Question

Question #91125

Answer 1

Convert the sentences into algebraic equations between each digit, then solve to get `0.013`.

Explanation:

Since the digits mentioned are the tenth place, the hundreth place, and a "last" digit, we could assume that this decimal must have three digits, as in

`"0.ABC"`,

where `A` is the tenth place, `B` is the hundredth place and `C` is the thousandth place, or the last digit.

The information given is that the last digit is three, so

`C = 3`,

Then the tenth place, `A`, is compared to the two other digits:

"you will find (that the tenth place is) a digit one less than the digit in my hundreth place ..."

which means

`A = B - 1`,

"... and (the tenth place is) three less than my other digit (which is the last digit)."

which means

`A = C - 3`.

Since we know `C = 3`, we immediately get that

`A = C - 3 = 3 - 3 = 0`,

and since we now know the value of `A`, we could solve for `B`:

`A = B - 1 rarr 0 = B - 1`

Simply add `1` to both sides of the equation to get `B = 1`.

So we have `A = 0`, `B = 1` and `C = 3`, meaning that the decimal must be `0.013`.