21.875 as a fraction

Charlotte

2 min read

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02-03-2025

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Converting decimals to fractions might seem daunting, but it's a straightforward process once you understand the steps. This article will guide you through converting the decimal 21.875 into its fractional equivalent. We'll break down the method, explain the reasoning, and provide you with a clear understanding of how to tackle similar conversions.

Understanding Decimal Places

Before we begin, let's quickly review decimal places. The number 21.875 has three digits after the decimal point. These represent thousandths. The 8 is in the tenths place, the 7 is in the hundredths place, and the 5 is in the thousandths place. This understanding is crucial for converting to a fraction.

Converting 21.875 to a Fraction

Here's how to convert 21.875 into a fraction:

1. Identify the decimal part: Separate the whole number (21) from the decimal part (.875).

2. Write the decimal as a fraction: The decimal .875 can be written as 875/1000. Remember, the number of decimal places tells us the denominator (1000 in this case, because there are three decimal places).

3. Simplify the fraction: Now we need to simplify 875/1000. Find the greatest common divisor (GCD) of 875 and 1000. The GCD of 875 and 1000 is 125. Divide both the numerator and the denominator by 125:

   875 ÷ 125 = 7 1000 ÷ 125 = 8

   This simplifies the fraction to 7/8.

4. Combine the whole number and fraction: We started with a whole number (21) and a fractional part (7/8). Combine these to get the final answer: 21 7/8.

Therefore, 21.875 as a fraction is 21 7/8.

Alternative Method: Using Powers of 10

Another approach uses powers of 10. Since there are three decimal places, we multiply both the numerator and denominator by 1000:

• 21.875 x 1000/1000 = 21875/1000

Then simplify as shown above. This will still result in the fraction 21 7/8.

Converting Other Decimals to Fractions

The same method applies to other decimals. Just remember these steps:

1. Write the decimal as a fraction over a power of 10 (10, 100, 1000, etc., depending on the number of decimal places).
2. Simplify the fraction by finding the greatest common divisor of the numerator and the denominator.
3. If there's a whole number, combine it with the simplified fraction.

Conclusion

Converting decimals like 21.875 to fractions is a valuable skill with applications in various fields. By following these steps, you can confidently convert any decimal number into its fractional equivalent. Remember to always simplify your fraction to its lowest terms for the most accurate representation. Now you know how to handle 21.875 and any other decimal you encounter!