To express the number \(0.0002077\) in scientific notation, we need to rewrite it in the form \(a \times 10^n\), where \(1 \leq |a| < 10\) and \(n\) is an integer.
- First, we identify the significant digits in the number \(0.0002077\), which are \(2077\).
- Next, we move the decimal point to the right until it is just to the right of the first non-zero digit. In this case, we move it 4 places to the right, so it will be \(2.077\).
- Since we moved the decimal point 4 places to the right, we must multiply by \(10\) to the power of \(-4\) (because moving to the right means a negative exponent).
Putting it all together, we can express \(0.0002077\) in scientific notation as:
\[ 2.077 \times 10^{-4} \]