How do you determine if a number can be written as a terminating decimal? Can 1/255, 3/255, 99/255, 100/255?

Answer 1

if & only if the only prime factors of the denominator are 2 & 5
255=3*5*17
1/255-no
3/255=1/85-no
99/255=33/85-no
100/255=20/51-no
51/255=1/5-yes.

Answer 2

Well, the first step actually often requires you to do the second step, so I will start with that as step one.

1) express the numerator and denominator as products of primes, and cross out any they have in common (reduce the fraction)

2) take the prime factors of the denominator and see if any are not 2 or 5 (the prime factors of 10).

If any are not 2 or 5, the number can NOT be expressed as a terminating decimal.

So for 1/255 we have 1 & 17x5x3. None are shared, and the denominator (255) has prime factors that are not 2 or 5. Therefore, 1/255 cannot be expressed as a terminating decimal. Cursory examination indicates that only 51/255, 102/255, 153/255, and 204/255 can be expressed as terminating decimals.

Answer 3

A fraction can be written as a terminating
decimal if
1). it is in lowest terms
2). the only prime factors of its denominator aree
2 and 5.
Why? Because only 2's and 5's can make
powers of 10, so that the long division comes
out exactly.
Let's apply this rule to your fractions:
255 = 3*5*17,
so 1/255 can't be written as a terminating decimal
3/255 = 1/85.
85 = 5*17, so no.
99/255 = 33/85.
Again 85 = 5*17, so no.
Finally,
100/255 = 20/51.
51 = 3*17, so no.
So none of these fractions can be written as
a terminating decimal.

Answer 4

Divide it out. i.e. 1 divided by 255 , 3 divided by 255 , etc
If it is beyond your ability to divide long-hand without a calculator then I don't know what to tell you.
There is no magic formula ; just basic arithmetic .

Answer 5

All fractions can be written either as recurring decimals or as terminating decimals. Fractions whose denominator only have prime factors of 2 and 5 can be written as terminating decimals. All other fractions can be written as recurring decimals only.