What are the limits of accuracy for 56.789 rounded to three decimal places?

The limits of accuracy for 56.789 rounded to three decimal places are 56.7885 and 56.7895.

When we round a number to three decimal places, we are essentially considering the thousandths place. For the number 56.789, the digit in the thousandths place is 9. To determine the limits of accuracy, we need to find the smallest and largest numbers that would round to 56.789 when rounded to three decimal places.

The smallest number that rounds to 56.789 is 56.7885. This is because any number less than 56.7885 would round down to 56.788 when rounded to three decimal places. For example, 56.7884 would round to 56.788, not 56.789.

The largest number that rounds to 56.789 is 56.7894999... (continuing indefinitely). However, for practical purposes, we often consider this as 56.7895, because any number greater than or equal to 56.7895 would round up to 56.790 when rounded to three decimal places. For example, 56.7895 itself rounds to 56.790.

Therefore, the range of numbers that round to 56.789 when rounded to three decimal places is from 56.7885 to just under 56.7895. This range ensures that any number within these limits will round to 56.789, maintaining the accuracy required for three decimal places.