Express 0.62as a fraction.
The Correct Answer and Explanation is:
To express the decimal 0.62 as a fraction, follow these steps:
- Identify the Decimal Place Value: The decimal 0.62 has two digits after the decimal point, indicating that it is in the hundredths place.
- Convert to Fraction: You can express 0.62 as a fraction by writing it over its place value. Since it is in the hundredths place, we can write:
[
0.62 = \frac{62}{100}
] - Simplify the Fraction: The next step is to simplify the fraction if possible. To simplify (\frac{62}{100}), we need to find the greatest common divisor (GCD) of the numerator (62) and the denominator (100).
- The factors of 62 are 1, 2, 31, and 62.
- The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. The largest common factor is 2.
- Divide Both Numerator and Denominator by the GCD:
[
\frac{62 \div 2}{100 \div 2} = \frac{31}{50}
] - Final Result: Thus, the decimal 0.62 expressed as a simplified fraction is:
[
0.62 = \frac{31}{50}
]
Explanation:
Understanding how to convert decimals to fractions is an important skill in mathematics, especially when working with ratios, percentages, and measurements. When converting a decimal to a fraction, identifying the place value helps determine the denominator. For instance, in the case of 0.62, the number 62 is in the hundredths position, which means it can be represented as 62 parts out of 100.
Simplifying fractions is equally essential because it helps in representing numbers in their simplest form, making them easier to understand and compare. The process of finding the GCD, as demonstrated, ensures that the fraction is reduced to its most basic representation. The final fraction (\frac{31}{50}) not only maintains the value of the decimal but also provides a clearer numerical relationship that can be useful in various mathematical contexts, including algebra, geometry, and beyond.