Convert 5.125 To A Fraction: Simple Steps Explained
Table of Contents :
To convert the decimal number 5.125 into a fraction, follow a series of simple steps that allow us to express decimals as fractions accurately. In this guide, we will break down the conversion process step-by-step, ensuring clarity and understanding at each phase.
Understanding Decimals and Fractions
Before diving into the conversion, it's essential to comprehend what decimals and fractions are.
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Decimal: A decimal is a way of expressing numbers that are not whole, using a point (or dot) to separate the whole number part from the fractional part. For example, in 5.125, "5" is the whole number, and "0.125" represents the fractional part.
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Fraction: A fraction consists of a numerator (the top part) and a denominator (the bottom part). It represents a part of a whole.
The Conversion Process
Let’s go through the steps to convert 5.125 to a fraction.
Step 1: Identify the Whole Number and the Decimal Part
The given number is 5.125. Here, 5 is the whole number, and 0.125 is the decimal part.
Step 2: Convert the Decimal to a Fraction
The decimal 0.125 can be converted to a fraction. To do this, we consider how many decimal places are present. In this case, there are three decimal places. We can express 0.125 as follows:
- 0.125 = 125/1000 (since 125 is in the third decimal place, we place it over 1000, which is 10^3)
Step 3: Simplify the Fraction
Next, we need to simplify the fraction 125/1000. We do this by finding the greatest common divisor (GCD) of 125 and 1000.
The GCD of 125 and 1000 is 125. Now, we can simplify:
- 125 ÷ 125 = 1
- 1000 ÷ 125 = 8
So, 0.125 = 1/8.
Step 4: Combine the Whole Number and the Fraction
Now that we have converted the decimal part into a fraction, we combine it with the whole number:
- The whole number is 5.
- The fractional part is 1/8.
Thus, we can write:
- 5.125 = 5 + 1/8
To express this as a single fraction, we convert 5 into a fraction with the same denominator (8):
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5 can be expressed as 5/1. To convert it, we multiply the numerator and denominator by 8:
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5 = 40/8
Now, we can combine the two fractions:
- 5 + 1/8 = 40/8 + 1/8 = (40 + 1)/8 = 41/8
Final Result
Thus, the decimal 5.125 can be expressed as a fraction:
5.125 = 41/8
Important Notes
It's always helpful to double-check your work by converting the resulting fraction back to a decimal to ensure the conversion was accurate.
- 41 ÷ 8 = 5.125, confirming our solution is correct!
Summary
Converting decimals to fractions can be straightforward if you follow the right steps. Here’s a quick recap of our conversion of 5.125 into a fraction:
- Identify the whole number and the decimal part.
- Convert the decimal to a fraction (0.125 = 1/8).
- Combine the whole number with the fraction (5 + 1/8).
- Express it as a single fraction (5.125 = 41/8).
By following these steps, you can easily convert any decimal to a fraction. With practice, you’ll become more comfortable with the process. Happy converting! 🎉