Question

Without using a calculator, convert 0.4 to a simplified fraction.

Answer 1

To convert the decimal 0.4 to a simplified fraction, we start by writing it as a fraction over 1:

\[
0.4 = \frac{0.4}{1}
\]

Since 0.4 has one decimal place, we can eliminate the decimal by multiplying both the numerator and denominator by 10:

\[
0.4 = \frac{0.4 \times 10}{1 \times 10} = \frac{4}{10}
\]

Next, we simplify the fraction \(\frac{4}{10}\). Both the numerator and the denominator can be divided by their greatest common divisor, which is 2:

\[
\frac{4 \div 2}{10 \div 2} = \frac{2}{5}
\]

Thus, the simplified fraction for 0.4 is

\[
\frac{2}{5}
\]