Question

What is the rule for adding/subtracting numbers in scientific notation with different powers?

a) Combine coefficients; keep the common exponent.
b) Multiply coefficients; add the common exponent.
c) Add coefficients; subtract the common exponent.
d) Divide coefficients; maintain the common exponent.

Answer 1

The rule for adding or subtracting numbers in scientific notation with different powers is to adjust one or both numbers to have the same exponent, then add or subtract the coefficients while maintaining the common exponent.

Step-by-step explanation:

When adding or subtracting numbers in scientific notation with different powers, the correct rule is to first adjust the numbers so they have the same exponent. Once the exponents are the same, you can combine the coefficients while keeping the common exponent unchanged. This does not match any of the provided options exactly, but the process is to make the exponents the same before combining the coefficients.

For example, consider the problem:

(1.36 × 10²) + (4.73 × 10³)

To solve this, you would adjust the exponent of the smaller number to match the larger one:

(0.136 × 10³) + (4.73 × 10³) = 4.866 × 10³

Observe that the coefficient 1.36 was modified to 0.136 to increase its exponent from 2 to 3 to match the other term. We then added the coefficients and kept the exponent of 10³.