Final answer:
To round 20.587554895 to the nearest ten-thousandth, we examine the hundred-thousandths place, which is 5, causing us to round up to 20.5876. This rounding technique is consistent across different mathematical operations.
Step-by-step explanation:
To round the number 20.587554895 to the nearest ten-thousandth, we need to look at the digit in the hundred-thousandths place. In this case, the ten-thousandths place is '7' and the hundred-thousandths place is '5'. According to rounding rules, since the hundred-thousandths digit is 5, we round up the ten-thousandths digit from '7' to '8'.
So, the number 20.587554895 rounded to the nearest ten-thousandth is 20.5876. This same concept applies whether we are multiplying and dividing by tens, or dealing with any other math operations – we always look at the digit immediately to the right of the place we're rounding to.
For example, when we multiply 1.9436 by 10, we get 19.436, and dividing 1.9436 by 10 gives us 0.19436. The same rounding principles would apply to the results of these operations as well.