1.58 as a fraction

Daniel Parker

2 min read

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28-02-2025

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Converting decimals to fractions might seem daunting, but it's a straightforward process once you understand the steps. This guide will walk you through how to express 1.58 as a fraction, explaining the logic behind each step. We'll even explore simplifying the fraction to its lowest terms.

Understanding Decimal Places

Before we begin, let's refresh our understanding of decimal places. The number 1.58 has:

• 1: This is the whole number part.
• .5: This represents five-tenths (5/10).
• .08: This represents eight-hundredths (8/100).

These decimal parts are crucial for converting the decimal to a fraction.

Converting 1.58 to a Fraction

Here's the step-by-step conversion of 1.58 to a fraction:

1. Write the decimal as a fraction over 1: This is our starting point. We write 1.58 as 1.58/1.

2. Multiply both numerator and denominator by 100: Since the decimal has two places after the decimal point (hundredths), we multiply both the numerator and the denominator by 100 to eliminate the decimal. This gives us (1.58 x 100) / (1 x 100) = 158/100.

3. Simplify the fraction: Now, we simplify 158/100 by finding the greatest common divisor (GCD) of 158 and 100. The GCD of 158 and 100 is 2. We divide both the numerator and denominator by 2: 158/2 = 79 and 100/2 = 50.

4. Final Result: This leaves us with the simplified fraction 79/50.

Therefore, 1.58 expressed as a fraction is 79/50.

Alternative Method: Breaking Down the Decimal

Another way to approach this is to break down the decimal into its component parts:

1. Separate the whole number: The whole number '1' remains as it is.

2. Convert the decimal part: The decimal part, 0.58, can be written as 58/100.

3. Simplify the decimal fraction: Similar to the previous method, we simplify 58/100 by dividing both numerator and denominator by their GCD (2), resulting in 29/50.

4. Combine the whole number and fraction: Finally, we add the whole number back in: 1 + 29/50 = 1 and 29/50, which is an improper fraction, 79/50.

Both methods arrive at the same simplified improper fraction: 79/50.

Converting Improper Fractions to Mixed Numbers

The fraction 79/50 is an improper fraction (the numerator is larger than the denominator). If you prefer a mixed number (a whole number and a fraction), you can convert it as follows:

1. Divide the numerator by the denominator: 79 ÷ 50 = 1 with a remainder of 29.

2. Write the mixed number: The quotient (1) becomes the whole number part, the remainder (29) becomes the numerator, and the denominator remains the same (50). Therefore, the mixed number equivalent is 1 29/50.

Conclusion

Converting decimals like 1.58 into fractions involves understanding place values and the process of simplifying fractions. Whether you choose the direct multiplication method or the breakdown method, both lead to the same accurate result. Remember to simplify your fraction to its lowest terms for the most concise representation. Now you know how to express 1.58 as a fraction - both as an improper fraction (79/50) and as a mixed number (1 29/50).