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$\bullet$ Googols and googolplexes! When the mathematician Edward Kasner asked his young nephew to coin a name for the huge number $10^{100}$ , the boy said googol. (a) Express the googol in standard notation as a 1 followed by the appropriate number of zeroes. (b) Approximately how many googols of atoms does our sun contain? For simplicity, assume that the sun consists of only protons and electrons, in equal numbers, which is approximately true. (Consult Appendix E.) (c) The googolplex is an even larger number, 10 to the googol power: $10^{\text { soogol. Express the googolplex in scientific notation. If you }}$ wrote it in standard notation with a 1 followed by the appropriate number of zeroes, how many zeroes would you need?

a) one hundredb) $=1.2 \times 10^{51}$ atomsc) The number of zeros in a googolplex after 1 is v.

Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

Cornell University

Hope College

University of Sheffield

University of Winnipeg

Lectures

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

09:56

In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

01:35

The Googolplex A googol is…

01:34

A googol is $10^{100},$ an…

02:41

Discuss: The Googolplex A …

00:50

Solve the given problems.<…

01:04

What is the value of a goo…

This is Chapter one problem 66. So for a part in this problem, it just asks you to write down what Google is. And so a googol is 10th 100. So it's gonna look like a one followed by 100 zeros. So just like 10 of the two was a one followed by two zeros, 10 in threes at one, followed by three zeros, one of the 100 of the one followed by 100 zeros. And I am not going to take them all out. Just know that there should be 100 of them in here. So that is a pretty big number, and part B were asked to compare this to what we expect to be another pretty big number, which is okay. Number of atoms in our son and in particular were looked trying. Figure out how many Googles are in How many Googles of Adams was. The cool is just the number are in our son. Well, so for that we can use some data from Appendix E. We've got the mass of the sun is 1.99 times 10 of the 30th kilograms, or about two times 10 to the 30 kilograms, the mass of a single atom in the sun. We can approximate weaken, even like underestimated by saying that the mass of a single atom and the sun is the mass of a proton and attract a lot of the sun really is made up of hydrogen atoms of hydrogen atoms or just a proton and electron, and an electron is about 10,000 times later than a proton. So the massive and left trump, the mass of a hydrogen atom, is basically the mass of a proton. So assuming that this mass here of the proton is the average master, when Adam in the sun, the number of atoms in the sun is going to be equal to the sun mass divided by the proton mass. And we're estimating so we can round our numbers a bit to that 22% of the 30 kilograms those kilograms are going to cancel and proton mass that 1.67 also rounds up to two times 10 to the minus 27 kilograms. And if we'd written the kilograms in the new radar hands nominator, they would cancel. So these two is also canceled and you end up with 10 to the 57 Adams in the sun. But how many is that in Googles? Google? We could do a conversion here. So one Google repeat that Geo right now is 10 to the 100. So there are 10 to the minus 43 googles of atoms in the Sun. In other word. In other words, even though the sun is so big and Adams are so small, the number of Google's it's only still a tiny, tiny, tiny, tiny fraction of a Google is the number of atoms in the sun. That's how valuable is now for part C. Going even further, it's talking about a googol plex, so the googol plex is tend to the Google power. And so to express that in scientific notation, that's going to be a one. Times tend to the something where the something up here is how many, how many zeroes there are in the number and how many zeros there should be a googol of zeroes. You would have to write out a Google again and again, like over here, does 100 zeros there, so it's even hard to write a googol plex in proper scientific notation. in standard notation. A googol plex is a one followed by a googol of zeroes. But this is unreadable. We already said that a googol of zeroes would be 10 43 times the number of atoms in the sun. So a Google is how many zeroes what you would need. Don't even begin to consider trying to actually write out kugel, flex and standard notation.

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