Rounding and Converting decimals?

Question

2 questions:

1. If asked to round a number with no numbers to the right of it, what do you do? For example, if asked to round .439 to the nearest thousandths or .435 what would it be and why? Since rounding is determined by the number to the right, if there's no number to the right, how can you round it?

2. How do you convert a repeating decimal to a fraction? There's some type of process that is involved and I don't know what that is. For example how do I convert .333333 ad infinitum into a fraction? Please explain the method to use for all repeating fractions. Thank you.

Answer 1

the first answer is incorrect for both (1) and (2).

(1) what you do is: the numbers .439 and .435 are *already* rounded to the nearest thousandths (or to 3 decimal places), so you don't do anything; just leave them alone.

another way of seeing this is to note that .439 = .4390 (right?). then the rules of rounding say that .4390 rounded to 3 decimal places = .439.

(2) yes, there is a method that works for all numbers with a repeating decimal:

start by setting x = .333333...

identify how many digits, say n, are in the repeating part. in this case, there is n = 1 digit that is repeated.

multiply both sides by 10^n. in this case, we have
10x = 3.33333....

subtract the first equation from the second:
10x = 3.333333... minus
x = .333333... equals
9x = 3

thus x = 3/9 = 1/3.

another example:

let x = .384615384615384615...

now n = 6, so multiply both sides by 10^6 = 1,000,000:

1,000,000x = 384615.384615384615...

subtract the first eqn from the second to get:

999,999x = 384,615
x = 384,615/999,999 = 5/13.

hope this helps!

Answer 2

The KEY to rounding something like 0.435 to the nearest thousandths (3 decimal places) is that there IS something afterwards, zero!

If I write 2, that's the same thing as 2.0, 2.00, 2.000, etc. Just because you don't see the zeros doesn't mean they're not there.

Remember the rounding rule, if the number to the RIGHT of where you want to round is a 5 or greater, then you add 1 to the number currently in that spot.

Answer 3

1)
.439 round off to the nearest thousndths will be = .400 thousandths

since it is four hundred thirty nine thousandths.

.435 will turn out = 400 still

because rounding off decimal numbers is determined to the left.
if there's no number to the right.

2)
.333333= 333333/1000000(in fraction)

Answer 4

1)
.439 round off to the nearest thousndths will be = .400 thousandths
since it is four hundred thirty nine thousandths.
.435 will turn out = .400 still
because rounding off decimal numbers is determined to the left.
if there's no number to the right.

2)
Let 0.33333333 be x
so, here,
10x = 3.3333333
10x - x = 9x = 3.3333333333 - 0.333333333
= 3

So, x = 3/9
= 1/3