Created by Sal Khan.
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- 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.
- is there an exercise for this video cause it seems quite cool(2 votes)
- so how would i enter a negative exponent?(2 votes)
- why does he use the carrot sign?(2 votes)
- what website do you use to show the questions(1 vote)
- 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)
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.