Exploring negative exponents with a base of 10

0:00- [Instructor] We're told to write 10 to the -4 as a simplified fraction and as a decimal. So pause this video, have a go at that. Okay, so let's first do it as a fraction. So 10 to the -4th power, the negative in an exponent just means 1 over 10 to the positive version of that exponent.

0:20So this is equal to 1 over 10 to the 4th, and, of course, this is equal to 1 over 10 to the 4th, we could write it out as 10 times 10. Actually, let me just do this. 10 times 10 times 10 times 10, or you might have been able to go just straight to this idea that if I have 10 to the 4th, that's going to be 1 followed by four 0s.

0:43So 1 followed by one, two, three, four 0s. And you could see it over here, 10 times 10 is 100, 100 times 10 is 1,000, 1,000 times 10 is 10,000. So there you have it, we've written it as a simplified fraction, now, let's write it as a decimal. So we really just have to write one ten-thousandth.

1:03So let's get our place values. So this right over here is the 10ths place, this is the hundredths place, this is the thousandths place, and this is the ten-thousandths place. So we have one ten-thousandth, so one ten-thousandth, we have no tenths, no hundredths, and no thousandths, so this is 0.0001.

1:30Another way to think about it is 10 to the -4, notice, to go from 1 to this right over here, we would have to move the decimal one, two, three, four to the left. So one way to think about it, if you multiply by 10 four times, you're gonna move the decimal four times to the right.

1:49If you do it 10 to the -4, you're gonna move the decimal four times to the left.