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34375 as a fraction

34375 as a fraction

2 min read 05-02-2025
34375 as a fraction

Meta Description: Learn how to convert the decimal 34375 into a fraction. This easy-to-follow guide breaks down the process step-by-step, including simplifying the fraction to its lowest terms. Perfect for students and anyone needing to understand decimal-to-fraction conversion!

Title Tag: 34375 as a Fraction: Simple Conversion Guide

Understanding Decimal to Fraction Conversion

Converting a decimal number like 34375 into a fraction involves understanding place value. Each digit in a decimal represents a power of ten. Let's break down how to convert 34375.

Step 1: Write the Decimal as a Fraction over 1

Our first step is simple: write the decimal number (34375) as the numerator of a fraction, with 1 as the denominator:

34375/1

Step 2: Multiply the Numerator and Denominator

To eliminate the decimal point, we need to multiply both the numerator and the denominator by a power of 10. Since there are five digits after the decimal point, we'll multiply by 100000:

(34375 * 100000) / (1 * 100000) = 3437500000/100000

Step 3: Simplify the Fraction

Now we need to simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. This is the largest number that divides both numbers evenly. Finding the GCD can sometimes be done by inspection, or you might need to use a method like the Euclidean algorithm. In this case, we can see that both numbers are divisible by 5, and it turns out that 125 is a common factor:

3437500000 / 100000 = 343750/1000 = 6875/200 = 1375/40 = 275/8 = 55/16

Therefore, 34375 as a fraction simplified to its lowest terms is 55/16.

Alternative Methods and Further Exploration

While the above method is straightforward, there are other ways to approach this conversion. You could also try expressing the decimal as a sum of fractions representing different place values and then combining them.

Checking Your Work

It's always a good idea to verify your answer. You can easily check this by performing the division: 55 divided by 16 equals 3.4375.

Conclusion

Converting decimals to fractions is a fundamental skill in mathematics. By following these steps and practicing, you'll become proficient at converting decimals, like 34375, into their fractional equivalents. Remember to always simplify your fraction to its lowest terms for the most accurate representation.

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