What is the fractional form of 0.02?
The Correct Answer and Explanation is:
The fractional form of 0.02 is ( \frac{1}{50} ).
Explanation:
To convert the decimal 0.02 into a fraction, follow these steps:
- Identify the Decimal Place Value:
The decimal number 0.02 has two digits after the decimal point. The last digit (2) is in the hundredths place. This means we can express 0.02 as ( \frac{2}{100} ), because the number 2 is in the hundredths place. - Simplify the Fraction:
The fraction ( \frac{2}{100} ) can be simplified by finding the greatest common divisor (GCD) of the numerator (2) and the denominator (100). The GCD of 2 and 100 is 2. To simplify, divide both the numerator and denominator by 2:
[
\frac{2 \div 2}{100 \div 2} = \frac{1}{50}
] - Result:
Therefore, the simplified fraction form of 0.02 is ( \frac{1}{50} ).
Additional Information:
Understanding the decimal-to-fraction conversion process is essential for many mathematical applications. Decimals like 0.02 can often be written as fractions, particularly when working with ratios, percentages, or when simplifying expressions in algebra or applied math. The process involves recognizing the place value of the decimal (in this case, hundredths) and expressing it as a fraction, then simplifying by dividing both the numerator and the denominator by their GCD.
For example:
- A decimal like 0.5 is equal to ( \frac{5}{10} ), which simplifies to ( \frac{1}{2} ).
- Similarly, 0.75 is equivalent to ( \frac{75}{100} ), which simplifies to ( \frac{3}{4} ).
Understanding how to work with fractions and decimals together is essential for solving problems involving ratios, rates, and percentages, especially in fields like finance, science, and engineering.