Write 0.000000732 in standard form.
Now standard form is a notation which is a compact way of writing very very small or
very very large numbers. It’s in this format here: 𝑎 times 10 to the power of 𝑛, where 𝑛 is an integer or a
whole number. And that can be positive or negative. And the value of 𝑎, well one is less than or equal to 𝑎 is less than 10.
Now if 𝑛 is positive, it means we are multiplying 𝑎 by 10 𝑛 times. But if 𝑛 is negative, then it means we’re dividing 𝑎 by 10 𝑛 times. If you recall from our index rules, we know that if we had, for example, 𝑎 times 10
to the negative three, that’s the same as saying 𝑎 times one over 10 to the
three. And since we’re now doing effectively a fraction calculation, it means we’ve got 𝑎
over one times one over 10 to the three.
Well, 𝑎 times one on the numerator gives us 𝑎. And one times 10 to the power of three on the denominator gives us 10 to the power of
three. So this means 𝑎 divided by 10 to the power of three.
Okay, so now we’ve recapped what standard form means, let’s answer the question. If we want to convert 0.000000732 into standard form, first of all, we have to decide
the value of 𝑎. And if one is gonna be less than or equal to 𝑎 is gonna be less than 10, we need to
find the first significant digit, in this case the seven. And our value of 𝑎 is gonna have its decimal point one place later. So in that case, 𝑎 is going to be 7.32.
Well, starting off with 7.32, I’ll be gonna have to multiply that by 10 lots of times
to get the number we’re looking for or are we going to have to divide it by 10 lots
of times. Well, look, if I multiply by 10, I’ve got 73.2. I’m going in the wrong direction, so that’s not going to work. But if I divide by 10, I’ve got 0.732, which is closer to the answer that we’re
looking for. So we’ve gotta work out how many times have I got to divide this number by 10 in
order to get the number I want.
Well, if I start off with my decimal point here, every time I divide by 10, I’m going
to end up with a number that’s got its decimal point one place further to the
left. So dividing by 10 once as we said is 0.732. So divide by 10 again, divide by 10 again, and again, and again, and again, and
again. That’s a total of seven times, and I’ve ended up with my decimal point in the correct
That means that, in standard form, we end up with the number 7.32 times 10 to the
negative seven, because we need to divide 7.32 by 10 seven times in order to get the
number that we were looking for.