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afontana511 said:
8.3 (0.4)

I'll explain one way of reasoning, using this expression.
Click to expand...

Here's a couple notes, first.

(1) If we multiply some number by 100, and then we divide the result by 100, we end up with the starting number.

EG: Multiply 44 by 100, and divide the result by 100.

44(100) = 4400

4400/100 = 44

(2) Multiplying decimal numbers by powers of 10 simply shifts the decimal point to the right. Dividing decimal numbers by powers of 10 simply shifts the decimal point to the left.

EG: Multiply 5.6 by 10:

Shift the decimal one place to the right: 5.6(10) = 56.0

Divide 5.6 by 100:

Shift the decimal point two places to the left: 5.6/100 = 0.056

The number of places that we shift is the same as the power of ten.

Here's how I use the facts above, to multiply 8.3(0.4), in my head.

I begin by multiplying each of the two factors by 10 because this results in factors that are Whole numbers.

8.3(10)(0.4)(10)

Of course, this causes the product to be 100 times bigger than what it's supposed to be, so I must remember to use fact (1) above, at the end, and divide my result by 100 (to compensate).

Multiplying each factor by 10^1 shifts the decimal one position to the right, so I get

83(4)

Now, because I've memorized the multiplication table, I already know that 8 times 4 is 32, so 80 times 4 is 320.

In other words, I'm viewing 83(4) in my head as (80+3)(4), which is the same as:

(80)(4) + (3)(4)

320 + (3)(4)

I also know that 3 times 4 is 12, so I need to add 320 + 12.

So far, the multiplications give me 332.

Now, since I started out multiplying the given expression by (10)(10), I must now divide by 100 to compensate.

100 is 10^2, so I shift the decimal two places to the left.

332/100 = 3.32

Hence, the product of 8.3(0.4) is 3.32 :D

If the mental effort required to do these steps (or understand them) is too much for you, then you'll need to learn how to multiply decimal numbers longhand, using paper and pencil.

Let us know, if you need lessons on longhand multiplication of decimal numbers, and somebody here will find a web site for you.

 
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