Question

A nail is 0.1875 inches thick. What is its thickness as a fraction?

Answer 1

Thickness of the nail as a fraction is `3/16`

Explanation:

As the nail is `0.1875` inches thick, its thickness, written here in decimal, in terms of fraction can be written as

`1875/10000`

The prime factors of numerator and denominator are

`(3xx5xx5xx5xx5)/(2xx2xx2xx2xx5xx5xx5xx5)`

or `(3xxcancel5xxcancel5xxcancel5xxcancel5)/(2xx2xx2xx2xxcancel5xxcancel5xxcancel5xxcancel5)`

= `3/16`

Hence, its thickness as a fraction is `3/16`

Answer 2

`3/16` of an inch

Explanation:

One way to find the fraction is as follows:

• Note that the fraction ends with a digit `5`, so is half of something simpler. So multiply by `2`:

  `2xx0.1875 = 0.375`

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* The resulting decimal also ends with `5`, so multiply that by `2` again:

`2xx0.375 = 0.75`

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* This still ends with `5`, so double again:

`2xx0.75 = 1.5`

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* Finally we get an integer by doubling again:

`2xx1.5 = 3`

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Looking back, notice that we have multiplied by `2^4 = 16`, so divide by `16` to get our fraction:

`0.1875 = 3/16`

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Footnote

If doubling had not eventually resulted in an integer, it would still make the problem simpler.

For example, if we were given `0.01875` instead of `0.1875` then we would arrive at `0.3` after doubling `4` times, then could write:

`0.01875 = 3/10*1/16 = 3/160`

Answer 3

`0.1875= 3/16`

Explanation:

A decimal can be written as a fraction with a power of 10 in the denominator.

`0.1875 = 1875/10000" "larr` now we have to simplify.

Note that a number is divisible by 25 if the last 2 digits are
`00" "25" "50" "75`

Also that a number is divisible by 125 if the last 3 digits are
`125" "375" "625" "875`

However, let's simplify using 25.

`(1875div25)/(10000div25) = 75/400" "larr` and again

`(75div25)/(400div25) = 3/16`