0.0625 as a fraction

Problem:

Converting $0.0625$ to a Fraction

Answer:

The decimal $0.0625$ can be expressed as the fraction $\frac{1}{16}$.

Method: Hints

To convert a decimal to a fraction, follow these steps:

1. Identify the place value: Determine the place value of the last digit in the decimal. For $0.0625$, the last digit is in the ten-thousandths place.
2. Write as a fraction: Express the decimal as a fraction with the corresponding place value as the denominator. For $0.0625$, this would be $\frac{625}{10000}$.
3. Simplify the fraction: Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD).

List of Calculations:

1. Identify the place value: The last digit '5' is in the ten-thousandths place.

   • Formula: None needed for this step.

2. Write as a fraction: Write $0.0625$ as $\frac{625}{10000}$.

   • Formula: None needed for this step.

3. Simplify the fraction: Find the GCD of $625$ and $10000$ and divide both by it.

   • Formula: $\frac{625 \div 625}{10000 \div 625} = \frac{1}{16}$.

Verification:

To ensure the answer is correct, multiply the denominator of the fraction by the fraction itself and see if you get the original decimal:

• $\frac{1}{16} \times 16 = 1$
• $0.0625 \times 16 = 1$

Since both operations yield the same result, the fraction $\frac{1}{16}$ is indeed the correct representation of the decimal $0.0625$.

Related Knowledge Points:

• Decimal to Fraction Conversion: To convert a decimal to a fraction, identify the place value of the last digit, write the decimal over that place value as a fraction, and then simplify.
• Simplifying Fractions: To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD).
• Place Value: The place value in decimals starts with tenths, hundredths, thousandths, and so on, moving to the right of the decimal point.

Detailed Explanation:

When converting the decimal $0.0625$ to a fraction, we first observe that the last digit '5' is in the ten-thousandths place. This means that we can write $0.0625$ as $\frac{625}{10000}$. To simplify this fraction, we need to find the greatest common divisor of $625$ and $10000$. Since $625$ is a factor of $10000$, the GCD is $625$. Dividing both the numerator and the denominator by $625$ gives us $\frac{1}{16}$, which is the simplest form of the fraction.

In conclusion, the decimal $0.0625$ is equivalent to the fraction $\frac{1}{16}$ when expressed in its simplest form.