In this example where we subtract decimals we do so up to the thousandths place. It's a little tricky, but not if we do it together. Created by Sal Khan.
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- 0 is one of the most important numbers but we don't realize it.(19 votes)
- The number 0 has special properties. Any number plus 0 is itself, any number minus 0 is itself, 0 minus any number is the number’s opposite, any number times 0 is 0, 0 divided by any nonzero number is 0, any nonzero number divided by 0 is undefined (positively or negatively infinite), and 0 divided by 0 is indeterminate.
In algebra, getting 0 on one side of a quadratic equation (that is, an equation with 2 as the highest exponent on the variable) is necessary in order to solve the quadratic by factoring or using the quadratic formula.
If you decide to study calculus later on, you will see that derivatives (slopes) of functions are set equal to 0 in order maximize or minimize functions. You will also frequently encounter the indeterminate expression 0/0 in limit problems.
If you decide to take linear algebra or analysis later on, you will see that 0 comes up amazingly often!(6 votes)
- when we add subtract multiply do we line up the deciml points(7 votes)
- Subtracting decimals uses the same setup as adding decimals: line up the decimal points, and then subtract. In cases where you are subtracting two decimals that extend to different place values, it often makes sense to add extra zeros to make the two numbers line up—this makes the subtraction a bit easier to follow.(2 votes)
- Is there a good video to watch explaining how to borrow from 0s, Sal seemed to do it from the left to the right and I've always learned to do it opposite, but I get these problems wrong because of one or two letters. Thanks!(0 votes)
- I'm not entirely sure if there's a separate video just for borrowing from zeros but I wouldn't be surprised if there was! I can give you the basic rundown.
When you borrow from a zero, you aren't actually borrowing from that zero. In fact, that zero borrows from the number next to it. Here's an example:
5.09 - 2.29 = ?
Here, you can see that 0 is needed to 'borrow' from 5 so that 2 can be subtracted from 0. Since 0 borrowed from a number that you need to multiply the place to the left (from the 5's 'point of view') 10 times to get the place you're in. So, now you have
3. 29 -
And you have your answer! Sorry if it was a bit confusing. Hope it helped though!
- Will you ever have 2 numbers that will have 2 decimals. For example: 123.456.778(3 votes)
- I don't understand how he's regrouping here. How does taking one off of 39 give you eleven tenths?(5 votes)
- if your top number is bigger than the bottom number, then the number will be 11 for 1, 12 for 2, 13 for 3 etc. But if you have a similar situation for the number beside you, then you have to take 1 of 11 to make it 10.(2 votes)
- I am so confused(4 votes)
- The most important step is to line up the decimal points first!
Once they are lined up, the rest is easy. Write 0’s for any missing digits, then subtract like you would with whole numbers.
In the answer, put the decimal point directly under the lined-up decimal points.
Have a blessed, wonderful day!(3 votes)
- In the video Sal shows the hundredths place borrows 1 tenth from 11 tenths in the tenths place, then the hundredths place turns out 10 tenths, shouldn't it be 1 tenth? Because we are taken just 1 tenth, the tenths place got 10 tenths after that, because of the hundredths place took just 1 tenth. What is the explanation?(3 votes)
- Basically you know the tenths place and hundredths place on a decimal? 0.12, 1 is the tenth place and two is the hundredth. This goes the same for fractions. 1/100 you say it as one hundredth same goes for the hundredth in the example decimal (0.12) except the hundredth is 2 so it'd be equivalent to 2/100. Does that help?(5 votes)
- when were numbers first used in history?(4 votes)
Let's try to calculate 39.1 minus 0.794, and so pause the video and try this on your own. All right, I'm assuming you've given a go at it, so now let's work through it together. So I'm going to rewrite this. It's 39.1 minus-- I'm going to line up the decimals so that I have the right place values below the right place values-- minus-- this 0 is in the ones place, so I'll put it in the ones place-- 0.794. And now we're ready to subtract. Now, how do we subtract 4 from nothingness here, and 9 from nothingness here? Well, the same thing as nothing is a 0. And so now we can start to think about how to subtract. Well, we still have the problem. Well, we're trying to subtract 4 from 0, so we're trying to subtract 9 from 0. So what we could do is take this one tenth and try to regroup it into the hundredths place and the thousandths place. So let's think about this. If we make this-- actually that's not actually going to solve our problem. Well we could do it, but then we're going to have zero tenths, and we're still going to have a problem here. So actually let me go to the ones place. So let me get rid of a ones, so that's eight ones, which is going to be 10 tenths. So that's going to now-- we're going to have 11 tenths. The 10 tenths from here plus 1 is 11 tenths. Now let's take one of those tenths so that we have 10 tenths, and give it to the hundredths. So that's going to be 10 hundredths. And now let's take one of those hundredths-- so now we have nine hundredths-- and give it to the thousandths. So that's going to be 10 thousandths. Now we're ready to subtract. So 10-- let me do this in yellow-- 10 minus 4 is 6. 9 minus 9 is 0. 10 minus 7 is 3. We have our decimal point. 8 minus 0 is 8. And then we have 3 minus nothing is 3. So we're done, 38.306.