Question

what is 0.636363636363... rounded to the nearest thousandth?

Answer 1

THTO.tht

Answer 2

Do you understand that?

Answer 3

You are learning about decimal places in school right?

Answer 4

yes

Answer 5

Okay so you know about number places to the left of the decimal already right?

Ones, tens, hundreds, thousands, and so on.

Answer 6

Yup

Answer 7

And no I do not know what THTO.tht means do tell

Answer 8

Okay so it's the same for numbers to the right of the decimal only we are dealing in fractions. Therefore, since there is no such fraction as a oneth i.e., \[\frac{ x }{ 1 }\] the first place past the decimal is tenths and so forth. So what would the next place be after tenths?

Answer 9

I'll explain that in a second.

Answer 10

x
_
10 ?

Answer 11

No the first place is the tenths place, so any number there is that number over 10 or \[\frac{ n }{ 10 }\]Since we are dealing with a decimal system every place is a multiple of ten. So just like when we are working on the left of the decimal point with whole numbers and multiply the next place by ten as we work away from the point, so to we do on the right, exceft instead of multiplying by ten we divide.

Therefore, 0.2 is two tenths and 0.02 is two hundredths. Does that make sense?

Answer 12

Yes but what I said was x over 10 isnt it the same thing as your example? (I cant write fractions one here)

Answer 13

Well I think you got confused because I ask what the next place after tenths was, but I just told you it was hundredths, so can you now guess what the place after hundredths is?

Answer 14

and 0.002 would be in the thousandths?

Answer 15

YES.

Answer 16

Oh! Thank makes much more sense!

Answer 17

So now that you know which place past the decimal is thousandths, you should know which number you need to round.

Answer 18

But as I know this how would it be applied to 0.63636363636...? Heres what its telling me.Write the number as a decimal, rounded to the nearest thousandth. For example 0.568. But since ) 0.63636363 is rational how do I type it?

Answer 19

By the way THTO.tht is just a short way of writing the first few places of the decimal system on both sides of the point.

THTO.tht = thousands hundreds tens ones.tenths hundredths thousandths

Answer 20

Oh thanks for that as well :)

Answer 21

It should be no different regardless of whether it is a repeating decimal or not.
0.6363636363 is going to be rounded to the thousandths the same way any other decimal would.
0.6363 using the 3 to round the 6. Make sense?

Answer 22

I get the upper part of your post but not the bottom, how is 3 now rounding to 6?

Answer 23

Although it might be worth mentioning (even though you don't really need to know this to answer the problem) that once you round a repeating decimal, it is no longer repeating even if the number doesn't change.

That number rounded to ten thousandths is 0.6363 and even though that still looks like a repeating decimal, it is not because you have changed it's value by rounding.

Answer 24

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO I GET IT NOW!
Is the answer 0.636?

Answer 25

Right.

Answer 26

I feel like an idiot

Answer 27

If it takes me this long to understand this how am I going to do Algebra honors 1?

Answer 28

O and I messed up. Your number rounded to ten thousandths is actually 0.6364 not 0.6363, so it does not look repeating anymore, but there are numbers that do. 0.833333333 for example.

0.8333333 is \[\frac{ 5 }{ 6 }\]and if you round it to 0.83 it is now \[\frac{ 83 }{ 100 }\]not a big difference numerically, but as a fraction it's a huge difference.

Answer 29

You'll do fine. you are a good listener and will catch on fast to anyone who is teaching ot tutoring you.

Answer 30

Thank you! I'll try to ask an actual question next time, this feels too easy to answer now

Answer 31

And I hope you have a great day!