Convert into fractions. 3.125. Please show how you are solving, please.
The Correct Answer and Explanation is:
To convert 3.125 into a fraction, we will follow step-by-step reasoning and then explain the logic clearly.
✅ Step-by-Step Conversion:
Step 1: Separate the whole number and the decimal.
3.125 has a whole number part: 3,
and a decimal part: 0.125.
We will convert the decimal part into a fraction, then add it to the whole number.
Step 2: Convert 0.125 into a fraction.
- 0.125 means “125 thousandths”, which can be written as:
0.125=12510000.125 = \frac{125}{1000}
Now simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 125: 125÷1251000÷125=18\frac{125 ÷ 125}{1000 ÷ 125} = \frac{1}{8}
Step 3: Add the whole number back.
Now add the whole number 3 to the simplified fraction: 3+18=248+18=2583 + \frac{1}{8} = \frac{24}{8} + \frac{1}{8} = \frac{25}{8}
✅ Final Answer:
258\boxed{\frac{25}{8}}
🧠 Explanation
To convert a decimal like 3.125 to a fraction, we begin by understanding what the number represents. The number 3.125 consists of a whole number (3) and a decimal (0.125). The decimal part tells us how much more than 3 we have. In this case, it’s one eighth more.
The decimal 0.125 is read as “one hundred twenty-five thousandths.” By writing it as a fraction over 1000, we get: 0.125=12510000.125 = \frac{125}{1000}
To simplify, we look for the greatest common divisor (GCD). The GCD of 125 and 1000 is 125. Dividing both parts gives: 1251000=18\frac{125}{1000} = \frac{1}{8}
Now we bring back the whole number part. We rewrite 3 as a fraction with the same denominator (8) to add it easily: 3=2483 = \frac{24}{8}
Then: 248+18=258\frac{24}{8} + \frac{1}{8} = \frac{25}{8}
This is called an improper fraction because the numerator (25) is larger than the denominator (8). Improper fractions are often used in math and science because they are easier to work with in equations.
So, 3.125 = 25/8. This method works for any decimal and helps develop a deep understanding of how numbers relate to each other in fraction form.
