0.100 as a fraction
Understand the Problem
The question is asking how to convert the decimal number 0.100 into a fraction. To do this, we can recognize that 0.100 is equivalent to 100/1000, which can be simplified.
Answer
The decimal 0.100 is equivalent to the fraction $\frac{1}{10}$.
Answer for screen readers
The fraction representation of the decimal 0.100 is $\frac{1}{10}$.
Steps to Solve
- Express the Decimal as a Fraction
To convert the decimal 0.100 into a fraction, recognize that it represents 100 out of 1000. Thus, we can express this as:
$$ \frac{100}{1000} $$
- Simplify the Fraction
Next, simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 100 and 1000 is 100. Divide both the numerator and denominator by 100:
$$ \frac{100 \div 100}{1000 \div 100} = \frac{1}{10} $$
- Final Fraction
The simplified fraction for the decimal 0.100 is:
$$ \frac{1}{10} $$
The fraction representation of the decimal 0.100 is $\frac{1}{10}$.
More Information
When converting decimals to fractions, it's important to note how many places are after the decimal point, as this determines the denominator when writing the fraction. In this case, 0.100 has three decimal places, initially leading us to 1000 as the denominator. However, simplifying the fraction gives a clearer result.
Tips
- Not simplifying the fraction after converting, which can lead to an incorrect or more complex answer.
- Miscounting the decimal places, which may result in an incorrect denominator.
