Final answer:
0.465 as a fraction in simplest form is 93/200, achieved by first converting it to 465/1000 and then simplifying by dividing both numerator and denominator by 5.
Step-by-step explanation:
The number 0.465 can be expressed as a fraction by placing it over 1 and then multiplying both numerator and denominator by a power of 10 to eliminate the decimal part.
In this case, multiplying by 1000 would yield 465/1000. Upon simplification, which involves cancelling out the common factors in both numerator and denominator, we find that both numbers are divisible by 5.
Therefore, you divide both by 5 to simplify the fraction.
Continuing this method of simplification, you would end up with 93/200 as the simplest form of the fraction for 0.465.