It'll go to the hundredths place, which you don't quite see here. Well in this situation, we are going to shift all theĭigits two places to the right and so let me put my places here, so that's the ones, tenths, hundredths, thousandths. What if we were to say 2.3 divided by 10 to the second power? Pause this video, try toįigure out what that is. Two is now in the tenths, three is now in the hundredths, but we could keep going. Going to shift one place to the right, so this two is going toĮnd up in the tenths place and the three is going to end Is the same thing as 10, so when we divide by 10, all of our digits are just So for example, what is 2.3 divided by, divided by 10 to the first power? Pause this video and Shifting our digits' places to the right. And if we divide by a power of 10, the same thing would happen, but we would now be Times 10 to some power, you are just shifting the digits So the pattern that you've probably seen is if you multiply a number Two places to the left, so it's going to be 300, and then we now have Three places to the left, so the two is going to becomeĢ000, which makes sense. So 2.3 times 10 to the third, the two is going to be shifted This is the same thingĪs multiplying by 1000. Shift everything three places to the left. Multiply by 10 again, so if we were to say 2.3 times 10 to the third power, well then we're going to This 3/10 will now be three 10s and we now have zero ones. And so this two will now be two hundreds. The ones place will go to the hundreds place, and the thing that is in the tenths place will go to the 10s place. Or you multiply by 10 twice, you're just going to shiftĮvery digit two places to the left. All right, well 10 to the second power, we already know that's equal to 100, and so when you multiply by 100 What is that going to be? Pause this video and see Now let's multiply 2.3 notīy 10 to the first power, which is just 10, but let's multiply it timesġ0 to the second power. Were to multiply it by 10, you'd say okay, that's about 20, so it makes sense that 2.3 times 10 is 23. Is in the tenths place will end up in the ones place. So the two, which is the ones place, one's up in the 10s place, and then three, which When you multiply by 10, you shift all the digits Well, that's the same thingĪs just multiplying it by 10, and we've seen already As three and 10 have no common factors, 3/10 is the simplest fraction that is equal to 0.3. In the case of 0.3, multiply each part by 10 to get the result 0.3 equals 3/10. Multiply the top and bottom parts of the fraction by 10 until both are whole numbers. And let's first just multiplyīy 10 to the first power. First, write down the decimal divided by one, which in this case would be 0.3/1. We multiply arbitrary things or divide arbitrary things by powers of 10. What we're going to do in this video is think about patterns when If we take 10 to the third power, that's going to be threeġ0s multiplied together, which is equal to 1000, which is also oneįollowed by three zeroes. If we have 10 to the second power, that means that we're gonna take two 10s, so a 10 and a 10, and we're gonna multiply them and so that's going to be 100. Say 10 to the first power, that means that we are just

In another video, we introduce ourselves to the idea of powers of 10.

0.3 times 10^3