Just when I was reading about the Indian Temple which has trillions of dollars in it’s vaults , I was like. . . I know 1, then 10, then 100, then 1000, then 10,000, then 100,000, then Million, 10 million, 100 million, billion, 10, 100, trillion, 10, 100 and so on. . I then thought of the powers of 10 where I can write 1 million as 106 or 10^6 (that’s 10 x 10 x 10 x 10 x 10 x 10)
So I can write huge numbers by just using the power of 10’s. . Quite amazing, isn’t it?
A thought crossed my mind, asking what comes after millions, billions and trillions ? So I did some research on that. . And guess what. . .
This Shit Gets Real
I bet . . After reading the Powers of 10, you’ll have nightmares even if you just think of numbers. Tell me if I’m wrong.
Warning: You might have sleepless nights after you read the whole article, so if you’re a weak-hearted person, proceed at your own risk.
So before things get completely out of control, let’s start with the still-understandable powers of 10
Powers of 10
Lets say that upto 1 million, where you can just add a zero if you wanna multiply by 10 and take out a zero if you wanna divide it by 10.
However, as you cross a million, the number of zeros increases, necessitating a different notation. That is why we employ the usage of powers of 10. Now get ready for the chaos that’s gonna occur in your brains when you think of this Power.
Fun Fact : The output of multiplying 9,845,625,675,438 by 8,372,745,993,275 is still less than 829.
As we go to larger and larger numbers, we’ll only deal with the powers of 10, since when we’re talking about really big numbers, the number of digits matters more than the digits themselves.
Each time we increase the power by one, we tenfold the size of the number we are on, drastically altering things. Let’s start with a million.
106 (1 million – 1,000,000) – In Maths, 1 million is one thousand thousand. After reading the whole article you’ll think of 1 million, as if you could count it on your fingers.
107 (10 million) – This brings us into a range of numbers that includes the number of steps required for an average man to walk around the Earth (40 million steps).
108 (100 million) – Now we’ve reached the total number of books ever written in human history (130 million), as well as the approximate number of words a person speaks in a lifetime (860 million). The odds of winning the truly big lotteries are also in this range. On an average,the chances of winning a Mega Millions lottery is 1 in 176,000,000. To put this in context, that’s about the number of seconds in six years. So it’s like knowing a pig would sneeze one and only once in the next six years and betting on one specific second—say, the 44th second of 6:12am on February 21st, 2022—and only chance of winning is if that one sneeze occurs precisely at that second.
So I’ll seriously advice you one thing : Never Ever buy Mega Millions Lottery tickets.
109 (1 billion – 1,000,000,000) – We have here the number of seconds in a 100 years (about 3 billion), as well as the number of people alive today (7.9 billion).
1010 (10 billion) – We’ve now reached the number of years since the Big Bang (13.7 billion) and number of seconds since Jesus Christ lived (60 billion).
1011 (100 billion) – This is based on the number of stars in the Milky Way and the number of galaxies in the observable universe (100-400 billion), thus even if a computer listed one observable galaxy every second since Christ, the entire universe would still not be done.
1012 (1 trillion – 1,000,000,000,000) – A million times a million. The number of pounds the scale would display if the whole human race was placed on it (~1 trillion), the number of seconds humans have existed (~100,000 years = 3 trillion seconds), and, higher than both of those totals combined, the number of miles in one light year (6 trillion). A trillion is so massive that tying a bow around the sun would take about 4 trillion millimetres of ribbon.
1013 (10 trillion) – The US nominal GDP in 2019 was just under $21 trillion, and the current debt is $23.3 trillions as of February 2020. The number of cells in the human body exceeds both of these (37 trillion).
1014 (100 trillion) – The amount of letters in every published book in human history, as well as the number of bacterias in your body, totals 100 trillion. The total wealth of the globe ($400.2 trillion) is also included in this range.
1015 (1 quadrillion) – Lets bid adieu to ordinary words now. The terms million, billion, and trillion are frequently used. No one ever uses the word quadrillion. Saying the word quadrillion is really uncool. 3 Instead, most people say “a million billion.” Anyways, there are roughly a quadrillion ants on the planet. When compared to the bacteria statement, it’s as if you have a tenth of the world’s ants inside your body.
1016 (10 quadrillion) – Now we arrive to the amount of playing cards you’d have to knock off the table mistakenly to cover the entire Earth (89 quadrillion). People on the other table won’t like that, right?
A few million trillions ago, we had discussed a statement : Each time we increase the power by one, we tenfold the size of the number. So in the coming -illions when we increase the powers of 10, the playing cards would cover too many earths.
1017 (100 quadrillion) – The number of seconds since the Big Bang. Also if you’d drop playing cards, it would cover the earth 10 times.
1018 (1 quintillion) – The phrase quintillion, also known as a billion billion, is even less cooler than quadrillion. The word quintillion is never mentioned by anyone with social skills. In any case, it’s the volume of water (in cubic meters) in the world’s oceans, as well as the number of atoms in a grain of salt (1.2 quintillion). Every beach on the planet has around 7.5 quintillion grains of sand—the same amount of atoms in six grains of salt.
1019 (10 quintillion) – The number of millimeters from here to the closest next star (38 quintillion millimeters). That’s 10 times the number of grains of sand in every beach on this planet.
1020 (100 quintillion) – The total number of meter-long steps required to walk across the Milky Way. So many songs and playlists to choose from. Have you heard of a Planck volume? It’s the smallest volume mentioned by scientists, so minuscule that 100 quintillion of them might fit in a proton. I’ll go over the Planck volumes in more detail later, as of now let’s shock you with the upcoming numbers. Way more to go with the powers of 10.
1021 (1 sextillion) – Now we’re reached a point where you won’t find any vocabulary. I’ve never in my life heard anyone say sextillion. Sounds weird too.
