Small numbers on the number line
About this video
A number line runs from 10^-8 to 10^-7 and is split into equal intervals of 1 x 10^-8. Sal finds point A by noticing it lies between 3 and 4 x 10^-8, where the space is split into 10 smaller parts, so A is 3.6 x 10^-8.
You'll be able to
- label tick marks on a number line using multiples of a power of 10.
- find the size of the smaller intervals between labelled ticks.
- name a point like 3.6 x 10^-8 on a number line.
Key words
- number line
- A line with numbers placed at equal spacing in order.
- interval
- The gap between two neighboring marks on a number line.
- 10^-8
- One hundred-millionth, 0.00000001, a very small positive number.
Transcript
- [Instructor] The number line goes from 10 to the 8 to 10 to the, oh, sorry, the number line goes from 10 to the -8 to 10 to the -7, and it's divided to equal intervals. Which value does point A represent, or what value does it represent? So let's think about this a little bit.
This is 1 x 10 to the -8. This would be 2 x 10 to the -8. This is 3 x 10 to the -8. This is 4 x 10 to the -8. So it's between these two. So one way to think about it is if this right over here, this is 3 x 10 to the -8 right over here, we're essentially taking between 3 and 4 x 10 to the -8 and we're splitting it into one, two, three, four, five, six, seven, eight, nine, 10 sections, so this one would be 3.1 x 10 to the -8.
This one over here is 3.2 x 10 to the -8, 3.3, 3.4, 3.5, and this one, the one we care about, is 3.6 x 10 to the -8 power. And you can verify that. You could go 3.7 x 10 to the -8, 3.8 x 10 to the -8, 3.9 x 10 to the -8, and then you would have 4 x 10 to the -8 power, which is exactly what that point represents.
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