.34375 to fraction

2 min read 01-03-2025

Converting decimals to fractions might seem daunting, but it's a straightforward process once you understand the steps. This guide will walk you through converting the decimal 0.34375 into its fractional equivalent. We'll break it down to make it easy to understand, even if you're not a math whiz.

Understanding Decimal Places

Before we begin, let's refresh our understanding of decimal places. The number 0.34375 has five decimal places. Each place represents a power of ten: tenths, hundredths, thousandths, ten-thousandths, and hundred-thousandths.

Step 1: Write the Decimal as a Fraction Over 1

The first step in converting 0.34375 to a fraction is to write it as a fraction with 1 as the denominator:

0.34375 / 1

Step 2: Multiply the Numerator and Denominator

To eliminate the decimal point, we need to multiply both the numerator and denominator by a power of 10. Since there are five decimal places, we'll multiply by 10⁵, which is 100,000:

(0.34375 * 100000) / (1 * 100000) = 34375 / 100000

Step 3: Simplify the Fraction

Now we have an improper fraction (where the numerator is larger than the denominator). To simplify, we need to find the greatest common divisor (GCD) of the numerator (34375) and the denominator (100000). The GCD is 3125.

Dividing both the numerator and the denominator by the GCD:

34375 ÷ 3125 = 11
100000 ÷ 3125 = 32

This simplifies our fraction to:

11/32

Therefore, 0.34375 as a fraction is 11/32.

Alternative Method: Using Place Value

Another way to approach this is to consider the place value of the last digit. The last digit, 5, is in the hundred-thousandths place. This means we can initially write the decimal as:

34375/100000

Then, simplify by finding the greatest common divisor, as shown above.

Converting Decimals to Fractions: A General Approach

The process outlined above can be applied to any decimal. Here's a summary of the steps:

Write the decimal as a fraction over 1.
Multiply both the numerator and denominator by 10 raised to the power of the number of decimal places.
Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by the GCD.

This method ensures you accurately convert any decimal to its simplest fractional form. Remember to always simplify the fraction to its lowest terms for the most concise representation. Using a calculator with a fraction function can also help you check your work and find the GCD quickly.