Final answer:
To transform the fraction 5/9 over 1/3 into a decimal, multiply 5/9 by the reciprocal of 1/3, which results in 5/3. Dividing 5 by 3 gives us the decimal 1.666..., which can be approximately written as 1.67.
Step-by-step explanation:
To express the fraction 5/9 over 1/3 as a decimal, we must first perform division to simplify the complex fraction. Dividing by a fraction is the same as multiplying by its reciprocal. Thus, we have:
- (5/9) ÷ (1/3)
- (5/9) × (3/1) (Multiplying by reciprocal of 1/3)
- 5/9 × 3/1 equals 5/3 (After multiplying numerators and denominators)
- To express 5/3 as a decimal, divide 5 by 3.
5 ÷ 3 = 1.666...
The decimal representation of 5/3 is approximately 1.67 when rounded to two decimal places.