0.165 as a fraction

2 min read 01-03-2025

Understanding how to convert decimals to fractions is a fundamental skill in mathematics. This article will guide you through the process of converting the decimal 0.165 into its fractional equivalent. We'll break it down step-by-step, making it easy to understand and replicate for other decimal conversions.

Understanding Decimal Places

Before we begin, let's review the meaning of decimal places. In the decimal 0.165:

The digit 1 is in the tenths place (1/10).
The digit 6 is in the hundredths place (6/100).
The digit 5 is in the thousandths place (5/1000).

This means 0.165 can be written as the sum of these fractions: 1/10 + 6/100 + 5/1000.

Converting 0.165 to a Fraction

Here's how to convert 0.165 to a fraction:

Write the decimal as a fraction over 1:

0.165/1
Multiply the numerator and denominator by a power of 10 to eliminate the decimal point:

Since there are three digits after the decimal point, we'll multiply by 1000:

(0.165 * 1000) / (1 * 1000) = 165/1000
Simplify the fraction:

We need to find the greatest common divisor (GCD) of 165 and 1000 to simplify the fraction. The GCD of 165 and 1000 is 5.

Divide both the numerator and the denominator by 5:

165 ÷ 5 = 33 1000 ÷ 5 = 200

Therefore, the simplified fraction is 33/200.

Therefore, 0.165 as a fraction is 33/200.

Alternative Method: Using the Place Value

Another way to approach this is to directly use the place value of the last digit. Since the last digit (5) is in the thousandths place, we can initially write the decimal as 165/1000. Then, simplify as shown above by dividing both the numerator and denominator by their greatest common divisor (5).

Checking Your Work

It's always a good idea to check your work. You can use a calculator to divide 33 by 200. You should get 0.165, confirming that your fraction conversion is correct.

Converting Other Decimals to Fractions

The steps outlined above can be used to convert any decimal to a fraction. Simply identify the place value of the last digit, write the decimal as a fraction, and simplify. Remember to always find the greatest common divisor to get the simplest form of the fraction.

Conclusion

Converting decimals to fractions is a valuable skill. By following these steps, you can confidently convert decimals like 0.165 into their fractional equivalent, which in this case is 33/200. Remember to practice to master this important mathematical concept.