Large numbers on the number line
About this video
A number line runs from 0 to 10^7 in 10 equal intervals, so each tick is 1 x 10^6. Sal rewrites 62 x 10^5 as 6.2 x 10^6 by dividing 62 by 10 and multiplying the power of 10 by 10, then finds it just past 6 x 10^6, at point C.
You'll be able to
- work out what each tick on a number line represents.
- rewrite a number like 62 x 10^5 as 6.2 x 10^6.
- locate a large number on a number line.
Key words
- power of 10
- 10 multiplied by itself a number of times, like 10^6 = 1,000,000.
- equal intervals
- Gaps on a number line that are all the same size.
- equivalent
- Written differently but equal in value.
Transcript
- [Instructor] The number line goes from 0 to 10 to the seventh power and is divided into 10 equal intervals, all right? Which point represents 62 times 10 to the fifth? Pause this video, have a go at that. All right, so let's see what's going on here. This is 1 times 10 to the sixth, 2 times 10 to six, 3, 4, 5, 6, 7, 8, 9, 10 times 10 to the sixth, which is, of course, 10 to the seventh.
Now, they're not telling us something times 10 to the sixth. They're telling us something times 10 to the fifth. But maybe we could write it in terms of 10 to the sixth. What we could do is if we multiply this times 10, in order to not change the value of this entire expression, of the entire number, we could also divide this by 10.
And so this number right over here is the same thing as, if we divide 62 by 10, that's 6.2 times 10 to the, if we multiply that by 10, that's times 10 to the sixth. Notice, these are the exact same numbers right over here. So what's 6.0, 6.2, I should say, times 10 to the sixth?
Well, it's gonna be a little bit more than 6 times 10 to the sixth. So this is 1 times 10 of the sixth. Actually, you got 2, 3, 4, 5. This is 6 times 10 to the sixth. Let me write that. This right over here is 6 times 10 to the sixth. And so, a fifth of the way, 0.2 of the way, or I'll say a fifth of the way between 6 times 10 to the sixth and 7 times 10 to the sixth, that looks like point C right over there.
So that point best represents 62 times 10 to the fifth.
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