1.429 as a fraction in simplest form

Breiz Heurope

2 min read

·

11-03-2025

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Converting decimals to fractions might seem daunting, but it's a straightforward process. This article will guide you through converting the decimal 1.429 into its simplest fraction form. We'll break down the steps and explain the reasoning behind each one. Understanding this process will equip you to tackle similar decimal-to-fraction conversions.

Understanding Decimal Places

Before we begin, let's refresh our understanding of decimal places. The number 1.429 has:

• 1: This is the ones place.
• 4: This is the tenths place (1/10).
• 2: This is the hundredths place (1/100).
• 9: This is the thousandths place (1/1000).

This means 1.429 can be understood as 1 + 0.4 + 0.02 + 0.009.

Step-by-Step Conversion

Here's how to convert 1.429 into a fraction:

1. Write the decimal as a fraction over 1:

This is our starting point. We write the decimal as a numerator and place it over the denominator 1:

1.429/1

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 denominator by 1000. This removes the decimal point:

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

3. Simplify the fraction:

Now we need to simplify the fraction to its lowest terms. We look for the greatest common divisor (GCD) of 1429 and 1000. In this case, there isn't a common divisor other than 1. Therefore, the fraction is already in its simplest form.

The Final Answer

Therefore, 1.429 as a fraction in its simplest form is 1429/1000.

Alternative Method: Breaking Down the Decimal

We could also approach this by breaking down the decimal into its component parts:

1.429 = 1 + 0.4 + 0.02 + 0.009

Convert each decimal part to a fraction:

• 1 = 1/1
• 0.4 = 4/10 = 2/5
• 0.02 = 2/100 = 1/50
• 0.009 = 9/1000

Then, add the fractions together, finding a common denominator (in this case, 1000):

(1000/1000) + (400/1000) + (20/1000) + (9/1000) = 1429/1000

This again confirms that the simplest form of the fraction is 1429/1000.

Conclusion

Converting decimals to fractions involves understanding place value and finding the greatest common divisor to simplify. 1.429, when expressed as a fraction in its simplest form, is 1429/1000. This method can be applied to convert other decimals to fractions as well. Remember to always simplify your fraction to its lowest terms for the most accurate representation.