1.429 as a fraction in simplest form

Daniel Parker

less than a minute read

·

02-03-2025

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Converting the decimal 1.429 into a fraction involves understanding place values and simplifying fractions. This seemingly simple task actually offers a great opportunity to review fundamental math concepts. Let's break down the process step-by-step.

Understanding Decimal Place Values

Before we begin, remember that each digit in a decimal number holds a specific place value. In 1.429:

• 1 is in the ones place (representing 1)
• 4 is in the tenths place (representing 4/10)
• 2 is in the hundredths place (representing 2/100)
• 9 is in the thousandths place (representing 9/1000)

Converting the Decimal to a Fraction

1. Write the decimal as a fraction over 1: We begin by writing 1.429 as a fraction: 1.429/1

2. Multiply the numerator and denominator by 1000: To remove the decimal point, we multiply both the numerator and the denominator by 1000 (since the decimal extends to the thousandths place). This gives us:

   (1.429 * 1000) / (1 * 1000) = 1429/1000

3. Check for common factors: Now we need to simplify the fraction by finding the greatest common divisor (GCD) of the numerator (1429) and the denominator (1000). Let's find if they share any common factors.

   • The factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.
   • 1429 is not divisible by any of these factors, except for 1.

Since the only common factor between 1429 and 1000 is 1, the fraction is already in its simplest form.

Therefore, 1.429 as a fraction in simplest form is $\boxed{1429/1000}$