23.75 as a fraction

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13-02-2025

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Meta Description: Learn how to convert the decimal 23.75 into a fraction. This comprehensive guide breaks down the process step-by-step, making it easy to understand for all skill levels. We'll cover the method, provide examples, and show you how to simplify your answer to its lowest terms. Mastering this conversion is crucial for various mathematical applications.

Understanding how to convert decimals to fractions is a fundamental skill in mathematics. This guide will walk you through converting the decimal 23.75 into a fraction. We'll explain the process clearly and concisely, ensuring you grasp the concept and can apply it to other decimal-to-fraction conversions.

Understanding Decimals and Fractions

Before we dive into the conversion, let's refresh our understanding of decimals and fractions. A decimal is a number expressed in the base-ten numeral system, using a decimal point to separate the integer part from the fractional part. A fraction, on the other hand, represents a part of a whole, expressed as a ratio of two numbers (numerator and denominator).

Converting 23.75 to a Fraction: A Step-by-Step Approach

Here's how to convert the decimal 23.75 into a fraction:

Step 1: Write the decimal as a fraction with a denominator of 1.

23.75/1

Step 2: Multiply both the numerator and the denominator by 100 to remove the decimal point. We use 100 because there are two digits after the decimal point. If there were three digits, we'd multiply by 1000, and so on.

(23.75 * 100) / (1 * 100) = 2375/100

Step 3: Simplify the fraction. This involves finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by it. The GCD of 2375 and 100 is 25.

2375 ÷ 25 = 95 100 ÷ 25 = 4

Therefore, the simplified fraction is:

95/4

Alternative Method: Breaking Down the Decimal

Another way to approach this conversion is by breaking down the decimal into its whole number and fractional parts.

23.75 can be written as 23 + 0.75

Now, convert 0.75 to a fraction:

0.75 = 75/100

Simplify 75/100 by dividing both the numerator and denominator by their GCD (25):

75 ÷ 25 = 3 100 ÷ 25 = 4

So 0.75 = 3/4

Now add the whole number back:

23 + 3/4 = 23 3/4 or as an improper fraction: (23 * 4 + 3) / 4 = 95/4

Practical Applications of Decimal to Fraction Conversions

Converting decimals to fractions is useful in many areas, including:

• Baking and Cooking: Recipes often use fractional measurements.
• Construction and Engineering: Precise measurements are critical.
• Finance: Calculating interest and proportions.
• General Mathematics: Solving equations and simplifying expressions.

Conclusion: Mastering Decimal to Fraction Conversions

Converting 23.75 to a fraction, resulting in 95/4, is straightforward using the methods outlined above. Understanding these processes allows for accurate calculations and problem-solving across various mathematical disciplines. Remember to always simplify your fractions to their lowest terms for the most concise representation. Practice converting other decimals to fractions to solidify your understanding.