Multiplying Decimals

Good morning students, today I'm going to show you an example of how to multiply decimals. So we are going to start with the number 146.3 times 12.5. Now remember when you are multiplying decimals, you want to stack the numbers and the number on top should probably be the number with the most digits. So first we need to decide what number that is. On this first number, we have four digits on the second number, we have one, two, three digits. Which means when I rewrite the problem stacked, I want to make sure that the number with four digits is on top just because it makes it easier on you in the end. So I'm going to rewrite this problem as 146.3 times 12.5. Once I have rewritten the problem as stacked, we want to rewrite the problem again without the decimals. Now remember, at the very end, we're going to come back and put the decimals in, so please don't forget that part. But for now, we're going to rewrite the problem without the decimals, so that we can just work on our multiplying. So this problem is going to become 100 and not 100. It would be one four 6 three. Times one, two, 5. Now once we get to this point, we are going to multiply just like we normally would with standard algorithm. We are going to ignore the fact that our problem started with decimals until the very end. So we are going to start with 5 times three, which is 15. We're going to bring the 5 down and bring that one up and over. 5 times 6 is 30 plus one is 31. 5 times four is 20 plus three is 23. And 5 times one is 5 plus two is 7. Now, once we have finished using this 5, we are going to be moving over to the two. When we do that, we need to make sure we add a zero placeholder in the ones place. Okay? So now that we move over to the two, we're going to multiply again. Two times three is 6. Two times 6 is 12. So we're going to bring the two down and bring the one over two times four is 8 plus one is 9. And two times one is two. Now we are finished with the two and we are moving on to the one, which means we are in the hundreds place, so we need two placeholders underneath. And then we can start multiplying. One times three is three, one times 6 is 6. One times four is 8. And one times one is one. Now we know we're ready to multiply because there are three digits on the bottom and we have three rows of numbers. So we can multiply or so we can add now. We are going to add 5 plus zero plus zero, which equals 5. 6 plus one plus zero is 7. Three plus three plus two is 6, 7, 8. So it's 8. 9 plus 7 9 ten 1112 34 is 16. Plus 6 is 22. We're going to bring that two up and over. And then 8 plus two is ten plus two is 12, bring that one up and over and one plus one is two. So now we have finished our multiplying. We get to go back and add that decimal. Now in order to figure out where the decimal is supposed to go, we have to go back to our original equation, which is up here at the top. I'm going to delete these lines, so I don't confuse you. So we're going to look up here at the top at our original equation. And we want to look at how many digits are behind the decimal in both of these numbers. In this first number, there's one digit behind the decimal, and then the second number, there's also one digit behind the decimal. If we add one plus one, we get two, which means in our answer, there should be two digits. Behind the decimal. So we are going to go to our answer and we are going to count from the right side to the left side, one, two, and then place our decimal. And if you want to rewrite your answer, so there's nothing distracting you from the answer. You can rewrite it as 2000 228 .75. This is your example for multiplying decimals.