Nepedia
Back to Discover
Advanced Reader
⚛️

Parts-per notation

physical science Maturity 9-11 Next article →

Parts-per notation is a set of pseudo-units used in science and engineering. These notations describe very small values of various dimensionless quantities. A dimensionless quantity is a pure number that has no associated units of measurement. This occurs because the notation describes a ratio of one quantity per another quantity. For example, it might describe a mole fraction or a mass fraction. Scientists use these ratios to express how much of a substance exists within a larger whole.

Fluorescein (2)
Fluorescein (2)

The mechanism of parts-per notation relies on comparing a small part to a much larger total. In mathematical expressions, the units of measurement always cancel out during the division process. This leaves a pure-number coefficient that is usually less than or equal to one. When these notations are used in regular prose, they are interpreted as comparative ratios. For instance, saying "2 ppb" is generally understood to mean two parts in a billion parts. This allows researchers to communicate incredibly tiny proportions without using cumbersome long-form numbers.

There are many distinct stages of parts-per notation, ranging from large to incredibly small. One part per hundred is represented by the percent sign (%). One part per thousand can be written using the permille sign (‰). One part per ten thousand is known as a permyriad, denoted by the sign (‱). Moving into much smaller scales, we find parts-per-million (ppm), parts-per-billion (ppb), and parts-per-trillion (ppt). The smallest common scale is parts-per-quadrillion (ppq). Each stage represents a massive jump in the scale of the total group being measured.

Different scientific disciplines apply these notations to specific types of measurements. In chemistry, parts-per notation often describes dilute solutions. This includes measuring the abundance of dissolved minerals or pollutants in water. For example, 1 ppm can represent a mass fraction of one milligram per liter of water. In physics and engineering, the notation expresses proportional phenomena. A metal alloy might expand a specific amount per degree Celsius. Land surveyors also use it to express the accuracy of laser rangefinders.

Fluorescein (2)
Fluorescein (2)

To understand the scale of these numbers, we can look at their real-world equivalents. One part per hundred is equivalent to about fourteen minutes out of a single day. One part per thousand is about ninety seconds out of a day. One part per million is roughly 32 seconds out of a year. One part per billion is about three seconds out of a century. One part per trillion is about thirty seconds out of every million years. Finally, one part per quadrillion is about two and a half minutes out of the 4.5 billion-year age of the Earth.

Image-Olympic Pool Munich 1972, color adj
Image-Olympic Pool Munich 1972, color adj

In specialized fields like nuclear magnetic resonance spectroscopy (NMR), parts-per notation is essential. Here, it is used to express chemical shift. This represents the difference between a measured frequency and a reference frequency in parts per million. Because the reference frequency depends on the instrument's magnetic field, using ppm provides a dimensionless quantity. This value does not depend on the specific strength of the instrument's field. This makes it much easier for scientists to compare different experimental results across different laboratories.

Despite its widespread use, parts-per notation faces several criticisms regarding clarity and standardization. The International System of Units (SI) does not formally include these notations. The International Bureau of Weights and Measures (BIPM) recognizes their use, but they are not official SI units. One major problem is the ambiguity of certain abbreviations. For example, "ppt" can mean parts-per-trillion or parts-per-thousand depending on the context. Furthermore, the terms "billion" and "trillion" can have different values in different countries. To avoid confusion, many experts prefer to write out the specific units, such as kg/kg or mol/mol.

631 words

Where will your curiosity go next?

Keep exploring at your chosen reading level.

🖼️ Images & Media (2)
File:Fluorescein (2).jpg
Fluorescein (2).jpg
File:Image-Olympic Pool Munich 1972, color adj.jpg
Image-Olympic Pool Munich 1972, color adj.jpg
More to explore

🔬 Go deeper

More advanced topics to explore

🪜 Step back

Simpler topics to build understanding

What is Nepedia?

A free, ad-free encyclopedia for children. Every article is written at five reading levels, so the same page works for a five-year-old and a fifteen-year-old — use the level switcher above to see this one change. No account needed to read.