.6875 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 guide will walk you through the process of converting the decimal 0.6875 into its fractional equivalent. We'll break it down step-by-step, making it easy to understand and replicate for other decimal-to-fraction conversions.

Understanding Decimal Places

Before we begin, let's quickly review decimal places. Each digit to the right of the decimal point represents a fraction of a power of 10. For example:

• 0.1 is one-tenth (1/10)
• 0.01 is one-hundredth (1/100)
• 0.001 is one-thousandth (1/1000)
• 0.0001 is one ten-thousandth (1/10000)

Converting .6875 to a Fraction

Our decimal, .6875, has four digits after the decimal point. This means the last digit is in the ten-thousandths place. Therefore, we can write .6875 as the fraction:

6875/10000

Simplifying the Fraction

This fraction isn't in its simplest form. To simplify, we need to find the greatest common divisor (GCD) of 6875 and 10000. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.

One way to find the GCD is by prime factorization. Let's find the prime factors of both numbers:

• 6875 = 5⁴ x 11
• 10000 = 2⁴ x 5⁴

The common factor is 5⁴ (which is 625). We can divide both the numerator and the denominator by 625:

6875 ÷ 625 = 11
10000 ÷ 625 = 16

This simplifies our fraction to:

11/16

Therefore, .6875 as a fraction is 11/16.

Alternative Method: Using Decimal Place Value

A quicker method uses the decimal place value directly. Since there are four decimal places, we can initially write the decimal as:

6875/10000

Then, we can simplify by dividing both the numerator and the denominator by 25 repeatedly until we get to the simplest form.

• 6875/10000 = 275/400 = 55/80 = 11/16

Conclusion

Converting decimals to fractions involves understanding place value and simplifying the resulting fraction. In this case, we successfully converted .6875 to its simplest fractional form: 11/16. Remember, the key is to find the greatest common divisor and divide both the numerator and the denominator to simplify the fraction to its lowest terms. This method works for any decimal you want to convert.