3x2x10^-3+4x10-2

[Chelsea2019]

I know that the correct answer is 4.6x10^-2 but I keep getting 4.6x10^-3.
3x2x10^-3 is 0.006. 4x10^-2 is 0.04. Add them together is 0.046. Add the powers -3+-2=-5. So 0.046x10^-5. But that's not standard form so multiply 0.046 by 100 to get 4.6. To compensate, divide powers by 100 to get from -5 to -3. But the correct answer is -2? I dont understand what I'm doing wrong? Please help

 

[HallsofIvy]

You add powers when you are multiplying powers of 10, not adding. 3x2x10^(-3) is 0.006 and 4x10^(-2) is 0.04 so 3x2x10^(-3)+ 4x10^(-2)= 0.006+ 0.04= 0.046.

IF the problem were (3x2x10^(-3))x(4x10^(-2)) then the answer would be 24 x 10^(-5)= 0.00024

 

[Deleted member 4993]

I know that the correct answer is 4.6x10^-2 but I keep getting 4.6x10^-3.
3x2x10^-3 is 0.006. 4x10^-2 is 0.04. Add them together is 0.046. Add the powers -3+-2=-5. So 0.046x10^-5. But that's not standard form so multiply 0.046 by 100 to get 4.6. To compensate, divide powers by 100 to get from -5 to -3. But the correct answer is -2? I dont understand what I'm doing wrong? Please help

3 * 2 * 10^(-3) + 4 * 10^(-2)............................Use '*' to indicate multiplication.

= 6 * 10^(-3) + 4 * 10^(-2)

= 6 * 10^(-3) + 40 * 10^(-3)

= 46 * 10^(-3)

= 4.6 * 10^(-2)..............................................Scientific Notation

 

[Chelsea2019]

Thank you so much! I finally understand

 

[Steven G]

You had the answer, just not in the form you wanted. The answer you got was 0.046. So why look back at the powers of 10 as you have already dealt with them! Just deal with 0.046 and get that in standard form. Again, it does not matter what you did with the powers of 10 (add them, multiply them, etc) after you arrive at what you think the answer is, which in your case was 0.046. It is now a new problem which is how do you write 0.046 in standard form.

 

[HallsofIvy]

3 * 2 * 10^(-3) + 4 * 10^(-2)............................Use '*' to indicate multiplication.

= 6 * 10^(-3) + 4 * 10^(-2)

= 6 * 10^(-3) + 40 * 10^(-3)

At this point you could also have written
"= 0.6 * 10^(-2)+ 4*10^(-2)"
so "= 4.6*10^(-2)" immediately. The crucial point is to get the same power of 10.
But I would prefer writing 0.006+ 0.04= 0.046 and then, if I wanted "scientific notation", change that to 4.6 * 10^(-2).

= 46 * 10^(-3)

= 4.6 * 10^(-2)..............................................Scientific Notation