What is 0.1875 as a Fraction: A Step-by-Step Guide

Converting decimal numbers to fractions is a fundamental skill in mathematics. In this article, we will specifically address how to convert 0.1875 into a fraction. Understanding this process can help you tackle similar decimal to fraction conversions with ease.

The Process of Converting 0.1875 to a Fraction

Let's begin with the decimal value 0.1875 and convert it step-by-step into its fractional equivalent. The process involves several steps, including basic arithmetic and simplification.

Step 1: Expressing the Decimal as a Fraction

First, we express the decimal 0.1875 as a fraction with a denominator that is a power of 10. Since 0.1875 has four decimal places, we can write it as:

[ 0.1875 frac{1875}{10000} ]Now, we have the decimal 0.1875 in the form of a fraction.

Step 2: Simplifying the Fraction

The next step is to simplify the fraction (frac{1875}{10000}) by finding the greatest common divisor (GCD) of the numerator and the denominator.

We start by dividing both the numerator and the denominator by 5:

[ frac{1875}{10000} frac{1875 div 5}{10000 div 5} frac{375}{2000} ]Next, we simplify (frac{375}{2000}) by dividing both the numerator and the denominator by 5:

[ frac{375}{2000} frac{375 div 5}{2000 div 5} frac{75}{400} ]We continue simplifying by dividing both the numerator and the denominator by 5:

[ frac{75}{400} frac{75 div 5}{400 div 5} frac{15}{80} ]Finally, we simplify (frac{15}{80}) by dividing both the numerator and the denominator by 5:

[ frac{15}{80} frac{15 div 5}{80 div 5} frac{3}{16} ]Conclusion

Therefore, the decimal 0.1875 can be expressed as the fraction (frac{3}{16}). This step-by-step approach can be applied to any similar decimal to fraction conversion.

Additional Tips for Converting Decimals to Fractions

Here are a few more tips to help you convert decimals to fractions smoothly:

Identify the Denominator: Count the number of decimal places and use that as the denominator of your initial fraction. Find the GCD: Determine the greatest common divisor of the numerator and the denominator. Reduce the Fraction: Divide both the numerator and the denominator by the GCD to simplify the fraction.

By following these steps and tips, you can easily convert any decimal to a fraction.