Final answer:
To simplify (8.2 × 10⁻⁸) - (3.7 × 10⁻⁹), adjust the second term to have the same power of 10 and then subtract, resulting in 7.83 × 10⁻⁸ in proper scientific notation.
Step-by-step explanation:
To simplify the expression (8.2 × 10⁻⁸) - (3.7 × 10⁻⁹), we should first ensure that both terms have the same exponent for the power of 10. Since they do not, we need to change one of them.
We can convert the second term from 10⁻⁹ to 10⁻⁸ to match the first term. To do this, we must also adjust the coefficient:
- (3.7 × 10⁻⁹) × (10/10) = (3.7 × 0.1) × 10⁻⁸ = 0.37 × 10⁻⁸
Now we subtract the second term from the first term:
- (8.2 × 10⁻⁸) - (0.37 × 10⁻⁸)
- 8.2 - 0.37 = 7.83
- So, the simplified expression is 7.83 × 10⁻⁸.
This is already in proper scientific notation since the coefficient is between 1 and 10.