Question

How do you multiply (1.8)(0.7) ?

Answer 1

`1.26`

Explanation:

You may convert numbers into fraction: `1.8` can be written as `18/10`, and `0.7` can be written as `7/10`

Then, the multiplication translates to

`18/10*7/10 = (18*7)/(100)`

Now you only need to multiply `18*7`, which is a "standard" multiplication between integers, and yields `126`, and dividing by 100 is simple, because you only need to shift the decimal place two steps to the left:

`126/100 = 1.26`

Answer 2

`1.26`

Explanation:

Here is a way to multiply decimal numbers:

1) First multiply the numbers without regard for the decimal points

Multiply `(1.8)(0.7)` as `18 xx 7` (ignoring the decimal points)

`color(white)(mm)` `1 8`
`color(white)()` `xx`     `7`
`color(white)(mm)`――
`color(white)(mm)` `126`

2) To determine where the decimal point goes, count the number of decimal places in both factors.

`1.8` has ONE decimal place
`0.7` also has ONE decimal place
That is a total of TWO decimal places

3) The answer has the same total

Write `126` with TWO decimal places, like this `1.26`

Answer:
`1.26`

`color(white)(mmmmm)`――――――――

Check

Check for reasonableness by estimating
`1.8 xx 0.7` is almost the same as `2 xx 1/2`

The estimate of `1` is reasonably close to `1.26,` so it's probably correct.

`Check`