Scientific notation is a useful means of writing out very large or very small numbers using powers of ten and exponents. Spelling out scientific notation numbers can be a mouthful. The number 5 x 106 could be said “five times ten to the six”, but it is easier to say “five million”. We have words that express the very large and the very small.
The same is true for the metric system or SI units. These measurements are based on powers of ten, just like scientific notation. Every three powers of ten has its own metric prefix. There are a couple of special powers of ten that have their own prefix outside the ‘every three’ pattern.
Examples of Powers of Ten
The wavelength of microwaves are on the order of 10-6 meters. The prefix for 10-6 is micro, so you can say the wavelength of a microwave is on the order of one micrometer. (This also makes it obvious why they’re called microwaves.) The symbol for micro is the Greek letter μ. 1 micrometer is written as 1 μm.
The distance between the Earth and the Moon is about 384,000,000 meters. The Mega prefix (symbol M) means one million, so you could say the distance is 384 Megameters or 384 Mm.
Substituting the metric prefix can make doing calculations easier in your head. Use the prefix that applies to your situation. This table of metric prefixes has the standard names for each prefix used in science and measurements. It also shows the symbol used to represent these prefixes, their ‘power of ten’ and the number you are actually replacing with the prefix.
Table of Powers of 10 Metric Prefixes
This expanded table of metric prefixes includes the four prefixes approved in 2022:
| Prefix | Symbol | Factor | Power of Ten |
|---|---|---|---|
| quetta | Q | 1,000,000,000,000,000,000,000,000,000,000 (1 nonillion) | 1030 |
| ronna | R | 1,000,000,000,000,000,000,000,000,000 (1 octillion) | 1027 |
| yotta | Y | 1,000,000,000,000,000,000,000,000 (1 septillion) | 10²⁴ |
| zetta | Z | 1,000,000,000,000,000,000,000 (1 sextillion) | 10²¹ |
| exa | E | 1,000,000,000,000,000,000 (1 quintillion) | 10¹⁸ |
| peta | P | 1,000,000,000,000,000 (1 quadrillion) | 10¹⁵ |
| tera | T | 1,000,000,000,000 (1 trillion) | 10¹² |
| giga | G | 1,000,000,000 (1 billion) | 10⁹ |
| mega | M | 1,000,000 (1 million) | 10⁶ |
| kilo | k | 1,000 (1 thousand) | 10³ |
| hecto | h | 100 (1 hundred) | 10² |
| deca | da | 10 (ten) | 10¹ |
| (base unit) | — | 1 | 10⁰ |
| deci | d | 0.1 (one tenth) | 10⁻¹ |
| centi | c | 0.01 (one hundredth) | 10⁻² |
| milli | m | 0.001 (one thousandth) | 10⁻³ |
| micro | μ | 0.000001 (one millionth) | 10⁻⁶ |
| nano | n | 0.000000001 (one billionth) | 10⁻⁹ |
| pico | p | 0.000000000001 (one trillionth) | 10⁻¹² |
| femto | f | 0.000000000000001 (one quadrillionth) | 10⁻¹⁵ |
| atto | a | 0.000000000000000001 (one quintillionth) | 10⁻¹⁸ |
| zepto | z | 0.000000000000000000001 (one sextillionth) | 10⁻²¹ |
| yocto | y | 0.000 000 000 000 000 000 000 001 (one septillionth) | 10⁻²⁴ |
| ronto | r | 0.000 000 000 000 000 000 000 000 001 (one octillionth) | 10⁻²⁷ |
| quecto | q | 0.000 000 000 000 000 000 000 000 000 001 (one nonillionth) | 10⁻³⁰ |
Why Were the New Metric Prefixes Needed?
The International System of Units (SI) introduced the prefixes ronna-, quetta-, ronto-, and quecto- in 2022. These additions are helpful for several reasons:
- Growing Needs in Data Science & Computing
- The global volume of digital data is in zettabytes and soon requires ronnabytes and quettabytes.
- Storage devices, supercomputers, and cloud storage benefit from clear standardization.
- Astronomy & Cosmology
- Distances in space already exceed yottameters. For example, one light-year is about 9.46 ronnameters.
- The mass of the Earth is approximately 6 ronnagrams.
- Subatomic & Quantum Physics
- Extremely small scales, such as atomic radii and fundamental particle masses, benefit from ronto- and quecto-.
- The mass of an electron is about 0.91 rontograms.
- Avoiding Confusion with Non-Metric Large-Number Naming
- Previously, scientists used informal terms like “brontobytes” or “hellabytes” for large data units.
- The SI prefixes provide an official, standardized naming system.
Brief History of Metric Prefixes
The use of metric prefixes dates back to the late 18th century when the metric system was first developed in France. The first set of prefixes in 1795 created a standardized way of expressing large and small quantities. These original prefixes were milli-, centi-, deci-, deca-, hecto-, and kilo-.
