Given x is an integer, when x is rounded off to 1 significant figure, the answer is 40. Write as a fraction, the ratio of the least possible value of x to the largest possible value of x.

Explanation:

Let's consider the number 39

We have 2 nonzero digits here, so we have 2 significant figures (sig fig for short).

The goal is to round this to one sig fig instead of two. The question is: do we keep the 3 or keep the 9 instead?

The answer is that we keep the 3 and toss the 9, but the 9 will mean we bump the 3 up to 4.

So 39 bumps up to 40 where the 0 is not a sig fig (review the many sig fig rules about how to deal with zeros). The zero is just a placeholder to help determine the magnitude of the number.

In other words, 39 is closest to 40 rather than 30. We can think of "40" as "4 tens" and even drop the unit "tens" to focus solely on that 4. It would be implied we're talking about the tens unit from then on. You hopefully agree at this point we definitely have one sig fig to focus on.

If we repeated the last set of steps for the number 38, then it also rounds to 40 when rounding to one sig fig. The same goes for 37, 36, and 35.

The values 35, 36, 37, 38, 39 all round to 40 when rounding to one sig fig.

Doing the same type of logic, but on the upper side of 40, we have the values {41,42,43,44} also rounding to 40. The value 45 won't work because it rounds to 50 instead.

Therefore, x can be any of the following integers:

35,36,37,38,39,40,41,42,43,44

and they all round to 40 when rounding to one sig fig.

The last step is to divide the smallest item of the last list mentioned over the largest item

35/44

The numerator and denominator have no factors in common other than 1. So the fraction cannot be further reduced.

step-by-step explanation:

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