Large numbers in standard form
Orders of magnitude exercise example 1
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.