23.75 as a fraction

2 min read 02-03-2025

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 23.75 into its fractional equivalent. We'll explore the method, explain the reasoning, and even show you how to simplify the resulting fraction to its lowest terms. Learning this skill is beneficial for various mathematical applications and improves your overall number sense.

Understanding Decimal Places

Before we begin, let's quickly review decimal places. The number 23.75 has two digits after the decimal point. The first digit after the decimal (7) represents tenths, and the second digit (5) represents hundredths. This means we can initially express 23.75 as a fraction with a denominator of 100.

Step 1: Write 23.75 as a Fraction over 100

Since there are two digits after the decimal point, we write 23.75 as the numerator over a denominator of 100:

23.75 = 2375/100

This initial fraction is perfectly acceptable, but it isn't in its simplest form yet.

Step 2: Simplify the Fraction

To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator (2375) and the denominator (100). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.

Finding the GCD can be done through prime factorization or using the Euclidean algorithm. For this example, we can observe that both 2375 and 100 are divisible by 25.

Dividing both the numerator and the denominator by 25, we get:

2375 ÷ 25 = 95 100 ÷ 25 = 4

Therefore, the simplified fraction is:

95/4

Step 3: Verify the Result

We can always check our work by converting the simplified fraction back into a decimal. Dividing 95 by 4 gives us 23.75, confirming our conversion is correct.

Alternative Method: Breaking Down the Decimal

Another approach involves breaking down the decimal into its whole number and fractional parts. We can rewrite 23.75 as:

23 + 0.75

Now, convert 0.75 to a fraction:

0.75 = 75/100 = 3/4 (simplified)

Finally, add the whole number and the simplified fraction:

23 + 3/4 = 23 ¾

This confirms that 23.75 is equal to 95/4 or 23 ¾.

Conclusion: 23.75 as a Fraction

Therefore, the decimal 23.75 can be expressed as the fraction 95/4 or the mixed number 23 ¾. Both are correct and equivalent representations. Understanding these conversion methods empowers you to confidently handle similar decimal-to-fraction conversions in the future. Remember to always simplify your fractions to their lowest terms for the most concise representation.