write the rational number in decimal form 27/99
Answers
A fraction written as a decimal is either terminating (has a fixed number of decimal places) or has a cycle of digits that repeat for ever. As we have 99 in the denominator I suspect that the decimal has an infinitely repeating set of digits.
Using a calculator I get
0.272727
...
.
The repeating part can be indicated by putting a bar over the appropriate digits. So I would chose to write this as:
0.27
¯¯¯¯
27
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
What if you do not have a calculator?
We are dividing 99 into a number that is less (do NOT use the word 'smaller')
However I can do a sort of cheat. 27 is the same as
270
×
1
10
This idea can be repeated as many times as you wish as long as you apply the
×
1
10
×
1
10
×
however many
1
10
you end up with. This will be clearer when I use it.
27
→
ddd
270
×
1
10
2
×
99
→
198
←
Subtract
−−−−−−−−−−−−−−−
ddddddddd
72
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
But
72
<
99
so write it as
720
×
1
10
ddddddddd
720
×
1
10
7
×
99
→
d
693
←
Subtract
−−−−−−−−−−−−−−−
dddddddddd
27
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
And so the cycle goes on and on for ever.
Thus so far we have:
27
×
1
10
×
1
10
=
0.27
But the repeats give:
0.27272727
...
...
→
0.27
¯¯¯¯
27