Answer:
1) -9.3465 × 10^8
2) 1.6214 × 10^-1
3) 1.33 × 10^-11
Explanation:
When solving arithmetic operations of numbers in scientific notation, there is a strategy that can be used.
First recognize the quotient(division) between the size of the numbers indicated by a multiple of 10 to a certain power. Remember, taking the quotients of like numbers with different powers is the subtraction of powers.
For example, to solve the first expression (problem one):
7.35 x 10^6 – 9.42 x 10^8
Divide 10^8 by 10^6 to get 10^2
So
it is like subtracting 7.35 and 9.42 × 10^2 which is 7.35 - 942, then once this expression is solved, multiply by the lowest multiple of 10 which is 10^6.
7.35 - 942 = -934.65 → -934.65 × 10^6 = (-9.3465 × 10^2) × 10^6 = -9.3465 × 10^8.
Long subtraction may need to be used when dealing with numbers that are far apart. Likewise long addition multiplication or division is used for very big or small numbers.
Anyway for the second expression (problem 2)
Addition in my opinion is much easier because it is really just adding on the bigger number. Subtraction may take a little longer but both processes are all based on the bigger number or the number with the greatest power of the multiple 10.
So 3.14 × 10^-3 + 1.59 × 10^-1
The quotient between 10^-1 and 10^-3 is the the difference between -3 and -1 which is 10^2
So again it is like adding 3.14 and 1.59 × 10^2 which is 3.14 + 159 = 162.14 = 1.6214 × 10^2. Now use the multiple of 10 with the largest contrast which is 10^-3 so 1.6214 × 10^2 × 10^-3 = 1.6214 × 10^(2-3) = 1.6214 × 10^-1.
