yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Decimal multiplication place value


3m read
·Nov 10, 2024

This is an exercise from Khan Academy. It tells us that the product 75 times 61 is equal to 4575. Use the previous fact to evaluate as a decimal this right over here: 7.5 times 0.061. Pause this video and see if you can have a go at it.

All right, now let's do this together. So the first thing that you might realize is that 7.5 is the same thing as 75 divided by 10. And 0.061, this is 61 thousandths. This right over here is the same thing as 61 divided by 1000.

We're going to take the product of these two things. Another way we could write this: 75 divided by 10. This is the same thing as 75 over 10, and I'm going to take the product of that and 61 thousandths, 61 divided by a thousand. So that would be 61 over a thousand.

Now, when we look at it either of these ways—well, actually, I'll do both of them at the same time—you could change the order of the multiplication and the division here. So you could start with 75 times 61, 75 times 61, and then divide that by 10, and then divide that by a thousand. You could do it that way, or you can look right over here and say, all right, if I'm taking this product, my numerator is going to be 75 times 61, 75 times 61, and then my denominator is going to be 10 times a thousand, which is essentially the same thing as dividing by 10 and then dividing by a thousand.

And, of course, that is going to be ten thousand. Now, on the left-hand side right over here, they told us what this is: it's four thousand five hundred and seventy-five. So it's four thousand five hundred and seventy-five divided by 10 and then divided by a thousand. Well, if I divide by 10 and then I divide by a thousand, that's equivalent to dividing by 10,000.

This is dividing by 10,000, and you can see that over here we're dividing by ten thousand as well, right over here. And the seventy-five times sixty-one, this is four thousand five hundred and seventy-five. Now they want us to evaluate it as a decimal.

We've now expressed it as a fraction, and I still haven't fully evaluated this yet. So we really want to think about this as four thousand five hundred seventy-five ten thousandths, and you can see that very explicitly here: this four thousand five hundred seventy-five ten thousandths. So, how do we write that? Well, if I have a decimal right over here, that's the tenths place. This is the hundredths, thousandths, ten-thousandths place.

So we have this many ten thousands: four thousand five hundred seventy-five ten thousandths, and we're done. So this is going to be zero point four five seven five. Now I know what some of you might be thinking.

Hey, I learned a technique where if I'm taking the product of two numbers, I could take the product of those two numbers. If I'm thinking the product of two numbers that are decimals, I could remove the decimals from them, essentially take their product, which they actually gave us right over here, and then count how many digits to the right of the decimal there were in our original number.

So we have one, two, three, four digits to the right of the decimal, and so what I do is I then move, I then make sure that there's four digits to the right of the decimal in the product. And so I would say, okay, one, two, three, four, that looks good. And I've got the same answer a lot faster than we just did it.

Well, the whole reason why I just did it the way I did is to show you why that works. When we take the product of the two numbers without the decimals, we're essentially ignoring the fact that the original product was dividing by 10 and dividing by a thousand. And that's because we had one digit behind to the right of the decimal here, and we had three digits to the right of the decimal there.

And so we later, after we take the product, we have to go and then actually take that product and divide by 10 and divide by a thousand, or divide by 10,000. So that's why you can then just say, all right, well now we have—we originally had four digits to the right, so we still have to have four digits to the right of the decimal point.

More Articles

View All
15 Life Changing Biographies of Successful People
Here’s a fact that will change your perspective about books forever: if they wrote it to make money, don’t read it. If they wrote it to tell you a story that will inspire and motivate you, it’s worth reading a thousand times. And this is what the followin…
2015 AP Chemistry free response 1d
Metal air cells need to be lightweight for many applications in order to transfer more electrons with a smaller mass. Sodium and calcium are investigated as potential anodes. A 1.0 gram anode of which of these metals would transfer more electrons, assumin…
Being Unhappy Is Very Inefficient
Besides, I’m too smart for it. The other objection is I don’t want it to lower my productivity. I don’t want to have less desire or less work ethic. Fact-check, and that is true. The more happy you are, the more content and peaceful you are. That’s less l…
HOW TO UNDERSTAND YOURSELF | MARCUS AURELIUS | STOICISM
The Stoic Greeks had the maxim, know thyself. How do we in this digital age come to know ourselves in terms of our personalities and, more importantly, our potential? In this video, you will learn eight transformative Stoic techniques to really know yours…
Torque and kinematics conceptual example
We are told a student hangs blocks with different masses from a pulley of mass m and radius r and releases them from rest. The student measures the time of the fall t and the magnitude of the angular velocity omega sub f when the block reaches a distance …
Finding inverses of rational functions | Equations | Algebra 2 | Khan Academy
All right, let’s say that we have the function f of x and it’s equal to 2x plus 5 over 4 minus 3x. What we want to do is figure out what is the inverse of our function. Pause this video and try to figure that out before we work on that together. All righ…