Question

How do you simplify `1.6 div 0.336`?

Answer 1

`1.6div0.336 = 4.76`

Explanation:

When you are dividing BY a decimal, it is possible to make the decimal into a whole number by multiplying by 10, 100 or 1000. etc

`1.6/0.336 xx1000/1000 = 1600/336`

This can now be divided by long division, double division or any similar method

`color(white)(xxx..x)4.76`
`336)bar(1600.00)`
`color(white)(xx.)ul1344darr`
`color(white)(xx....)2560`
`color(white)(xx....)ul2352darr`
`color(white)(xxx....)2080`
`color(white)(xxx....)ul2016`
`color(white)(xxxxx....)64`

Answer 2

`100/21`

Explanation:

Assuming you can't simply use a calculator, the only way I see to simplify this expression is translating everything to fractions: we have

`1.6 = 16/10 = 8/5`

and

`0.336 = 336/1000 = 42/125`

Now, if you want to divide by a fraction, you have to multiply for the inverse of that fraction: dividing by `3/5` is the same thing as multiplying by `5/3`, so

`1.6 : 0.336 = 8/5 : 42/125 = 8/5 * 125/42`

And now we can do cross canceling:

`8/5 * 125/42 = 4*25/21 = 100/21`