What is 3.625 written as a fraction in lowest terms?
The Correct Answer and Explanation is:
To convert the decimal 3.625 to a fraction in its lowest terms, we need to follow a systematic process. Here’s a step-by-step explanation:
Step 1: Separate the whole number and decimal part
The number 3.625 consists of two parts:
- The whole number 3.
- The decimal part 0.625.
We will first convert 0.625 to a fraction and then add it to the whole number.
Step 2: Convert the decimal part to a fraction
To convert 0.625 to a fraction, we note that it has three decimal places. This means that 0.625 is the same as 625 thousandths, or:
[
0.625 = \frac{625}{1000}
]
Step 3: Simplify the fraction
Next, we simplify the fraction 625/1000 by finding the greatest common divisor (GCD) of 625 and 1000.
- The prime factorization of 625 is ( 5^4 ).
- The prime factorization of 1000 is ( 2^3 \times 5^3 ).
The GCD is ( 5^3 = 125 ), so we divide both the numerator and denominator by 125:
[
\frac{625}{1000} = \frac{625 \div 125}{1000 \div 125} = \frac{5}{8}
]
Thus, 0.625 as a fraction is 5/8.
Step 4: Add the whole number
Now, we can combine the whole number 3 and the fractional part 5/8:
[
3 + \frac{5}{8} = \frac{3 \times 8}{8} + \frac{5}{8} = \frac{24}{8} + \frac{5}{8} = \frac{29}{8}
]
Final Answer:
So, 3.625 as a fraction in lowest terms is:
[
\frac{29}{8}
]
Explanation:
We converted the decimal 3.625 by separating it into a whole number and a decimal part, converting the decimal to a fraction, and simplifying it. Finally, we combined the whole number and the fraction to get 29/8 as the final result.