Express 8,460,000,000 in the standard form 𝑎 times ten to the 𝑛th power.
So here we have a pretty large number, and the standard form is a way to represent this really large number in a smaller way. So what does the standard form really represent? The standard form is 𝑎 times ten to the 𝑛th power, where 𝑎 is greater than or equal to one but less than ten and 𝑛 is an integer.
When a number’s written in standard form, the power of the ten indicates the number of places the decimal point should be moved to the right. So we need to keep moving the decimal point in our number to the left until the number is in standard form, the 𝑎 that we’re looking at.
So we need to make our really large number into the standard form for 𝑎, so it has to be greater than or equal to one, but less than ten. So how do we do that? Well, here’s our number, and technically it has a decimal point, so we need to make that really large number greater than or equal to one, but less than ten, so let’s move our decimal point until we have that kind of number.
Moving it one decimal place now makes it in the millions; that’s still way too big. At this spot, we would be 8460 and that’s still not less than ten, but if we moved it here, that would be 8.46; that is between one and ten, where it can be one but it has to be less than ten. So 𝑎 is equal to 8.4.
So how many decimal places did we move? One, two, and as we keep going, it goes all the way up to nine. So 𝑛 is equal to nine, so we can have final answer of 8.46 times ten to the ninth power.