I’m having trouble with physics, could you show the work so I can see how to do this?

(6.28 x 10^13)km^3 + 8.3 x 10^11

I see that the 6.28 x 10^3 term has units of km^3.

But I don’t see any units for the 8.3 x 10^11 term.

These two terms can only be added together if they have the same units.

I will make the assumption that you mistyped this problem and that both terms should have the same units.

(6.28 x 10^13)km^3 + (8.3 x 10^11)km^3

Now that they both have the same units, we can drop the units to make our calculations simpler. But before we can add these two terms, we need to convert one of them so that they both have the same 10 exponent.

We have two choices. We can modify the first term or the second term.

FIRST CHOICE

To modify the first term, we need to convert 10^13 to 10^11.

To decrease the 10 exponent value by 2, we will have to move the decimal point for 6.28 two places to the right to keep that term in balance. As a result, this will not change its value, only its appearance.

6.28 x 10^13 = 628 x 10^11

So now our equation is

(628 x 10^11) + (8.3 x 10^11)

Because the 10 exponents are now identical, we can add these two terms.

(628 + 8.3) x 10^11

636.3 x 10^11 – – – > FIRST CHOICE FINAL ANSWER

SECOND CHOICE

To modify the second term, we need to convert 10^11 to 10^13.

To increase the 10 exponent value by 2, we will have to move the decimal point for 8.3 two places to the left to keep that term in balance. As a result, this will not change its value, only its appearance.

8.3 x 10^11 = 0.083 x 10^13

So now our equation is

(6.28 x 10^13) + (0.083 x 10^13)

Because the 10 exponents are now identical, we can add these two terms.

(6.28 + 0.083) x 10^13

6.363 x 10^13 – – – > SECOND CHOICE FINAL ANSWER

Although the answers for our two choices look different, they are the same value.

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