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

Multiplying decimals using estimation


3m read
·Nov 10, 2024

So let's see if we can come up ways to compute what 2.8 times four point seven three is. So pause this video and try to work it out. Actually, I'll give you a hint: try to figure out just using the digits, not even paying attention to the decimals, the digits that the product would have, and then use estimation to think about where to place the decimal in your product so you get a reasonable answer.

All right, now let's do this together. So let's just imagine that we were multiplying these numbers without decimals. So that would be a situation where we would have 473 times 28. We could try to compute that. So we could think about, let's multiply everything times the 8. So 3 times 8 is 24. 7 times 8 is 56 plus 2 is 58. Then 4 times 8 is 32 plus 5 is 37.

Next, we could multiply everything times the 2. I'll cross those out so I don't get confused. 3 times 2 is going to be 6, and we have to be very careful. We are now in the tens place, so we want a zero here. 3 times 2 tens is going to be six tens. 7 times 2 is 14. Four times two is eight plus one is nine.

We add everything together, and we get 4 plus 0 is 4. 8 plus 6 is 14. Then 1 plus 7 plus 4 is 12. After that, we get 1 plus 3 is 4 plus 9 is equal to 13. So we know that the final answer has the digits 1, 3, 2, 4, 4 in that order: 1, 3, 2, 4, 4.

Now we have to think about where we would put a decimal for this to be a reasonable answer. Here's where estimation is useful. We know that two point eight times four point seven three is going to be roughly equal to what? Well, two point eight is pretty close to three, so I'll estimate two point eight as being three. Four point seven three is, if I had to estimate it, I’d say hey, it'd be pretty close to 5. So this should be pretty close to 3 times 5, which should be close to 15.

If I were to put the decimal there, that's way more than 15, so that doesn't seem reasonable. Even if I were to put the decimal there, one thousand three hundred twenty-four point four is still way more than fifteen. Far to put the decimal there, still way more than fifteen. If I were to put the decimal there, hey, that actually feels about right: thirteen and 244 thousandths is approaching fifteen. It's in the ballpark and actually the closest, 'cause if we were to put the decimal there, then we go to one point three two four four, which is a lot less than fifteen.

So if we want this to be roughly equal to fifteen, we definitely would want to put the decimal right over there. This is the most reasonable computation we can do because we know the digits are going to be 1, 3, 2, 4, 4. This helps us put the decimal in the future.

We're going to come up with ways of doing it where you don't necessarily have to estimate, but I encourage you that estimation is always key. If you ever in your life forget some type of method or process for multiplying decimals, it's the estimation that allows you to understand whether you're coming up with a reasonable answer.

This is really important because of the decimal. There’s—there’s a remember reading a news story a couple of years ago where someone put in a stock trade where they got the decimal wrong, and because of that, they essentially sold 10 times as many shares as they were supposed to. So they lost hundreds of millions of dollars. So anyway, decimals are important.

More Articles

View All
Biodiversity | Biodiversity and human impacts | High school biology | Khan Academy
Today we’re going to talk about biodiversity. So, biodiversity, as you might have guessed, comes from two words: biological and diversity. Essentially, it’s the variations or the diversity present between living things. Now, I grew up in the sunny state …
Oceans 101 | National Geographic
Oceans cover over 70 percent of the Earth’s surface. They not only serve as the planet’s largest habitat, but also help to regulate the global climate. The ocean is a continuous body of salt water that surrounds the continents. It is divided into four ma…
The Backwards Brain Bicycle - Smarter Every Day 133
Hey, it’s me Destin. Welcome back to Smarter Every Day. You’ve heard people say, “It’s just like riding a bike,” meaning it’s really easy and you can’t forget how to do it, right? But I did something. I did something that damaged my mind. It happened on t…
Genius: Aretha | Behind the Scenes with the A-Team
Hey, marker. Chat, here we go, and action. The queen of souls, I was looking the word up—genius, an exceptional quality. So, of course, Aretha Franklin has an exceptional quality. She has her beautiful voice, her amazing and brilliant piano playing, and …
First Look at Jane | National Geographic
Louis Leakey sent me to Gombe because he believed that an understanding of chimpanzees in the wild would help him to better guess how our Stone-Age ancestors may have behaved. It had long been thought that we were the only creatures on earth that used and…
How To Get Rich According To Ray Dalio
There are a million ways to make a million dollars, and in this video, we’re looking at one of them. Ray Dalio, the founder of Bridgewater Associates, the largest hedge fund in the world, is a role model for the world of finance. With a net worth of over …