Question

Can .4444… and .581372… be written as a fraction

Answer 1

Yes, both \(0.4444\ldots\) and \(0.581372\ldots\) can be written as fractions.

1. **For \(0.4444\ldots\)**:
- Let \(x = 0.4444\ldots\).
- Then, we can write:
\[
10x = 4.4444\ldots
\]
- Now, we subtract the first equation from the second:
\[
10x - x = 4.4444\ldots - 0.4444\ldots
\]
\[
9x = 4
\]
- Dividing both sides by 9 gives:
\[
x = \frac{4}{9}
\]

Therefore, \(0.4444\ldots = \frac{4}{9}\).

2. **For \(0.581372\ldots\)** (assuming it continues as \(0.581372581372\ldots\) with a repeating section):
- Let \(y = 0.581372581372\ldots\).
- The repeating part is 6 digits long, so we multiply by \(10^6\) (or 1,000,000):
\[
1,000,000y = 581372.581372\ldots
\]
- Now, we subtract:
\[
1,000,000y - y = 581372.581372\ldots - 0.581372581372\ldots
\]
\[
999,999y = 581372
\]
- Dividing both sides by 999,999 gives:
\[
y = \frac{581372}{999999}
\]

This fraction can be simplified with a calculator or by finding the GCD of the numerator and denominator.

Thus, \(0.581372581372\ldots = \frac{581372}{999999}\).

In summary:
- \(0.4444\ldots = \frac{4}{9}\)
- \(0.581372\ldots\) as a fraction is approximately \(\frac{581372}{999999}\), which may be simplified further.