To express [tex]\( 7.89 \times 10^{-8} \)[/tex] in common notation, follow these steps:
1. Understand the scientific notation: The number [tex]\( 7.89 \times 10^{-8} \)[/tex] means we need to move the decimal point 8 places to the left.
2. Initial positioning: The number 7.89 has its decimal point right after the 7.
3. Shift the decimal point:
- Move the decimal point 8 places to the left from its current position.
- As we move the decimal point, each place we shift it to the left adds zeros to the left of the number.
4. Actual shifting: Starting from the decimal point in 7.89, represent the shifts step by step:
- Move 1 place to the left: 0.789
- Move 2 places to the left: 0.0789
- Move 3 places to the left: 0.00789
- Move 4 places to the left: 0.000789
- Move 5 places to the left: 0.0000789
- Move 6 places to the left: 0.00000789
- Move 7 places to the left: 0.000000789
- Move 8 places to the left: 0.0000000789
After 8 places, the decimal point is placed and we fill in leading zeros as necessary.
5. Result: The final common notation displaying the number is:
[tex]\[ 0.00000008 \][/tex]
Thus, [tex]\( 7.89 \times 10^{-8} \)[/tex] expressed in common notation is [tex]\( 0.00000008 \)[/tex].
