Question

What is $8.65 x 9.2?

Answer 1

`$79.58`

Explanation:

Although this is a plain multiplication, there are a few things we can note here.

Firstly the number of decimal places..

When multiplying with decimals, count the number of decimal places first. There are 3, but then why are there are only 2 in the answer?

If you look at the last digit in each number, you will see why..

`5 xx 2 = 10` So even though the decimal place is there, it will be a zero which will not be shown. The full answer would be `79.580`

In addition to that, the unit are Dollars, so only 2 decimal places will be shown to indicate the cents.

In estimating an answer we have a number that is almost 9, multiplied by by a bit more than 9.

`9xx9 = 81` so an answer of `$79.85` is quite acceptable.

Answer 2

`$79.58`

Explanation:

Don't like decimals so lets do a sort of cheat.

Write `8.65" as "865xx1/100`

Now write `9.2" as "92xx1/10`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This gives us `865xx92xx1/100xx1/10`

`=79580xx1/1000`

`color(brown)("There are 3 zeros is "1/1000)`

Before we consider the decimal place write `79580" as " 79580.0`

`color(brown)("Keeping the decimal place where it is slide the number to the right 3 places.")`

Giving:

`79.58 ->$79.58`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Comment")`

Some people say move the decimal point I much prefer 'sliding the numbers.

`color(brown)("Reason: ")`

By example consider `3.0 xx10`

You are changing counting in units to counting in tens so the 3 'slides' to the left occupying the position of the tens.

`color(brown)("This is just a case of personal preference")`