Compare and contrast adding/subtracting numbers written in scientific notation

Question

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

When adding or subtracting numbers written in scientific notation, the first step is to make sure the exponents of the numbers are the same. If they are not, one or both of the numbers need to be manipulated to match the exponent of the other number. Once the exponents are the same, the numbers can be added or subtracted like regular numbers, while keeping the common exponent.

On the other hand, when multiplying numbers in scientific notation, the first step is to multiply the decimal parts of the numbers, and then the exponents are added together. The result is then adjusted, if necessary, to be in scientific notation form.

Similarly, when dividing numbers in scientific notation, the decimal parts are divided, and the exponents are subtracted from each other. The result is also adjusted, if needed, to be in scientific notation form.

The steps in each case are similar in that there is a manipulation of the exponents and an operation performed on the non-exponential parts. However, the difference lies in the specific operation performed on the non-exponential parts (addition/subtraction in one case, and multiplication/division in the other) and the adjustment of the result to scientific notation form.

The easiest operation among the four (adding, subtracting, multiplying, dividing) in scientific notation depends on the specific numbers involved. In general, adding and subtracting numbers in scientific notation tend to be easier, as there is no need for multiplication or division of the decimal parts. However, this can vary depending on the specific values and complexity of the numbers being operated on. Ultimately, the ease of the operation depends on the individual's comfort and familiarity with scientific notation calculations.