1023 (100 sextillion) – The number of stars in the observable universe, as a rough estimate. The figure 602 sextillion, or 6.02 x 1023—is a mole, or Avogadro’s Amount, and the number of hydrogen atoms in a gram of hydrogen.
1024 (1 septillion) – A trillion trillions. The weight of Earth is about six septillion kilograms.
1025 (10 septillion) – The number of drops of water in all the oceans on earth.
1027 (1 octillion) – It would take 1 octillion peas to fill the Earth if it were hollow.
So, let’s take a giant leap ahead into a completely other domain where the Earth’s volume is too small and the Big Bang is too recent to use as an example for these Powers of 10. Only the observable universe—a sphere roughly 92 billion light years across—can handle the enormity we’re dealing with.
Just to get an idea or visualization about the whole universe, you can check this article
Let’s continue with the Powers of 10
1080 – To get to 1080, you take a trillion and you multiply it by a trillion, by a trillion, by a trillion, by a trillion, by a trillion, by a hundred million. So, why did I come to a halt at this particular number? Because it’s a widely accepted estimate count of the total number of atoms in the universe.
1086 – You’d need 1086 peas to pack the whole observable universe sphere with peas. Imagine the size of the observable universe and then the size of a pea. Now you get how the powers of 10 is so enormous ?
1090 – This is the number of medium-sized grains of sand (say diameter 0.5mm) required to fill the whole universe.
We’re almost at the end of the powers of 10.
A Googol – 10100
One day in 1938, when American mathematician Edward Kasner got very cute , he asked his 9-year-old nephew Milton to come up with a term for 10100— one with 100 zeros — the term googol was coined. Milton, a bumbling 9-year-old, proposed “googol”. Kasner seems to have thought that this was a logical answer, so he ran with it, and that was the end of it. 10100 is since then called Googol.
So how huge is a googol?
It’s 10 billion times the number of grains of sand that could fit in the whole universe. Imagine the universe as a sandstorm, with minute grains of sand strewn across tens of billions of light years above, below, in front of, and behind the Earth. There is no end to the sand. You could drive a plane across the sand for trillions of years in any direction at full speed and never reach the finish. Sand, sand, sand, sand, sand, sand, sand, sand everywhere. And we’re talking about the number of sand grains. . You feel me now? Now that’s what I was telling you. . The Powers of 10 . . Powers of 10 . . powers of 10.
You think you’ve imagined how enormous a googol is? No
Imagine stopping the plane at some point, reaching out the window, and grabbing one grain of sand to examine under a powerful microscope—only to discover that it’s actually 10 billion minuscule grains encased in a membrane, all the same size as a single grain of sand. If every single grain of sand in this example was made up of 10 billion smaller grains, the total number of microscopic grains would be a googol.
We’re now out of capacity on both the small and large scales to put these powers of 10 figures into the physical universe, but here are three more for you:
10113 – The number of hydrogen atoms it would take to pack the whole universe.
10122 – The number of protons you could fit in the whole universe.
10185 – Returning to the Planck volume (the tiniest volume ever described in science), How many of these tiniest objects could be crammed into the largest thing known to man, the observable universe? 10185. We’ve achieved the largest number for which the physical world can be utilised to visualise it, without being able to go smaller or larger on either end.
A Googolplex – 10googol
Remember Edward Kasner we talked about a few powers of 10 ago ?(I used the term powers of 10 because millions, billions and trillions have no meaning here and rest other names aren’t cool enough ) Yes the one who asked his nephew for a name and he suggested googol.
Krasner couldn’t keep his pants on with this sweet new schtick after popularising the newly-named googol, so he asked his nephew to propose another term. He had hardly finished the question when Milton burst out laughing, screaming the number googolplex, which he described as “one, followed by writing zeroes until you get tired” in true Milton fashion.
But that doesn’t sound logical, right? ‘Writing zeros until you get tired’
At this point, Krasner exhibited an unusual calm, dismissing Milton and defining the number as 10googol, or 1 with a googol zeros written after it. A googolplex looks like this with its written using the powers of 10.
A googol is a number 10 billion times larger than the grains of sand that would fill the cosmos, or a 1 with just 100 zeros after it. Can you picture what kind of number is generated when a googol zero is added after the one?
There’s no way to comprehend that number; the best we can hope for is an understanding of how long it would take to write it. What I put above is merely the exponent—to write a googolplex out, you’ll need to write a googol zeros. Let’s start by figuring out where we’ll put these zeros.
Filling the universe with sand only gets you a ten billionth of the way to a googol, so we’d have to fill it to the brim with sand, obtain a very little pen, and write 10 billion zeros on each grain of sand. You’d see 10 billion minuscule zeros if you did this and then looked at a finished grain under a microscope. If you did that on every single grain of sand filling the universe, you’d have successfully written down the number googolplex.
So, I just found a research on how quickly a human can fairly write zeros, and it takes 10 seconds to write 36 zeros. If you wrote zeros for 16 hours a day, every single day, from the age of 5 to 85, You’d finish one half of a grain of sand in a lifetime. To finish one grain of sand, it would take two full human lives. In the history of the species, around 107 billion people have lived. If every human spent every single moment of their life writing zeros on grains of sand, we would have filled a cube with completed sand grains with a side of 1.7m (roughly the height of a human). That is it.
Now I understand, that the powers of 10 is very tough to explain, and tough to understand as well.
In the future post about the final one, you’ll see at a googolplex to the googolplexth power like a kid saying “100 plus 100!” when asked to say the biggest number he could think of. I guarantee you that you can never ever imagine about these powers of 10.
From this exact moment, when you hear or see someone saying millions and billions as if they were very big numbers, ask them to visit Moonjis and read this post.