0.165 as a fraction

Breiz Heurope

2 min read

·

11-03-2025

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Meta Description: Learn how to convert the decimal 0.165 into a fraction. This comprehensive guide provides a step-by-step explanation, simplifying the process and helping you understand the underlying principles. We'll cover the method, simplify the result, and offer examples to solidify your understanding of decimal-to-fraction conversion.

Converting decimals to fractions is a fundamental skill in mathematics. This guide will walk you through the process of converting the decimal 0.165 into its fractional equivalent. We'll not only show you how to do it but also explain the reasoning behind each step.

Understanding the Process

The key to converting decimals to fractions lies in recognizing the place value of each digit. The number 0.165 has three digits after the decimal point: a 1 in the tenths place, a 6 in the hundredths place, and a 5 in the thousandths place. This means we can express 0.165 as:

• 1/10 + 6/100 + 5/1000

Converting 0.165 to a Fraction: Step-by-Step

1. Write the decimal as a fraction over 1: This is our starting point. We write 0.165 as 0.165/1.

2. Multiply the numerator and denominator by 1000: Since there are three digits after the decimal point, we multiply both the numerator and denominator by 1000 (10 to the power of 3). This removes the decimal point from the numerator. The result is:

   (0.165 × 1000) / (1 × 1000) = 165/1000

3. Simplify the fraction: Now, we need to simplify the fraction 165/1000 by finding the greatest common divisor (GCD) of 165 and 1000. The GCD is 5.

4. Divide both the numerator and the denominator by the GCD: Dividing both 165 and 1000 by 5 gives us:

   165 ÷ 5 = 33 1000 ÷ 5 = 200

   Therefore, the simplified fraction is 33/200.

Why This Works

Multiplying by a power of 10 (10, 100, 1000, etc.) shifts the decimal point to the right. This effectively removes the decimal point and turns the decimal into a whole number in the numerator. The denominator reflects the power of 10 used, representing the place value of the last digit after the decimal. Simplifying the fraction reduces it to its lowest terms.

Example: Converting Another Decimal

Let's try converting 0.35 to a fraction:

1. Write as a fraction: 0.35/1
2. Multiply by 100: (0.35 × 100) / (1 × 100) = 35/100
3. Simplify: The GCD of 35 and 100 is 5. 35 ÷ 5 = 7 and 100 ÷ 5 = 20.
4. Simplified fraction: 7/20

Conclusion

Converting decimals to fractions involves understanding place value and simplifying the resulting fraction. By following the steps outlined above, you can confidently convert any decimal, such as 0.165, which we found to be equivalent to the fraction 33/200. Remember to always simplify your fraction to its lowest terms for the most accurate representation.