.125 as a fraction

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16-01-2025

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Understanding how to convert decimals to fractions is a fundamental skill in mathematics. This article will guide you through the process of converting the decimal .125 into its fractional equivalent. We'll break down the steps, explain the reasoning, and show you how to simplify the fraction to its lowest terms. By the end, you'll be able to confidently convert similar decimals to fractions.

Understanding Decimals and Fractions

Before we begin, let's quickly review the basics. A decimal represents a part of a whole number, using a base-ten system. A fraction, on the other hand, represents a part of a whole number using a numerator (top number) and a denominator (bottom number). The denominator indicates how many equal parts the whole is divided into, and the numerator indicates how many of those parts are being considered.

Converting .125 to a Fraction: Step-by-Step

Here's how to convert the decimal .125 into a fraction:

Step 1: Write the decimal as a fraction over 1.

This is the first step in converting any decimal to a fraction. We write .125 as:

.125/1

Step 2: Multiply both the numerator and denominator by a power of 10 to eliminate the decimal.

Since .125 has three digits after the decimal point, we'll multiply both the numerator and the denominator by 1000 (10 to the power of 3):

(0.125 * 1000) / (1 * 1000) = 125/1000

Step 3: Simplify the fraction.

Now, we need to simplify the fraction 125/1000 to its lowest terms. To do this, we find the greatest common divisor (GCD) of 125 and 1000. The GCD of 125 and 1000 is 125.

Divide both the numerator and denominator by 125:

125 ÷ 125 = 1 1000 ÷ 125 = 8

Therefore, the simplified fraction is:

1/8

Why is .125 equal to 1/8?

The fraction 1/8 represents one part out of eight equal parts. If you divide 1 by 8, you get 0.125. This confirms that our conversion is correct. Understanding this relationship between decimals and fractions is crucial for various mathematical applications.

Frequently Asked Questions (FAQ)

Q: How do I convert other decimals to fractions?

A: Follow the same steps outlined above. The power of 10 you multiply by will depend on the number of digits after the decimal point. For example, for 0.5 you would multiply by 10, for 0.25 you would multiply by 100, and so on.

Q: What if the resulting fraction isn't easily simplified?

A: You can use a calculator or prime factorization to find the greatest common divisor and simplify the fraction to its lowest terms.

Q: Are there any online tools to help with decimal to fraction conversion?

A: Yes, many online calculators and converters are available that can quickly and accurately convert decimals to fractions.

Conclusion

Converting .125 to a fraction is a straightforward process involving multiplying by a power of 10 to eliminate the decimal, and then simplifying the resulting fraction to its lowest terms. Understanding this process allows you to easily convert other decimals to fractions and strengthens your overall understanding of fractions and decimals. Remember the final answer: .125 is equal to 1/8.