(2x10^3)(3x10^8)
(8x10^4)
I get confused after this step:
[(2/8x)(10^3/10^4)] [(3/8x)(10^8/10^4)]
My result: =(4x10^-1) (2.6x10^4)
I need to get here:
=7.5x10^6
(2x10^3)(3x10^8)
(8x10^4)
I get confused after this step:
[(2/8x)(10^3/10^4)] [(3/8x)(10^8/10^4)]
My result: =(4x10^-1) (2.6x10^4)
I need to get here:
=7.5x10^6
That step is not correct.
Are you familiar with the Order of Operations?
Once you divide 2 by 8, you do not again divide 3 by 8.
Same with 10^3/10^4. Once you do that, there is not a second division by 10^4.
Each division happens only once, moving from left to right.
Maybe you are confusing the situation (2 + 3)/8. Here, both the 2 and the 3 do get divided by 8, but only because the 2 and 3 are added. In your exercise, they are not added, they are multiplied (i.e., factors).
There are different approaches. I like to use properties of exponents to multiply the numerator and then divide by the denominator.
First, the Commutative Property of Multiplication allows us to re-order the factors in the numerator.
(2)(3)(10^3)(10^8)
This becomes 6 x 10^(3 + 8)
Now we divide by 8 x 10^4, and write
(6/8) x (10^11/10^4)
6/8 = 3/4
10^11 divided by 10^4 is 10^(11 - 4).
That gives a decimal answer of 0.75 x 10^7
But scientific notation requires shifting the decimal point one place to the right (because the decimal number must be greater than 1), which means the power of ten needs to shift one place less than before, so the exponent goes down by 1.
7.5 x 10^6
That makes since. Thanks.
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