A quotient is the answer when you divide numbers
The convention is that you divide the second number listed into the first.
So your question is asking #0.00685 -:0.76#
You can change the way numbers look as long as you include something that changes it back to how it should be.
#color(blue)("Lets play with making the numbers more manageable")#
#color(brown)("Lets consider "0.00684 )#
#0.00684 = 0.0684xx1/10#
#0.00684=0.684xx1/10xx1/10#
#0.00684=6.84xx1/10xx1/10xx1/10#
#0.00684=68.4xx1/10xx1/10xx1/10xx1/10#
#0.00684=684.0xx1/10xx1/10xx1/10xx1/10xx1/10#
This is the same as #684xx1/100000#
#color(brown)("Using the same approach on "0.76" we have "76.0xx1/100 )#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#
#0.00684 -: 0.76# is the same as:
#(684xx1/100000) -:(76xx1/100)#
#color(brown)("Lets do just the "684-:76" first")#
#color(magenta)("684-:76 = 9)# by calculator
#color(brown)("Now we deal with the "1/100000-:1/100)#
When dividing fractions turn the right hand one upside down and multiply. This is a shortcut that really works.
So
#1/100000-:1/100" is the same as "1/100000-:100/1 = 100/100000#
#(cancel(100)^1)/(cancel(100000)^1000) =color(magenta)(1/1000) larr" cancelling out"#
#color(brown)("Putting the 2 parts together")#
#color(magenta)(9xx1/1000 = 0.009)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Foot note")#
The above is correct. When I checked it in a calculator it produced a minutely different answer. This will be due to rounding errors within its processes.
