Lesson - Parts-Per Notation

Parts-per notation is used to describe very small quantities of chemical concentrations. Most of the time, chemical concentrations are expressed in percentages. However, it is important to understand the relationship between the concentration expressed as a percentage and the concentration expressed in parts-per notation. An Operator should understand Parts-per Notation for a solution. Mrs. Keegan Gold video shown below provides an overview of this. Please feel free to take notes as you watch.

Commonly used parts-per notation is below: 

Parts-per Notation Parts-per Acronym Value Value in Scientific Notation
Parts per Hundred pph 0.01 10-2
Parts per Million ppm 0.000001 10-6
Parts per Billion ppb 0.000000001 10-9
Parts per Trillion ppt 0.000000000001 10-12

Because the amounts are small, examples will help. 

One part per million is the equivalent of a drop of ink in 55 gallons of water.

One part per billion is the equivalent of one drop of ink in 55 barrels of water.
One part per billion is the equivalent of the width of a human hair within 68 miles.

One part per trillion is the equivalent of one drop in 500,000 barrels of water. 
One part per trillion is the equivalent to six inches in 93 million miles, the distance to the sun.

In chemical dosage-related problems, concentrations are typically expressed in parts per 
million, ppm. Therefore, we are most interested in converting a percentage to ppm and ppm to 
a percentage. If you divide 1,000,000 (1 ppm) by 100 (100%), you get the following: 

LaTeX: \frac{1ppm}{100\%}=\frac{1,000,000}{100}=10,0001ppm100%=1,000,000100=10,000

Therefore, a solution with a 1% chemical concentration can also be expressed as a solution with 
a 10,000-ppm chemical concentration.

1% = 10,000 ppm

To convert between a percentage and ppm, multiply the percent solution by 10,000. Note that you do not convert the percentage to a decimal before multiplying. It has already been accounted for in the conversion.

Percent Concentration ppm
1% 10,000 ppm
2% 20,000 ppm
3% 30,000 ppm
10% 100,000 ppm

Example: What is the ppm of a 25% solution?

25 x 10,000 = 25,000 ppm

Example: A water utility uses a 0.5% sodium hypochlorite solution to disinfect a well. What 
is the ppm concentration of the solution? 

To solve this problem, you need to take the percent of the solution given in the problem and multiply by 10,000 in order to have an answer in parts per million.

0.5 x 10,000 = 5,000 ppm

Now let’s look at the differences between parts per million (ppm), parts per billion (ppb), and parts per trillion (ppt.) As water quality regulations become more stringent and laboratory analysis techniques get better and better, contaminants are being identified at smaller and smaller concentrations. Most water quality standards are expressed in ppm or milligrams per liter (mg/L), but many are expressed in ppb or micrograms per liter (ug/L), and a few are expressed in ppt or nanograms per liter (ng/L). Another way to express the amount of contaminant in water supplies is as follows.

1,000,000 = 1 million
1,000,000,000 = 1 billion
1,000,000,000,000 = 1 trillion

Based on this, one billion is equal to one thousand million and one trillion is equal to one thousand billion.

1 billion = 1,000 million
1 trillion = 1,000 billion 

So how does this relate to our very small concentrations of ppm, ppb, and ppt?

1 ppm = 1,000 ppb = 1,000,000 ppt

The expression above says that 1 part of a small number (ppm) equals 1,000 parts of a smaller number (ppb) which equals 1,000,000 parts of an even smaller number (ppt). You can further  simplify the difference between ppb and ppt as follows.

1 ppb = 1,000 ppt

Example: Complete the following table with the corresponding unit for the various water quality Maximum Contaminant Levels (MCL). 

Constituent ppm ppb ppt
Arsenic 14
Chromium 0.19
Nitrate (NO3) 57
Perchlorate 7,400
Vinyl chloride 0.8

To complete the chart, we will start with the first constituent, Arsenic, and work our way down competing one row at a time.

To convert ppb to ppm, you divide ppb by 1,000.

Arsenic: 14 ppb x LaTeX: \frac{ 1 ppm}{1,000 ppb } = 0.014 ppm1ppm1,000ppb=0.014ppm

to convert ppb to ppt, you multiply ppb by 1,000.

Arsenic: 14 ppb x LaTeX: \frac{1,000,000 ppt}{1,000 ppb} = 14 ppb x \frac{1,000}{1 ppb} = 14,000ppt 1,000,000ppt1,000ppb=14ppbx1,0001ppb=14,000ppt

Now, we are going to move to the row for Chromium. To convert ppm to ppb, you multiply ppm by 1,000. 

Chromium: 0.19 ppm x LaTeX: \frac{ 1,000 ppb}{1 ppm} = 190 ppb1,000ppb1ppm=190ppb

To convert ppb to ppt, you multiply ppb by 1,000.

Chromium: 190 ppb x LaTeX: \frac{1,000,000 ppt}{1,000 ppb} = 190 ppb x \frac{1,000 ppt}{1 ppb} = 190,000 ppt1,000,000ppt1,000ppb=190ppbx1,000ppt1ppb=190,000ppt

And now we are moving to the row for Nitrate. To convert ppm to ppb, you multiply ppm by 1,000. 

Nitrate (NO3) : 57 ppm x LaTeX: \frac{1,000 ppb}{1 ppm} = 57,000 ppb1,000ppb1ppm=57,000ppb

To convert ppb to ppt, you multiply ppb by 1,000. 

Nitrate (NO3) : 57,000 ppb x LaTeX: \frac{1,000 ppt}{1 ppb} = 57,000,000 ppt1,000ppt1ppb=57,000,000ppt

Now, we are moving to the row for Perchlorate. To convert ppt to ppb, you divide ppt by 1,000. 

Perchlorate: 7,400 ppt x LaTeX: \frac{1 ppb}{1,000 ppt} = 7.4 ppb1ppb1,000ppt=7.4ppb

To convert ppb to ppm, you divide ppb by 1,000. 

Perchlorate: 7.4 ppb x LaTeX: \frac{1 ppm}{1,000 ppb} =0.0074 ppm1ppm1,000ppb=0.0074ppm

And finally, we are moving to the row for Vinyl Chloride. To convert ppb to ppm, you divide ppb by 1,000. 

Vinyl chloride: 0.8 ppb x LaTeX: \frac{1 ppm}{1,000 ppb} = 0.0008 ppm1ppm1,000ppb=0.0008ppm

To convert ppb to ppt, you multiply ppb by 1,000.

Vinyl chloride: 0.8 ppb x LaTeX: \frac{1,000 ppt}{1 ppb} = 800 ppt1,000ppt1ppb=800ppt

Here is the completed table with the numbers calculated in bold. 

Constituent ppm ppb ppt
Arsenic 0.014 14 14,000
Chromium 0.19 190 190,000
Nitrate (NO3) 57 57,000 57,000,000
Perchlorate 0.0074 7.4 7,400
Vinyl chloride 0.0008 0.8 800

 

The information for this page is from the book titled "Advanced Waterworks Mathematics" version 1.6 dated 2021.Written by Michael Alvord, Regina Blasberg, Stephanie Anagnoson, and Ernesto.An Open Educational Resources Publication by College of the Canyons. 
The content in this book is licensed under a Creative Commons Attribution 4.0
International License.