The Math of Science Challenge Four

THE MATH OF SCIENCE CHALLENGE FOUR

ADDING AND SUBTRACTING NUMBERS IN SCIENTIFIC  NOTATION

Remember our vocabulary:  Coefficient is the number in front, the base or the power is the "10", and the raised number is the exponent.

To add or subtract numbers in scientific notation, we need both exponents of our powers of 10 to be the same number.

Example:

6.4 x 10⁶  +   .0023  X  10⁶   can be added as follows:

     6.4         x 10⁶

  +   .0023  x 10⁶

        6.4023 x 10⁶

The tricky part is when the exponents on the powers of 10 are different.  Then you have a two step problem.  First you have to change the exponent to be the same, and then you have to do your addition or subtraction. 

Changing the exponents to be the same:

The two exponents of the base 10 have to be the same for the numbers written in scientific notation to be added or subtracted. We can change any exponent greater or smaller to make exponents the same value. To change the smaller exponent to the greater, identify the difference between the two exponents and move the decimal point of the coefficient with the smaller exponent to the left the same number of places. Similarly, to change the greater exponent to the smaller, identify the difference between the two exponents and move the decimal point of the coefficient with the greater exponent to the right the same number of places.

STEP ONE:

(4.8 x 10²)  +   (1.3 x 10⁴)

Exponent=2       Exponent=4

First we have to get both our exponents to be the same.  We want to adjust the number with the smaller exponent to match the larger exponent.

1. Find the difference between the exponents  4-2=2

2.  We move the decimal two places to the left because it is positive.  So our smaller exponent number 4.8 x 10²  now becomes .048 x 10⁴

STEP TWO:

Now add our numbers in scientific notation together.

               .048 x 10⁴     

+           1.3     x 10⁴

              1.348 x 10⁴