To determine the correct sign between \(1.0 \times 10^{-9}\) and \(0.0000001\), we first convert both numbers into the same format for easier comparison.
- The scientific notation \(1.0 \times 10^{-9}\) is equal to \(0.000000001\).
- The decimal \(0.0000001\) can also be expressed in scientific notation as \(1.0 \times 10^{-7}\).
Now, let's compare the two numbers:
- \(1.0 \times 10^{-9} = 0.000000001\)
- \(0.0000001 = 1.0 \times 10^{-7}\)
Since \(0.000000001\) is less than \(0.0000001\), we can conclude:
\[ 1.0 \times 10^{-9} < 0.0000001 \]
Thus, the correct sign to make the statement true is:
\[ < \]