How is multiplying and dividing numbers in scientific notation ifferent from adding and subtracting in scientific notation?

Question

How can you do this please?

Answer 1

The question is kind of vague, but I think that one important thing is that you can always multiply and divide two number regardless of what the exponent is, but that's not true for addiction and subtraction -- you have to be careful with the exponents.

 

To show this, look at a specific example. Let

 

x = 43650 = 4.365 * 10⁴

y = 97 = 9.7 * 10¹

 

To get xy, you can just do

 

(4.365 * 10⁴)(9.7 * 10¹) = (4.365 * 9.7)(10⁴ * 10¹) = 42.3405 * 10⁵ = 4.23405 * 10⁶

 

But if looked at x + y

 

(4.365 * 10⁴) + (9.7 * 10¹) ≠ (4.365 + 9.7) * (10⁴ + 10¹) WRONG

 

If you want to add them directly, you need to give the numbers the same exponent.

 

x = 4365.0 * 10¹ -->

 

x + y = (4365.0 + 9.7) * 10¹ = 4374.7 * 10¹ = 4.3747 * 10⁴