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### Course: Arithmetic (all content)>Unit 6

Lesson 6: Adding decimals: standard algorithm

Adding decimals is easy when you follow these steps: line up the decimal points, fill in any missing digits with zeros, and then add the numbers from the smallest place value to the largest. By following this method, you can accurately add decimals and solve real-world problems. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• what is bigger 5.30 or 5.1000
• 5.30 is larger because 3/10 is larger than 1/10
• How do you add negative decimals
• well, if you have say -0.5 + -1.5, you would think of it as a number line. SO our first number is -0.5, so we go -0.5 spaces to the left since left is negative on a number line. Then since you are adding another negative number, you go left 1.5 more spaces from tthe -0.5 you are already at, tto get -2.0, so basically add tthe numbers like they are two positive numbers then put the negative infront.
Comment if you understand.
• so if i had to add 7.056 to 6098. what does that maank
• As with every addition problem, it becomes much easier if you just line up the places up correctly:
6098.000
+ 7.056
From here, we just add the places in order. From the thousandths place, we get a 6, since 0 + 6 = 6. For the next places:
0 + 5 = 5
0 + 0 = 0
8 + 7 = 15, carry the 1 over to the next place
1 + 9 + 0 = 10, carry the 1 over to the next place
1 + 0 = 1
6 + 0 = 6
From this, we put all the separate problems together for the final answer. This is 6098 + 7.056 = 6105.056
Hope this helped!
• So i dont get how you do this could you please tell me?
• do a sheet of paper
doing something like 15.80 + 8.20
0 + 0 = 0
8 + 2 = 10
carry the 1
5 + 8 + 1 = 14
carry the one
1 + 1 is 2
you get 24.
just so you know something like 5.20 + 4.60 is 9.80, so we do need the decimal point.
• What is up with the audio??
• Why is it that if a number goes before xero then you can put as many s you want but if it goes after you cant
• Alright.
Does 9 and 09 and 000009 all have the same value? Yes.
Does 9 and 90 and 900000 all have the same value? No.
If it comes before a number, and also before the decimal, a zero makes no difference in the value of the number. If it comes after a number but before the decimal, though, it does.
Hope this helps!
• on adding decimals 4 does not make any sense plz help
Say you have 1.054+3.002+7.514
Take away the decimal points.
1054
+ 3002
+ 7514
Now, just add to get your over all number (this example's final total is 11570) Since you have this total, you need to add the decimal point.
Find the number with the most amount of numbers behind the decimal, and make it so that 11570 has 3 numbers behind the decimal, which would be 11.570, or 11.57.
• Stop asking for upvotes, this is not what this is for.if they say upvote for anything don’t do it, they just doing it for fame, so pls you guys stop asking for it and don’t upvote anyone who is asking for it. Upvotes are only if what they say is helpful to the question, asking a question,or nice, if they ask and they have a lot of upvotes or not, then down vote them they won’t know but it’s the best you can do to stop it.
• cause if you are karennnn
• Isn't 56.0000000 the same as 56.0
or 0.56
• Yes, because it does not matter how many zeroes(0) there are at the end of the decimal
(1 vote)
• So 1.320000000000 is the same as 1.32
• Yes that's right no matter how many 0's you have Careron it's still the same.

## Video transcript

We need to add 7.056 to 605.7 to 5.67. Now when you're adding any number, you always want to make sure you line up numbers in the same place. And especially when you're dealing with decimals, the easiest way to do that is to just line up the decimals. So let's do that. So the first number right here is 7.056. This second number right here is 605.7. And then this last number is 5.67. So now we have everything lined up. Everything that's in the ones place is below or above everything else in the ones place. Everything in the tenths place is below or above everything else in the tenths place, and so on and so forth. So we can add. So let's add it. So you want to start off in the smallest place. So you start off here. This is the tenths, hundredths, thousandths place. This is literally 6 thousandths, and you want to add it to the other thousandths. There aren't any other thousandths. So you can view it two ways. You can just bring in this 6 down, or you could view this 605.7 as the same thing as 605.700. You can add as many zeroes to the right of this decimal, to the right of the 7, as you want, since we're sitting on the right side of the decimal, without changing its value. You can also do it here. This 5.67, you can write it as 5.670. When you write it like this, and you have 6 plus 0 plus 0 is 6. And you keep going. 5 plus 0 plus 7 is 12. You write the 2 in the hundredths place, and carry the 1. 1 plus 0 plus 7 is 8, plus 6 is 14. Write the 4, regroup the 1 into the ones place. 1 plus 7 is 8. 8 plus 5 is 13. 13 plus 5 is 18. This is 18. Carry or regroup the 1. 1 plus 0 is just 1. And then finally. You have the 6 in the hundreds place. Nothing gets added to it, so you can just bring down that 6 and it's right there. And you don't want to forget the decimal. And so when you add the numbers you get 618.426, or 618 and 426 thousandths. And we're done.