In my textbook, I was given these directions to follow when doing these problems:
**Multiply. Express each result in Scientific Notation**
1. (4 x 10^9)(6 x 10^6)
My work:
(400,000,000)(600,000)=
240,000,000,000,000
My answer:
2.4 x 10^14
Am I right?
2. (5 x 10^7)(3.6 x 10^3)
My work:
(5,000,000)(3,600)=
18,000,000,000
My answer:
1.8 x 10^10
Am I right?
wait no...#1 is 2.4 x 10^16
and #2 is 1.8 x 10^11
Easy to lose count with all those zeros
I do them this way
(4 x 10^9)(6 x 10^6)
= (4x6)(10^9 x 10^6)
= 24 x 10^15
= 2.4 x 10^16
(5 x 10^7)(3.6 x 10^3)
= 18 x 10^10
= 1.8 x 10^11
YOu were right with your corrected post
For the first problem, you correctly multiplied the numbers outside the exponent: 4 x 6 = 24. However, you made an error when multiplying the numbers inside the exponent: 10^9 x 10^6 = 10^(9+6) = 10^15.
To express the result in scientific notation, you need to move the decimal point to the appropriate position so that there is only one non-zero digit to the left of the decimal point. In this case, your answer should be:
(4 x 10^9)(6 x 10^6) = 24 x 10^15 = 2.4 x 10^16
Therefore, your answer for the first problem is incorrect.
For the second problem, again, you multiplied the numbers outside the exponent correctly: 5 x 3.6 = 18. And you also multiplied the numbers inside the exponent correctly: 10^7 x 10^3 = 10^(7+3) = 10^10.
To express the result in scientific notation, you need to move the decimal point to have only one non-zero digit to the left of the decimal point. Your answer is:
(5 x 10^7)(3.6 x 10^3) = 18 x 10^10 = 1.8 x 10^11
Therefore, your answer for the second problem is incorrect as well.