Final answer:
To express 3.12 as a fraction in lowest terms, we convert it to 312/100 and then simplify by dividing both numerator and denominator by 4, resulting in the fraction 78/25, option b).
Step-by-step explanation:
To express the decimal 3.12 as a fraction in lowest terms, we first recognize that 3.12 is the same as 3 + 0.12. This can be written as a fraction where 3 becomes ⅓/1 and 0.12 is written with a denominator that represents the place value of the last digit. In this case, 0.12 is 12 hundredths, so it is written as 12/100.
We can then combine these two fractions, converting 3 to a fraction with a denominator of 1: 3 = 300/100, which gives us 300/100 + 12/100 = 312/100. Finally, we simplify this fraction by finding the greatest common divisor of the numerator and denominator. In this case, both can be divided by 4 to simplify the fraction, leading us to 78/25.
Therefore, the decimal 3.12 expressed as a fraction in lowest terms is 78/25, which corresponds to option b).