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Addition or subtraction gets easier when you express your numbers as coefficients of identical powers of 10. To wrestle your numbers into this form, you may need to use coefficients less than 1 or greater than 10. So scientific notation is a bit too strict for addition and subtraction, but exponential notation still serves you well.

Remember: To add two numbers easily by using exponential notation, first express each number as a coefficient and a power of 10, making sure that 10 has the same exponent in each number. Then add the coefficients. To subtract numbers in exponential notation, follow the same steps but subtract the coefficients.

Examples

Q. Use exponential notation to add these numbers: .

A. . First, write both numbers with the same power of 10:

Next, add the coefficients:

Finally, join your new coefficient to the shared power of 10:

Q. Use exponential notation to subtract: .

A. . First, convert both numbers to the same power of 10. We’ve chosen 10^– 2:

Next, subtract the coefficients:

Then join your new coefficient to the shared power of 10:

Practice Questions

1. Add .

2. Subtract .

3. Use exponential notation to add .

4. Use exponential notation to subtract .

Practice Answers

1. . Because the numbers are each already expressed with identical powers of 10, you can simply add the coefficients: . Then join the new coefficient with the original power of 10.

2. . Because the numbers are each expressed with the same power of 10, you can simply subtract the coefficients: . Then join the new coefficient with the original power of 10.

3. (or an equivalent expression). First, convert the numbers so they each use the same power of 10: and . Here, we use 10^– 3, but you can use a different power as long as the power is the same for each number. Next, add the coefficients: . Finally, join the new coefficient with the shared power of 10.

4. (or an equivalent expression). First, convert the numbers so each uses the same power of 10: and . Here, we’ve picked 10², but any power is fine as long as the two numbers have the same power. Then subtract the coefficients: . Finally, join the new coefficient with the shared power of 10.