How do you convert 4.6 (6 repeating) to a fraction?

1 Answer
Apr 24, 2016

#4 2/3#

Explanation:

Formatting Tip: For a repeating number us the command 'bar'

So for 4.666 repeating I would write 4.66bar6. If you write this but with the hash symbol at the beginning and end you get #4.66bar6#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Solved by inspection")#

Known: #1/3 -> 0.3333bar3#

So #2/3 -> 0.6666bar6#

Thus #4.66bar6 = 4 2/3#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Solved mathematically")#
Let #x = 4.66bar6#

Then #10x=46.66bar6#

So #10x-x= 46.66bar6#
#" "underline(" "4.66bar6color(white)(.))" subtract"#
#" "9x=42#

Divide both sides by 9

#x=42/9 = 4 2/3#