The concept of the “greatest nonzero place” involves identifying the highest place value in a number that is not zero. This concept is helpful for rounding numbers or understanding their magnitude. When rounding to the greatest nonzero place, you look for the leftmost nonzero digit and round the number accordingly. Each digit in a number carries a place value based on its position. For instance, in the number 4,567, 4 is in the thousands place, 5 is in the hundreds place, 6 is in the tens place, and 7 is in the ones place. In this case, the greatest nonzero place is the thousands place because 4 is a nonzero digit.

Here are some examples to understand this concept:

**Example: 0.047***The greatest nonzero place here is the hundredths place (4 is in the hundredths place). To round 0.047 to the greatest nonzero place, you look at the next digit (7 in the thousandths place). Since 7 is greater than 5, you round up. So, result: 0.05*.

**Example: 9.807***The greatest nonzero place is the ones place (9 is in the ones place). The next digit is 8 in the tenths place. Since 8 is greater than 5, you round up. So, result: 10*.

**Example: 0.00872***The greatest nonzero place is the thousandths place (8 is in the thousandths place). The next digit is 7 in the ten-thousandths place. Since 7 is greater than 5, you round up. So, result: 0.009*.

**Example: 6,327.39***The greatest nonzero place is the thousands place (6 in the thousands place). The next digit is 3 in the hundreds place. Since 3 is smaller than 5, you round down. So, result: 6,000*.