Next, subtract the exponent in the denominator from the exponent in the numerator:
Then join your new coefficient to your new power of 10:
Practice Questions
1. Multiply
.
2. Divide
.
3. Using scientific notation, multiply
.
4. Using scientific notation, divide
.
Practice Answers
1.
. First, multiply the coefficients:
. Then multiply the powers of 10 by adding the exponents:
. The raw calculation yields
, which converts to the given answer when you express it in scientific notation.
2.
. The ease of math with scientific notation shines through in this problem. Dividing the coefficients yields a coefficient quotient of
, and dividing the powers of 10 (by subtracting their exponents) yields a quotient of
. Marrying the two quotients produces the given answer, already in scientific notation.
3.1.82. First, convert each number to scientific notation:
and
. Next, multiply the coefficients:
. Then add the exponents on the powers of 10:
. Finally, join the new coefficient with the new power:
. Expressed in scientific notation, this answer is
. (Note: Looking back at the original numbers, you see that both factors have only two significant figures; therefore, you should round your answer to match that number of sig figs, making it 1.8. See the later sections “Identifying Significant Figures” and “Doing Arithmetic with Significant Figures” for details.)
4.
. First, convert each number to scientific notation:
and
. Then divide the coefficients:
. Next, subtract the exponent in the denominator from the exponent in the numerator to get the new power of 10:
. Join the new coefficient with the new power:
. Finally, express gratitude that the answer is already conveniently expressed in scientific notation.
Using Scientific Notation to Add and Subtract
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:
of scientific notation: 
