Can someone please help me
1 answer:
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Answer:
An irrational number can never be represented precisely in decimal form.
Step-by-step explanation:
<em>A number can be precisely represented in decimal form if you can give a rule for the construction of its decimal part,</em>
for example:
2.246973973973973... (an infinite tail of 973's repeated over and over)
7.35 (a tail of zeroes)
If this the case, then the number is a RATIONAL NUMBER, i.e, the QUOTIENT OF TWO INTEGERS.
Let's show this for the first example and then a way to show the general situation will arise naturally.
Suppose N = 2.246973973973...
You can always multiply by a suitable power of 10 until you get a number with only the repeated chain in the tail
for example:
1)
but also
2)
Subtracting 1) from 2) we get
Now, the infinite tail disappears
But
We have then
999000.N=226747
and
We do not need to simplify this fraction, because we only wanted to show that N is a quotient of two integers.
We arrive then to the following conclusion:
If an irrational number could be represented precisely in decimal form, then it would have to be the quotient of two integers, which is a contradiction.
So, an irrational number can never be represented precisely in decimal form.