centi | c | 10⁻² | centimeter (cm) |
| Deci | d | 10⁻¹ | deciliter (dL) |
Unit Conversion Process
When converting from one unit to another, follow these steps:
- Determine whether you are converting from a larger unit to a smaller one or vice versa.
- Determine whether the answer you will calculate will be larger or smaller than the starting number.
- Identify the conversion factor.
- Set up the calculation so that the units you have will cancel and the units you want will remain.
- Check the result. Does it make sense based on your answer to the first step?
Example
- We are going to convert 3000 meters to kilometers. This means we are going from a smaller unit (meters) to a larger one (kilometers).
- We expect our calculation to produce a smaller number of kilometers than the number of meters we have at the start.
- The conversion factor is 1000 (1000 meters = 1 kilometer).
- Yes, the result makes sense. Kilometers are much larger than meters so our result must be a smaller number of kilometers compared to the number of meters we started with.
Practice!
Using the Unit Conversion Process outlined above, try some problems on your own. Then use the calculator widget to check your answers.
- Convert 1ooo meters to centimeters.
- Convert 500 microliters to milliliters.
- Convert 10 liters to cubic meters.
- Convert 25 milliliters to cubic millimeters.
- Convert 1 meter to nanometers.
- Convert 65 grams to kilograms.
- Convert 0.234 milliliters to microliters.
- Convert 0.5 kilograms to picograms.