Last question of my algebra one home work, I am REALLY confused.

Question

Determine whether the following statement is sometimes true, always true, and never true. If it is sometimes true, give an example making it true, also give an example that makes it false. If the statement is never true, rewrite it so that it is true. If the statement is always true, explain why.

 

47. A terminating decimal is a rational number

Answer 1

A terminating decimal means that the decimal point does end at some time:

0.25; 1.11111; 1.234567; 4.7; 32.32768213642314213431

the question is can these numbers turned into rationals.

Let's try to use some of the ones I gave:

.25 = ²⁵/₁₀₀

1.11111 = 1 ¹¹¹¹¹/₁₀₀₀₀₀

1.234567 = 1 ²³⁴⁵⁶⁷/_1000000

32.32768213642314213431 = 32 ^{32768213642314213431}/_{100000000000000000000}

 

May question to you is this: if any decimal terminates, is there any way you can not place it over some value of ¹/₁₀^x? The answer to that will answer your own problem.