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### Course: Class 7 > Unit 5

Lesson 5: Large numbers in standard form# Orders of magnitude exercise example 1

Created by Sal Khan.

## Want to join the conversation?

- What does the carrot sign mean?(28 votes)
**Weyoweyoweyo**. Watch out, here comes the grammar wagon!

It's actually spelled caret and has many uses. Here it's being used to express exponentiation.

http://en.wikipedia.org/wiki/Caret(40 votes)

- is there an exercise for this video cause it seems quite cool(2 votes)
- so how would i enter a negative exponent?(2 votes)
- Enter this - before your exponent. Example: -3^4(2 votes)

- why does he use the carrot sign?(2 votes)
- The carrot sign means the exponent so 5 to the 4th power would be written as 5^4(1 vote)

- what website do you use to show the questions(1 vote)
- The website in the video is KhanAcademy. That is what KhanAcademy used to look like.(2 votes)

- Can someone help me understand this question?

By how many orders of magnitude do a $20 bill and a nickel differ?(1 vote)- if I understand the Wikipedia source (https://en.wikipedia.org/wiki/Order_of_magnitude) correctly:

One order of magnitude is 10 to the first power. Two orders of magnitude is 10 to the second power. And so on.

20$ = 2 * 10^3 cents

1 nickel = 5 * 10^0 cents

The difference in the powers of ten (the difference between the exponents of 10) between the two quantities is 3. Therefore they differ by three orders of magnitude.

Only powers of 10 are considered, not single digits less than 10.

...

However, my reply needs expert confirmation. Someone with more experience is welcome to throw some cents :)(2 votes)

- Is there an actual introduction to order of magnitude because I don't fully understand it yet(0 votes)
- For some reason i can't ad the caret sign and can't get past this task because of it.(1 vote)
- Sometimes if your computer is set to a different language layout, that'll affect the symbols you get when you hold shift and type a number key. If you're trying shift-6 for the caret, check that your computer is set to use the U.S. layout (or research where the caret sign is for the layout it is set to use).(0 votes)

- could Sal please explain Orders of Magnitude? from searching KA, i see we only have these couple of exercise videos. but i see from googling that there's a lot more to it, including references to logarithmic scales and how they're used specifically for rounding estimates. (i think we backed into that in the Mt. Everest estimate exercise example.) or are we doing something different here? thanks!!(1 vote)
- how do i find the order of magnitude for something?(1 vote)

## Video transcript

So we're told that Mount
Everest is 29,029 feet tall. Estimate Mount Everest's
height by rewriting it as a number in the form x times
10 to the y-th power feet, where x and y are
single-digit numbers. So let's think about
how we would do this. So x and y have to be
single-digit numbers. So if we were to write it
in scientific notation, we could write something
like, let's see, it would be 2.9029 times 10. And actually, I'm
going to be careful. Times I should write like that. I'll use this little caret sign. I'm pressing shift and
6 to get the caret sign. Times 10 to the-- and
I moved the decimal. Let's see, in order to
go from 2 to 20,000, I have to add 1, 2, 3, 4 zeroes,
so times 10 to the fourth. So that's what I would
do if they were just asking us to write it
in scientific notation. But they're not
asking us to write it in scientific notation. They're saying estimate
Mount Everest's height by writing it in
this form, where x and y are
single-digit numbers. So as I wrote it
right over here, 2.0929 is not a
single-digit number. 4 is a single-digit number. So at least I got
the y part right. But I need to write this
part, which, in this form, this would be the x. I need to write that as
a single-digit number. And the key is that they
want me to estimate. So if I were to estimate
2.9029, I would write that as 3. So I'm going to go with
3 times 10 to the fourth. And if I were to expand out
3 times 10 to the fourth, it would be 30,000 feet. So my estimate
seems pretty good. So let's check. There we go.