The fraction equivalent of 0.0005 is 1/2000.
Converting 0.0005 to a Fraction: A Step-by-Step Guide
Converting a decimal to a fraction involves understanding place values and simplifying the resulting fraction to its lowest terms. For the decimal 0.0005, the process is straightforward and can be broken down into clear steps.
Step 1: Identify the Place Value
The first crucial step is to determine the place value of the last non-zero digit in the decimal.
- In 0.0005, the digit '5' is in the fourth decimal place.
- The place values after the decimal point are: tenths (0.1), hundredths (0.01), thousandths (0.001), and ten-thousandths (0.0001).
- Since '5' is in the ten-thousandths place, this means 0.0005 represents 5 parts out of 10,000.
Step 2: Write as an Initial Fraction
Based on its place value, the decimal can be written as a fraction where the numerator is the digits after the decimal point and the denominator is the corresponding power of 10 (10, 100, 1000, 10000, etc.).
- Therefore, 0.0005 is initially expressed as 5/10000.
Step 3: Simplify the Fraction to its Lowest Terms
To get the exact and simplest form of the fraction, you need to reduce it to its lowest terms. This is done by dividing both the numerator and the denominator by their Greatest Common Divisor (GCD).
- For the fraction 5/10000, we need to find the GCD of 5 and 10000.
- The GCD of 5 and 10000 is 5.
- Now, divide both parts of the fraction by this GCD:
- Numerator: 5 ÷ 5 = 1
- Denominator: 10000 ÷ 5 = 2000
Step 4: State the Final Simplified Fraction
After simplifying, the fraction is in its simplest form, where the numerator and denominator have no common factors other than 1.
- The simplified fraction is 1/2000.
Summary of Conversion
The conversion process can be summarized in the following table for clarity:
| Step | Description | Calculation | Result |
|---|---|---|---|
| 1. Decimal Input | The decimal to be converted | 0.0005 | |
| 2. Initial Fraction | Write the decimal as a fraction based on place value | 5 / 10000 | 5/10000 |
| 3. Find GCD | Determine the Greatest Common Divisor of numerator and denominator | GCD(5, 10000) = 5 | 5 |
| 4. Simplify Numerator | Divide the numerator by the GCD | 5 ÷ 5 | 1 |
| 5. Simplify Denominator | Divide the denominator by the GCD | 10000 ÷ 5 | 2000 |
| 6. Final Fraction | Combine the simplified numerator and denominator | 1 / 2000 | 1/2000 |
This systematic approach ensures an accurate conversion of any decimal to its simplest fractional form.
