What is the smallest number with digits to the thousandths place that will round to 34.6?

34.601

To find the smallest number with digits to the thousandths place that will round to 34.6, we need to understand the concept of rounding numbers.

Rounding a number means to replace it with another number that is approximately equal but has fewer digits. In this case, we want to find the smallest number that, when rounded to the nearest tenth, will give us 34.6.

To round to the nearest tenth, we look at the digit in the hundredths place. If it is 5 or greater, we round up, and if it is less than 5, we round down.

Let's start with a number in which the thousandths digit is 0: 34.600. This number already has one decimal place after the tenth, so it won't be rounded.

Next, we decrease the thousandths place by 1, resulting in 34.599. This number is still rounded to 34.6 because the hundredths place digit (9) is greater than 5.

Continuing this pattern, we decrease the thousandths digit by 1 each time until we find the smallest number that rounds to 34.6. After several iterations, we find that 34.593 is the smallest number that rounds to 34.6 when rounded to the nearest tenth.

Therefore, the smallest number with digits to the thousandths place that will round to 34.6 is 34.593.