Question

How do i express this a ratio of integers?
6.254545454545454.........

Answer 1

1. Write the equation:
n=6.254545...
2. Multiply that equation by 100 because there are two digits that repeat and 100 has two zeros.
3. Write the new equation ABOVE the Step 1 equation.
4. Subtract the bottom equation from the top.
5. Solve the resulting equation for n

Answer 2

n x 100 = 625.45454....

Answer 3

625.4545454...
6.254545454... -
________________

Answer 4

100n=625.454545...
n= 6.254545...

Answer 5

subtract what you have written above?

Answer 6

yes. And notice that you end up with a string of zeros.

Answer 7

99n=619.20000000000....

Answer 8

99n= 619.20000000...

Answer 9

Yep

Answer 10

Divide both sides by 99 and drop the zeros

Answer 11

\[n=\frac{619.2}{99}\]

Answer 12

6.245454545...

Answer 13

Now multiply that fraction by 10 over 10 to get rid of the decimal and then reduce the fraction.

Answer 14

that's what we did before too... correct?

Answer 15

\[n=\frac{619.2}{99}\times \frac{10}{10}=\frac{6192}{990}\]

Answer 16

sorry...yes

Answer 17

the answer in my solution manual is 6.2 +54/10^3 + 54/ 10^5
sorry I should have mentioned that earlier....so how do we get there

Answer 18

Well I guess I don't understand because the directions say to write the number as a ratio of integers. The answer you gave is NOT a ratio let alone a ratio of 2 integers.

Answer 19

Is is because the repeating digits are in the thousands position and so on?

Answer 20

that's what my book says too....so is the solution manual off?

Answer 21

Yes

Answer 22

54/(10^3) is not a ratio of integers?

Answer 23

Yes it is but that is only a small part of the solution you posted.

Answer 24

It's like saying that 1/2 +3/4 + 1/7 is the ratio of two integers and it clearly isn't.

Answer 25

I'm sooo sorry....

Answer 26

here is the complete solution ...I'M SOOO SILLY

Answer 27

344/55

Answer 28

yes

Answer 29

That is the answer.

Answer 30

\[\frac{6192}{990}=\frac{344}{55}\]

Answer 31

6.2545454...=6.2+54/10^3 +....= (6.2 + 54/10^3)/(1-(1/10^2))= 62/10 +54/990=
6192/990= 344/55

Answer 32

THANKS SOO MUCH....makes perfect sense now....

Answer 33

yw

Answer 34

cool thanks.
soo....
1. Write the equation: n=6.254545... 2. Multiply that equation by 100 because there are two digits that repeat and 100 has two zeros. 3. Write the new equation ABOVE the Step 1 equation. 4. Subtract the bottom equation from the top. 5. Solve the resulting equation for n

use these instructions whenever i need to change and expression into a ratio of integers