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## Arithmetic (all content)

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

Lesson 6: Adding decimals: standard algorithm# Adding three decimals

CCSS.Math:

Sal adds 7.056+605.7+5.67 using the "standard algorithm". Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- what is bigger 5.30 or 5.1000(119 votes)
- 5.30 is larger because 3/10 is larger than 1/10(20 votes)

- How do you add negative decimals(8 votes)
- 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.(6 votes)

- So i dont get how you do this could you please tell me?(7 votes)
- 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

combine those answers together

you get 24.

just so you know something like 5.20 + 4.60 is 9.80, so we do need the decimal point.(3 votes)

- so if i had to add 7.056 to 6098. what does that maank(4 votes)
- 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!(6 votes)

- on adding decimals 4 does not make any sense plz help(4 votes)
- Adding decimals is like adding normal numbers, with an addition of a decimal point.

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.(2 votes)

- So 1.320000000000 is the same as 1.32(2 votes)
- Yes that's right no matter how many 0's you have Careron it's still the same.(5 votes)

- 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(3 votes)
- 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!(3 votes)

- Isn't 56.0000000 the same as 56.0

or 0.56(3 votes)- the first two you said are the same but the third is a completely different number(2 votes)

- The numbers to the right of the decimal are technically considered negative numbers, right? And if so, how does it work compared to the negative numbers unit?(3 votes)
- why did sal put 605.7 longer then the rest of the numbers is it important or is that how you add three numbers

thank you for answering(2 votes)- yummy Yoda soda(2 votes)

## 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.