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Mathematics 12 Online
OpenStudy (jadebirdfly):

i have no clue how to do this please help

OpenStudy (jadebirdfly):

OpenStudy (sunnnystrong):

The little line above the number is the sign that denotes that the number doesnt terminate

OpenStudy (jadebirdfly):

yeah i know that but i don't know how to solve it

jhonyy9 (jhonyy9):

write 72=9*8 and 27=9*3

jhonyy9 (jhonyy9):

for example

OpenStudy (sunnnystrong):

Yes, you need to convert it to a fraction first.

OpenStudy (sunnnystrong):

.72 repeating = 72/99 .27 repeating = 27/99

OpenStudy (jadebirdfly):

why

OpenStudy (mathmate):

The way to convert a repeating decimal can be done as follows: For the repeating decimal 6.36 (where the digits 36 repeat forever) can be expressed as decimal: 6+36/99=6+4/9=\(6\frac{4}{9}\). Similarly, if all six digits following decimal point repeat, 5.142857=5+142857/999999=\(5\frac{1}{7}\), and so on. So convert the two repeating decimals to fractions and simplify.

OpenStudy (mathmate):

The explanation for 0.36(repeating)=36/99 is as follows: x=0.36(repeating) ...........(1) 100x=36.36 (repeating)..........(2) (2)-(1) 99x = 36 x=36/99

OpenStudy (sunnnystrong):

@Mathmate is correct. When dividing, multiplying, adding, or subtracting repeating decimals you must convert it to a fraction first

OpenStudy (sunnnystrong):

When dividing two fractions,you need to flip the second fraction and multiply by the reciprical.

OpenStudy (jadebirdfly):

oh ok thanks

OpenStudy (sshayer):

\[x=\frac{ 0.727272... }{ 0.272727... }=\frac{ 727272... }{ 272727... }=\frac{ 72\left( 0.101010.... \right) }{ 27\left( 0.101010... \right) }\]\[=\frac{ 72 }{ 27 }=\frac{ 8 }{ 3 }=2\frac{ 2 }{ 3 }\]

OpenStudy (awesomemiss):

0.72 divided by 0.27 equals 2 2/3 because 0.72= 72 and 0.27=27 so it is 72 divided by 27 which is 8/3 of 2 2/3

OpenStudy (awesomemiss):

i meant 8/3 or 2 2/3

OpenStudy (awesomemiss):

@jadebirdfly you there?

OpenStudy (mathstudent55):

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