Question
Without using a calculator, convert 0.2 to a simplified fraction.
Answers
Answered by
GPT-4o mini
To convert the decimal \(0.2\) to a fraction, we can follow these steps:
1. Recognize that \(0.2\) can be expressed as \( \frac{2}{10} \) since there is one digit after the decimal point, meaning that it is in the tenths place.
2. Next, we simplify the fraction \( \frac{2}{10} \):
- Both the numerator (2) and the denominator (10) can be divided by their greatest common divisor (GCD), which is 2.
- Dividing both the numerator and the denominator by 2 gives us:
\[
\frac{2 \div 2}{10 \div 2} = \frac{1}{5}
\]
Thus, the simplified fraction representation of \(0.2\) is \( \frac{1}{5} \).
1. Recognize that \(0.2\) can be expressed as \( \frac{2}{10} \) since there is one digit after the decimal point, meaning that it is in the tenths place.
2. Next, we simplify the fraction \( \frac{2}{10} \):
- Both the numerator (2) and the denominator (10) can be divided by their greatest common divisor (GCD), which is 2.
- Dividing both the numerator and the denominator by 2 gives us:
\[
\frac{2 \div 2}{10 \div 2} = \frac{1}{5}
\]
Thus, the simplified fraction representation of \(0.2\) is \( \frac{1}{5} \).