Question Video: Converting Numbers into Scientific Notation Mathematics • 8th Grade

Video Transcript

What is forty million written in scientific notation?

Scientific notation is a compact way of writing very large or very small numbers. Scientific notation is in the form, 𝑎 times ten to the 𝑏. Or 𝑎 is your factor, greater than or equal to one but less than ten, and 𝑏 will be your power of ten, which is your exponent. Let’s first begin by writing forty million.

Forty million is the same as forty million point zero, meaning let’s add in a decimal point. It’s important to have a decimal point because we will be moving it in order to put our number in scientific notation. We need to move our decimal point to the right of the first nonzero digit, when you’re looking at your number left to right. So the first nonzero digit would be four. And we need to move our decimal point to the right of that first nonzero digit. So now we need to scout and actually see how many places did we move our decimal point.

So going back to where our decimal point originally was, we moved our decimal point seven places. If we move our decimal point to the left, we will have a positive exponent as our power of ten. If we would move our decimal place to the right, we would have a negative exponent as our power of ten.

So forty million written in scientific notation would be four times ten to the seventh. If we think about our answer, four times ten to the seventh, four is our factor. And then we will be multiplying by ten to the seventh power. Ten to the seventh power is ten multiplied to itself seven times, and that answer is ten million. And four times ten million is forty million. So our final answer, what is forty million written in scientific notation, it is four times ten to the seventh power.