4. Compare and contrast adding/subtracting numbers written in scientific notation with multiplying/dividing numbers written in scientific notation. How are the steps in each case similar? How are they different? Do you think adding, subtracting, multiplying, or dividing numbers written in scientific notation is easiest? Why?

Answer 1

Adding and subtracting numbers written in scientific notation involves keeping the exponents the same and adding/subtracting the coefficients. On the other hand, multiplying numbers in scientific notation requires multiplying the coefficients and adding the exponents, while dividing involves dividing the coefficients and subtracting the exponents.

The steps for adding and subtracting in scientific notation are similar because you firstly ensure that the exponents of both numbers are the same. Then, you can directly add or subtract the coefficients. Finally, you normalize the result to make it a number between 1 and 10 by adjusting the exponent if necessary.

The steps for multiplying and dividing in scientific notation are similar in terms of rearranging the numbers, but differ in the actual operation. For multiplication, you multiply the coefficients and add the exponents, and for division, you divide the coefficients and subtract the exponents. Again, the result must be normalized by adjusting the exponent, if necessary.

Regarding which operation is easiest, it depends on personal preferences and comfort with arithmetic operations. Some may find adding and subtracting easier because it only involves adding/subtracting coefficients. Others may find multiplying and dividing easier because they are more familiar with those operations. Ultimately, with practice, all four operations can be performed easily.