Think very, very big and very, very small numbers

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I hope this post finds you well.

Peta and femto are prefixes placed in front of units, like the gram. They are used to help us communicate very large and small numbers to each other. Scientist and engineers use prefixes all the time. Here I will help you understand two very rarely used prefixes and bring to your attention to their usage in CO₂ mitigation discussions.

First let us talk about unit of measure. To measure is to quantity some type of object, say the distance between your home and the store. If the bank is 3 times the distance to the store, then describing the distance to someone else you would say “The distance to the bank is 3 times that of the distance to the store”. In this case you are comparing the distance to the store to the distance to the bank by using a multiplier, 3. In this case the unit of measure would be the distance to the store.

This is Ok, sort of, kind of. It would work in ancient times. But would not it be better if the unit of measure would be smaller. So, that other people will know what you are talking about, we need everyone to agree upon some length. Say the meter.

We will treat this meter as a unit and this will be our number that we will multiply, to describe the distance to the bank. So, if the store is 100 meters away and the bank is 3 time that, then it is 300 meters. Here when we describe the distance to some place, we are only giving the multiplier and telling you the unit we use is meters. Think of the meter is an agreed upon multiplicand, and the number you provide is the multiplier. You multiply the units with some factor to measure the objects distance.

Now the prefix. Another case we need to consider is when the distance is very far away. This is where the prefix is used. Example, the distance to the next town is 24000 meters away. It would be hard to grasp that distance and cumbersome to give the multiplier of 24000 to your friend. To overcome this, we append a prefix to the unit distance (meter) to make thing easier. The kilo is such a prefix and it means to multiply by 1000. So, 1 kilometer is 1000 meters. The 1 is multiplied by 1000. Another way to write this is 1 km or 1000m. The ‘m’ is used instead of meter and the km is used instead of kilometer. So, for 24,000 meters, add the kilo to meter and it is 24 kilometers, written 24 km. The k is just a multiplier, 1000. Just add three zeros to the number when you see the “k” letter in front of the unit of measure (m).
Cars and their CO₂ emissions

I would like to bring your attention to CO₂ emissions by passenger cars and the contribution of CO₂ sequestration by trees. This is important because a recent study has shown that they absorb more than previously thought. Which is good. However, in these studies the scientist uses a prefix which is very rarely used. I thought I would try and explain it.

The numbers I use in this article are kind of estimates. The more articles you read on numbers of cars, the more you realize that you are never going to get an exact amount. The numbers are large and probably accurate to +/- 10 million cars. One reference stated that in 2022, there were 1.45 billion vehicles, of which 1.1 billion are passenger cars.

Here is the quantity that has a rarely used prefix. About 238 million gas-powered passenger cars emit 1 petagrams of CO₂ each year. petagram? Hmmm, if you are thinking what I am thinking, what is a petagram?

Peta is a prefix to a unit, used to make a very large numbers easier to understand and converse with each other. It is a 1 followed by 15 zeros. That is 1,000,000,000,000,000 grams. Or, a better way to say it, 1 Petagrams. Note if there are 1.1 billion passenger cars on the road then that is 4.62 Petagrams of CO₂ emissions emitted each year.

Sounds overwhelming. This is the end, perhaps. NO! It turns out plants sequester 157 Petagrams of CO₂ globally each year. Now, there are other CO₂ emitters and we are emitting more than the plants can sequester them. That is why the CO₂ concentration is at 420ppm up from 280 at the start of the industrial revolution.

The other prefix is for very, very small numbers, and that is the femto prefix. The femto prefix is a multiplier of 14 zeroes from the decimal point with a one at the end. That is 0.000000000000001 which is 1 femto. Let us use time or the second as the unit of measure. So, 1 femtosecond is 14 zeros following the decimal point, or 0.000000000000001, written 1.0 fs. Another way to write is 1×10-15 s.

Why did I mention this? It turns out the CO₂ molecule absorbs energy reflected off the earth for about 15 femtoseconds. Then it promptly reflects it back out, where some emissions go into space and others back to earth, heating the surface more than it should. This is why we are warming and why the air at 30,000 feet is still -48 °F.

It is easier to say 15 fs or 15 femtoseconds than it is to pronounce 13 zeros followed by 15. Just thought I would mention this because some people have mentioned that the earth is not warming, just look at the temperature at 33,000 feet. It is too cold there. See! Well, it is because of the re-emission of the energy from the CO₂ molecule.

I hope this helps. Don’t be bewildered when you see these two rarely used prefixes. There just used in very, very large and very, very small numbers.

Reference:

1. Here is a great article by Tina Casey titled “After 40 Years, New Carbon Sequestration Study Confirms the Value of Trees” https://www.triplepundit.com/story/2024/carbon-sequestration-study-trees/813271
2. A guide to metric (SI) prefix units can be found at the National Institute of Standards and Technology (NIST) web site, https://www.nist.gov/pml/owm/metric-si-prefixes . Note: ‘pml’ stands for Physical Measurement Laboratory, ‘owm’ is the Office of Weights and Measures and metric-si-prefixes is the web page.
3. Number of cars. Here is a site designed to inform how many cars are being built. https://www.worldometers.info/cars/.