an irrational number can become rational by dropping a few decimal places?

Question

a)true or b)false

Answer 1

No. The decimal representation of every irrational number involves an infinite and non periodic sequence of decimal places. If you drop a finite number of them, you still get a number with an infinite and non periodic decimal representation, so still an irrational number.

Answer 2

As others have said, the answer is no. Here's a proof (admittedly non-rigorous):

If you are changing a finite number of digits in the decimal expansion, there must be a last one. Let's arbitrarily say it is at decimal position #10000. However, that means the decimal positions after #10000 already followed an unending repeating sequence. Since the change to the original number did not touch the digits after #10000, the original number already had an unending repeating sequence, therefore the number before the change was already rational.

Now, it occurs to me that there are irrational numbers that can be turned into rational numbers by making a countably infinite number of changes. For example, consider the number 1+ 1/10^1) + 1/(10^2) + 1(10^6) + 1(10^24) + ...., with each exponent of 10 being a factorial. This number is irrational, but we can make it rational by changing decimal positions 1, 2, 6, 24, etc. to 0. What is interesting about this is that the number of changes in this case is countably infinite, but the number of irrational numbers is uncountably infinite.

Answer 3

this question does not extremely make sense through fact an irrational variety has infinitely many decimal places. If we've been to drop all yet some (that's, if we dropped infinitely many decimal places) with the aid of truncating the variety, then definite, it may be rational, so i assume the respond is A. genuine.

Answer 4

irrational numbers have no defined decimal ( its infinite) .... so if you write a "complete" decimal, that number is rational....

so if you can write a complete decimal, it is rational

example ..... 1/3 is rational.... but 0.333333333..... is not.... if you write a definite decimal ( .33333 is 33333/100000 and a fraction is rational)

if you drop a few decimal points, you change the VALUE of the original value..... is dropping a few decimals the same value .. no....

so dropping a few decmals makes a irrational # a rational one.... it just changes the value of the irrational number


just to clarify the pi question .....
when pi is written as 22/7, it is rational..... not always irrational

Answer 5

false.

An irrational number has an infinite number of decimals, you cannot just drop a "few".

Answer 6

False, because almost all irrational numbers are transcendental i.e., with infinite length non-recurring decimal expansions.

Answer 7

You can round an irrational number to a rational number.

For example:
pi = 3.1415926535897932384626433832795... (irrational)

But you can round it any way you like:
3.14
3.1416
3.1415926534
etc.
All are rational.

However, pi itself is still always irrational.

Answer 8

FALSE You would have to drop an infinity # of decimals.