Multiplying a whole number by a decimal with an unknown var.

[yo4561]

Happy Wednesday!

Let's say I have the following that I would like to simplify: 2(4.000G).

My initial reaction is to simplify this down to 8.000G. However, I learned that it would actually simplify to 2 (4 + G/1000) ...
Is this because you don't know if there were will be carry carry over in what the G is to the thousandths place (e.g. G could be 9 and 2 times 9 equals 18, and now I have a one in thousandths place?)

[esledge]

Let's say I have the following that I would like to simplify: 2(4.000G).

My initial reaction is to simplify this down to 8.000G. However, I learned that it would actually simplify to 2 (4 + G/1000) ...

You've got the concept, but watch the decimal places; it would actually simplify to 2(4 + G/10,000). Here's a tip: count the total number of places (not just the number of zeros!) after the decimal, and make sure there are that many zeros in the power of 10 in the denominator. So here, that's 4 places after the decimal (from the 0, 0, 0, and G after the decimal) and thus 4 zeros in the 10,000 in the denominator.

Is this because you don't know if there were will be carry carry over in what the G is to the thousandths place (e.g. G could be 9 and 2 times 9 equals 18, and now I have a one in thousandths place?)

Exactly, carryover is the thing.

If G = 1, then 2(4.000G) = 2(4.0001) = 8.0002
If G = 4, then 2(4.000G) = 2(4.0004) = 8.0008 (still no carryover)
If G = 5, then 2(4.000G) = 2(4.0005) = 8.0010 (carryover starts here! Note that 10/10,000 = 1/1,000.)

In your example, G = 9, so 2(4.000G) = 2(4.0009) = 8.0018. You now have an 8 in the ten thousandths place, and a 1 in the thousandths place.