Question

How do you express the following decimals as fractions?
.9999...
5.373737...
thank you

Answer 1

The usual trick is a simple multiplication. I'll do the first one. You do the second.

N = 0.99999....

Then 10N = 9.9999999....

10N - N = 9.99999... - 0.99999...

9N = 9

N = 1 <== Weren't expecting that, were you? :-)

Clearly, there is some interesting conversation to be had around the multiplication and addition of infinite decimals, but that is the idea.

M = 5.3737....

Go!

Answer 2

ok thanks

Answer 3

\[\huge\frac{ 532 }{ 99 }\]

Answer 4

second one!!

Answer 5

Do I follow the same steps as the first one? I can't get a decent fraction for N

Answer 6

N = 5.373737....
Then 10N = 53.73737....
10N - N = 48.36363...
9N = 48.36363

Answer 7

there is a shortcut for this question!!

Answer 8

ahahah! Define "decent".

M = 5.373737...

What I didn't say, is the unmotivated multiplication needs to be enough for the entire repetitive part of the decimals. When I had 0.99999, I used 10, because only a single digit repeats. You'll need 100!

100M = 537.373737....

Answer 9

u dont need to do all these steps!!

Answer 10

oh i see

Answer 11

It is important to note that unique answers don't care how you find them. There may be shortcuts and alternate methodologies. You need to figure out what makes the most sense to you and helps you along your way.

Answer 12

do i also do 100M-M or is it 100M-10M

Answer 13

There was no 10M.

M = 5.373737...
100M = 537.373737...

100M - M = ??

Answer 14

ok thank i got 532/9 now

Answer 15

I hope not. 100M - M = 99M

Answer 16

ya thats what i meant to type

Answer 17

You should see quickly that the number of repeating digits is always the number of 9s you get in the denominator.

Answer 18

529/99

Answer 19

AHHH
532/99

Answer 20

Care to take a few more tries? :-)

Answer 21

sure