What should you do before adding or subtracting numbers in standard form?

When working with numbers in standard form, it is important to ensure that the powers of ten are the same before performing addition or subtraction. Standard form represents numbers as a product of a number between 1 and 10 and a power of ten, such as ( a \times 10^n ).

For example, if you have two numbers in standard form like ( 2.5 \times 10^3 ) and ( 3.0 \times 10^4 ), you cannot simply add or subtract them directly because they are scaled by different powers of ten. To correctly perform the operation, you first need to adjust the powers of ten to the same value.

This means that you could convert ( 3.0 \times 10^4 ) to ( 30.0 \times 10^3 ), allowing you to add it to ( 2.5 \times 10^3 ) as both numbers are now expressed in terms of ( 10^3 ). Once the powers of ten are aligned, you can proceed with the arithmetic operation properly. This step ensures accuracy in calculations, which is fundamental in mathematics.