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How to Do Subtraction With Exponential Numbers

Scientists tend to work with quantities that are either extremely large or exceptionally small. The number of molecules in a drop of water, for example, is many billions. To make these numbers manageable, scientists have developed the use of exponential numbers, otherwise known as scientific notation. Exponential numbers appear in the form of A x 10^n, where A is the coefficient and n is the exponent. This expression means that A should be multiplied by a value derived by multiplying "n" 10s together. You can subtract two such exponential expressions by first bringing them to a common exponent.

Things You'll Need

Calculator

Instructions

- 1
  Write out the two exponential numbers that you wish to subtract. For example, you might want to subtract 3.2 x 10^2 from 6.5 x 10^3.
- 2
  Calculate the difference between the exponents of the two numbers. This number will be referred to as "b". In the case of the example, the difference is 3 - 2, and so the value of b is 1.
- 3
  Rewrite the greater of the two numbers, changing its exponent to the same value as the exponent of the other number and, at the same time, moving the decimal place of its coefficient b spaces to the right. The two numbers will now have the same exponent. For the example, you would rewrite 6.5 x 10^3 as 65 x 10^2.
- 4
  Now that the exponents of the two numbers are the same, simply subtract the smaller coefficient from the larger one. The calculation in the example would be 65 - 3.2, giving the result 61.8.
- 5
  Write the value you just calculated as the coefficient of an exponential number having the same exponent as the two numbers you just subtracted. For the example, you would write 61.8 x 10^2, since 2 was the common exponent you arrived at for the two numbers.
- 6
  Move the decimal place of the new number's coefficient, if necessary, so the coefficient is equal to 1 or greater but is less than 10. Keep track of how many places you had to move the decimal. The example would require you to move the decimal place one space to the left to change 61.8 to 6.18.
- 7
  Rewrite your new number, increasing the exponent by the same value as the number of places you just moved the decimal place in the coefficient. The result is the difference between your two original numbers. In the example, since you moved the decimal one place, you will increase the exponent by 1 from 2 to 3 and rewrite the answer as 6.18 x 10^3.

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