.05 as a fraction

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16-01-2025

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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 0.05 into its fractional equivalent. We'll break down the steps, explain the reasoning, and show you how to simplify the fraction to its lowest terms.

Understanding Decimal Places

Before we begin, let's refresh our understanding of decimal places. The decimal point separates the whole number part from the fractional part. In the decimal 0.05, the '0' to the left of the decimal point indicates there are no whole numbers. The '0' immediately after the decimal point represents the tenths place, and the '5' represents the hundredths place. Therefore, 0.05 represents five hundredths.

Converting 0.05 to a Fraction

The decimal 0.05 can be directly written as a fraction based on its place value:

• Step 1: Write the decimal as a fraction with a denominator of 100. Since the last digit (5) is in the hundredths place, we write the number 5 as the numerator and 100 as the denominator: 5/100.

• Step 2: Simplify the fraction. To simplify the fraction, we find the greatest common divisor (GCD) of the numerator (5) and the denominator (100). The GCD of 5 and 100 is 5.

• Step 3: Divide both the numerator and the denominator by the GCD. Dividing both 5 and 100 by 5, we get: 1/20

Therefore, 0.05 expressed as a fraction in its simplest form is 1/20.

Alternative Method: Using Decimal Multiplication

Another approach is to multiply both the numerator and the denominator by a power of 10 to remove the decimal point. Since there are two digits after the decimal point, we'll multiply by 100:

• Step 1: Write the decimal as a fraction: 0.05/1

• Step 2: Multiply both the numerator and denominator by 100: (0.05 * 100) / (1 * 100) = 5/100

• Step 3: Simplify the fraction (as shown above): 5/100 simplifies to 1/20.

This method achieves the same result: 0.05 is equivalent to the fraction 1/20.

Conclusion

Converting decimals to fractions involves understanding place value and simplifying fractions. We've demonstrated two methods for converting 0.05 to its fractional equivalent, resulting in the simplified fraction 1/20. Remember, always simplify your fractions to their lowest terms for the most accurate representation. Mastering this skill will significantly enhance your mathematical abilities.