0.165 in fraction

Daniel Parker

2 min read

·

24-02-2025

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The decimal 0.165 might seem simple, but converting it to a fraction requires understanding place value and simplifying fractions. This guide breaks down the process, making it easy to understand. We'll learn how to convert 0.165 to its simplest fraction form and explore similar decimal-to-fraction conversions.

Understanding Decimal Place Value

Before converting, it's crucial to understand how decimal places work. Each place to the right of the decimal point represents a decreasing power of 10: tenths, hundredths, thousandths, and so on. In 0.165, the '1' is in the tenths place, the '6' is in the hundredths place, and the '5' is in the thousandths place.

Converting 0.165 to a Fraction

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: Because the last digit (5) is in the thousandths place, we multiply both the top and bottom by 1000 to remove the decimal point. This gives us 165/1000.

3. Simplify the fraction: Now, we need to find the greatest common divisor (GCD) of 165 and 1000 to simplify the fraction to its lowest terms. The GCD of 165 and 1000 is 5.

4. Divide both numerator and denominator by the GCD: Dividing both 165 and 1000 by 5, we get 33/200.

Therefore, 0.165 as a fraction in its simplest form is 33/200.

Other Examples of Decimal to Fraction Conversions

Let's look at a few more examples to solidify your understanding:

• 0.75: This is 75/100. Simplifying by dividing by 25 gives us 3/4.

• 0.2: This is 2/10. Simplifying by dividing by 2 gives us 1/5.

• 0.625: This is 625/1000. Simplifying by dividing by 125 gives us 5/8.

Tips for Converting Decimals to Fractions

• Identify the place value: Determine the smallest place value used in the decimal (tenths, hundredths, thousandths, etc.). This dictates the denominator.

• Remove the decimal point: Multiply both the numerator and denominator by a power of 10 to remove the decimal point.

• Simplify: Always simplify the fraction to its lowest terms by finding the GCD of the numerator and denominator.

• Practice: The more you practice, the easier it will become.

Conclusion

Converting decimals like 0.165 to fractions involves a straightforward process. By understanding place value and simplifying fractions, you can easily convert any decimal into its equivalent fractional representation. Remember the steps, and you’ll master this skill in no time! Now you know that 0.165 is equal to the simplified fraction 33/200.