As scientific progress expanded, new prefixes were gradually added:
- SI Standardization (1960): The International System of Units (SI) formally adopted many of the prefixes used today.
- Technological Growth (1975–1991): As computing and scientific advancements demanded larger and smaller measurements, femto- to yotta- were added.
- Recent Additions (2022): The most recent update introduced ronna-, quetta-, ronto-, and quecto- to address the growing need for naming extremely large and small values, especially in fields like data science and astronomy.
Practical Tips for Remembering the Order of Metric Prefixes
Remembering all the metric prefixes in order is challenging, so here are some strategies to help:
Mnemonic Devices
The best mnemonic device is a phrase that is easy to remember, so change the words according to what works best for you:
- For Large Prefixes (10³ to 10²⁷):
- “Kids Have Dropped Over Dead Counting Many Gigantic Turtles Per Every Zoo Yawning Rapidly Quietly.”
- (Kilo, Hecto, Deca, (base), Deci, Centi, Milli, Micro, Nano, Pico, Femto, Atto, Zepto, Yocto, Ronto, Quecto)
- For Small Prefixes (10⁻³ to 10⁻³⁰):
- “Many New People Feel Awkward Zooming Yesterday, Running Quietly.”
- (Milli, Micro, Nano, Pico, Femto, Atto, Zepto, Yocto, Ronto, Quecto)
Grouping Prefixes
Grouping prefixes in sets of three is another strategy, aligning them with powers of ten:
- Thousand (10³): kilo-, mega-, giga-, tera-, peta-, exa-, zetta-, yotta-, ronna-, quetta-
- Fractional Thousandths (10⁻³): milli-, micro-, nano-, pico-, femto-, atto-, zepto-, yocto-, ronto-, quecto-
Metric vs. Binary Prefixes
Metric prefixes follow a base-10 system, while binary prefixes are used in computing to reflect powers of 2.
Differences Between Metric and Binary Prefixes
| Prefix | Metric Value (SI) | Binary Equivalent (IEC Standard) |
|---|---|---|
| kilo (k) | 1,000 (10³) | kibibyte (KiB) = 1,024 (2¹⁰) |
| mega (M) | 1,000,000 (10⁶) | mebibyte (MiB) = 1,048,576 (2²⁰) |
| giga (G) | 1,000,000,000 (10⁹) | gibibyte (GiB) = 1,073,741,824 (2³⁰) |
| tera (T) | 1,000,000,000,000 (10¹²) | tebibyte (TiB) = 1,099,511,627,776 (2⁴⁰) |
Why This Distinction Matters
- Computing and Data Storage: A 1 TB (terabyte) hard drive contains 1 trillion bytes (10¹²), but a 1 TiB (tebibyte) storage device holds 1.1 trillion bytes (2⁴⁰).
- Potential Confusion: Many operating systems incorrectly label mebibytes and gibibytes as MB and GB, even though their values differ.
Clarifying these differences helps avoid misinterpretations in fields like data storage, file sizes, and RAM capacity.
Common Misconceptions About Metric Prefixes
1. “Mega always means one million.”
While mega- (M) in SI units always represents 10⁶ (1,000,000), in computing, it is sometimes incorrectly used for binary numbers, where a “megabyte” might mean 1,048,576 bytes instead.
2. “Micro is the smallest prefix.”
Many assume micro- (μ, 10⁻⁶) is the smallest prefix because it’s commonly used in medicine and biology (e.g., micrometers, micrograms). However, SI includes much smaller prefixes down to quecto- (q, 10⁻³⁰).
3. “Metric prefixes only apply to SI units.”
While primarily used in scientific units, metric prefixes are also applied in:
- Currency (e.g., millibitcoin = 0.001 BTC)
- Data storage (e.g., gigabit, terabyte)
- Time (e.g., milliseconds, nanoseconds)
4. “Milli- and centi- mean the same thing.”
Some students confuse milli- (10⁻³, one thousandth) with centi- (10⁻², one hundredth). However, their values differ:
- 1 millimeter (mm) = 0.001 meters
- 1 centimeter (cm) = 0.01 meters
5. “A kilogram can’t be a base unit because it contains a prefix.”
The kilogram is the SI base unit for mass. It is a historical quirk, rather than a strict rule violation. The metric system originally defined mass in terms of grams, but later standardized the kilogram as the base unit.
References
- Adam, David (2019). “Metric prefixes sought for extreme numbers.” Science. 363 (6428): 681. doi:10.1126/science.363.6428.68
- Brown, Richard J.C. (2019). “Considerations on compound SI prefixes”. Measurement. 140: 237–239. doi:10.1016/j.measurement.2019.04.024
- International Bureau of Weights and Measures (2022). The International System of Units (9th ed.). ISBN 978-92-822-2272-0.
- Sample, Ian (2022). “Earth weighs in at six ronnagrams as new prefixes picked for big and small“. The Guardian.