We need to change 5.01*10^(-3) so that the -3 turns into -4. The exponents need to match up so we can add up the bases. To go from -3 to -4, we subtract 1. In other words, we're moving in the negative direction to make the decimal move 1 spot to the left. To counter balance things, we move the decimal of 5.01 one spot to the right to get 50.1
This all means 5.01*10^(-3) is equal to 50.1*10^(-4)
Use a calculator to get 5.01*10^(-3) = 0.00501 50.1*10^(-4) = 0.00501 and we get the same decimal value
So the original expression ( 2.12*10^(-4) ) + ( 5.01*10^(-3) ) turns into ( 2.12*10^(-4) ) + ( 50.1*10^(-4) )
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The exponents are now the same so we can add up the bases 2.12 and 50.1 2.12+50.1 = 52.22
So, ( 2.12*10^(-4) ) + ( 50.1*10^(-4) ) = 52.22*10^(-4)
Now convert to scientific notation Move the decimal 1 spot to the left, we need to add 1 to the exponent to counter balance this 52.22*10^(-4) ----> 5.222*10^(-3)
The final answer is 5.222*10^(-3)
We can check the answer with a calculator ( 2.12*10^(-4) ) + ( 5.01*10^(-3) ) = 0.005222 which converts to 5.222*10^(-3) This confirms the correct answer.
