Answer:
a) 345
b) 0.0000002
Explanation:
a) We can multiply the 2.3 and 1.5 and 10^4 and 10^-2 together and simplify at the end.
Step 1: Working out 2.3 * 1.5:
2.3 * 1.5 = 3.45
Step 2: Working out 10^4 * 10^-2:
The product rule of exponents states that when you're multiplying the same bases with different exponents, you add the exponents.
So, 10^4 * 10^-2 = 10^(4 + (-2)) = 10^(4 - 2) = 10^2
Step 3: Simplifying:
Thus, we have 3.45*10^2 = 3.45 * 100 = 345
Step 4: Checking our answer:
We can check by doing the operations inside each parentheses instead of taking them out and seeing whether we still get 345 (i.e., the answer we got when we multiplied common terms instead):
(2.3 * 10^4) * (1.5 * 10^-2)
(2.3 * 10000) * (1.5 * 0.01)
23000 * 0.015
345
Thus, our answer is correct and 345 is the standard form of (2.3 * 10^4) * (1.5 * 10^-2)
b) Similar to our process for part a), we can divide 3.6 by 1.8 and then divide 10^-5 by 10^2 and simplify at the end.
Step 1: Working out 3.8 / 1.8:
3.6 / 1.8 = 2
Step 2: Working out 10^-5 / 10^2:
The quotient rule of exponents states that when we divide the same bases with different exponents, we subtract the exponents.
Thus, 10^-5 / 10^2 = 10^(-5 - 2) = 10^-7
Step 3: Simplifying:
2 * 10^-7 = 2 * 0.0000001 = 0.0000002
Step 4: Checking our answer:
We can check by doing the operations inside each parentheses instead of taking them out and seeing whether we still get 0.0000002 (i.e., the answer we got when we multiplied common terms instead):
(3.6 * 10^-5) / (1.8 * 10^2)
(3.6 * 0.00001) / (1.8 * 100)
0.000036 / 180
0.0000002
Thus, our answer is correct and 0.0000002 is the standard form of (3.6 * 10^-5) / (1.8 * 10^2)