Question

How do you find the product of `1.81\times 0.5`?

Answer 1

`0.905`

Explanation:

`color(blue)("This is a really fast approach - there are others")`

`0.5` is the same as `5/10 = 1/2`

So just halve the `1.81`

Observe that `2xx9=18`

`1.81xx1/2=0.905`

It is important that you put the 0 to the left of the decimal point. Apart from anything else, it helps to draw attention to the decimal point. Its existence is emphasised by the 'apparent' bigger gap between the numbers 0 and 9. Otherwise someone may get confused and think you wrote 905 (nine hundred and five)

Answer 2

`1color(blue)(.81) xx 0color(blue)(.5) = 0color(blue)(.905)`

Explanation:

The 'product' is the answer to a multiplication.

In general, to multiply with decimals.

Ignore all the decimals and just multiply the numbers.
You can do this by any method - long multiplication, distributive law, any short cut using mental arithmetic, as long as you get the answer.

`181 xx 5 = 905`

Now count how many decimal places there were in all the numbers being multiplied: `1color(blue)(.81) xx 0color(blue)(.5)`

In this case there are three.

Show that same number of decimal places in the answer.

`1color(blue)(.81) xx 0color(blue)(.5) = 0color(blue)(.905)`