What Is 1.625 As A Fraction

What is 1.625 as a Fraction? A Step-by-Step Guide

Meta Description: Learn how to convert the decimal 1.625 into a fraction. This guide provides a simple, step-by-step method, perfect for students and anyone needing to understand decimal-to-fraction conversion. We'll also explore simplifying fractions.

Converting decimals to fractions might seem daunting at first, but it's a straightforward process once you understand the underlying principles. This article will walk you through converting 1.625 into a fraction, explaining each step clearly. We'll also cover simplifying the fraction to its lowest terms, ensuring you have a complete understanding of the process.

Understanding Decimal Places

Before we begin, let's briefly review decimal place values. In the number 1.625:

• 1 is in the ones place.
• 6 is in the tenths place (representing 6/10).
• 2 is in the hundredths place (representing 2/100).
• 5 is in the thousandths place (representing 5/1000).

This understanding is crucial for converting decimals to fractions.

Converting 1.625 to a Fraction: Step-by-Step

1. Write the decimal as a fraction over 1: This is our starting point. We can write 1.625 as 1.625/1.

2. Multiply the numerator and denominator by 1000: Because the decimal extends to the thousandths place (three decimal places), we multiply both the numerator and the denominator by 1000 to eliminate the decimal point. This is equivalent to multiplying by 1 (1000/1000 = 1), so we don't change the value of the number. This gives us:

   (1.625 x 1000) / (1 x 1000) = 1625/1000

3. Simplify the fraction: Now we need to simplify the fraction 1625/1000 to its lowest terms. We find the greatest common divisor (GCD) of 1625 and 1000. The GCD of 1625 and 1000 is 125. Divide both the numerator and the denominator by 125:

   1625 ÷ 125 = 13 1000 ÷ 125 = 8

   This simplifies the fraction to 13/8.

4. Convert to a mixed number (optional): The fraction 13/8 is an improper fraction (the numerator is larger than the denominator). We can convert this to a mixed number by dividing the numerator by the denominator:

   13 ÷ 8 = 1 with a remainder of 5.

   Therefore, 13/8 can be written as the mixed number 1 5/8.

Therefore, 1.625 as a fraction is 13/8 or 1 5/8.

Key Takeaways and Further Exploration

This process can be applied to any decimal number. Remember to multiply by a power of 10 (10, 100, 1000, etc.) corresponding to the number of decimal places. Always simplify the resulting fraction to its lowest terms for the most accurate representation. Practice converting other decimals to fractions to solidify your understanding of this essential mathematical skill. You can explore further by working with more complex decimals and practicing finding the greatest common divisor efficiently.