Question

When adding or subtracting with scientific notation,why is it important to have the same power of 10?

Answer 1

Explanation:

Because we perform something like common factor, so this guarantee that corresponding digits have regarding coefficients have the same place value. Remember that a number written in scientific notation is given by the product of a number between 1 and 10 and another number that is power of 10. For example, let's write two examples about this:

Addition:

$a=2\times 10^3 \\ \\ b=4\times 10^3 \\ \\ \\ Then: \\ \\ a+b=2\times 10^3+4\times 10^3 \\ \\ =(2+4)\times 10^3 \\ \\ =5\times 10^3$

Addition:

$a=2\times 10^3 \\ \\ b=4\times 10^3 \\ \\ \\ Then: \\ \\ a+b=2\times 10^3+4\times 10^3 \\ \\ =(2+4)\times 10^3 \\ \\ =6\times 10^3$

Subtraction:

$a=7\times 10^5 \\ \\ b=2\times 10^5 \\ \\ \\ Then: \\ \\ a-b=7\times 10^5-2\times 10^5 \\ \\ =(7-2)\times 10^5 \\ \\ =5\times 10^5$