What is 0.055 as a fraction in simplest form?
The Correct Answer and Explanation is :
To convert the decimal 0.055 into a fraction, we can follow these steps:
- Understanding the Decimal: The decimal 0.055 represents fifty-five thousandths. This means that the value can be written as ( \frac{55}{1000} ) because the last digit (5) is in the thousandths place.
- Setting Up the Fraction: We start with:
[
0.055 = \frac{55}{1000}
] - Simplifying the Fraction: The next step is to simplify ( \frac{55}{1000} ). To do this, we need to find the greatest common divisor (GCD) of the numerator (55) and the denominator (1000).
- Finding the GCD: The factors of 55 are 1, 5, 11, and 55. The factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000. The largest common factor between 55 and 1000 is 5.
- Dividing by the GCD: Now, we divide both the numerator and the denominator by their GCD (5):
[
\frac{55 \div 5}{1000 \div 5} = \frac{11}{200}
] - Final Result: Therefore, the fraction in its simplest form is:
[
0.055 = \frac{11}{200}
]
Summary:
In conclusion, the decimal 0.055 can be expressed as the fraction ( \frac{55}{1000} ). By simplifying this fraction using the GCD, we find that it reduces to ( \frac{11}{200} ). This process illustrates how decimals can be converted to fractions by recognizing the place value of the decimal, establishing an initial fraction, and then simplifying it to its simplest form through finding and using the greatest common divisor. This skill is fundamental in mathematics as it allows for a clearer understanding of numerical values and their relationships.