It takes the planet Neptune about 164.8 years to revolve once around the sun. What are the least and greatest numbers written in hundreths that could round to 164.8? Explain your answer.

164.75

164.84

i want to know why

To determine the least and greatest numbers written in hundredths that could round to 164.8, we need to understand how rounding works. Rounding is the process of approximating a number to the nearest specified place value.

In the case of rounding to the hundredths place (the decimal place two places to the right of the decimal point), we look at the digit in the thousandths place (the decimal place three places to the right of the decimal point).

If the digit in the thousandths place is 0, 1, 2, 3, or 4, we round down, which means we keep the digits in the hundredths place and everything after it the same.

If the digit in the thousandths place is 5, 6, 7, 8, or 9, we round up, which means we increase the digit in the hundredths place by 1 and drop all the digits after.

Given that the number we're rounding is 164.8, we can determine the least and greatest numbers that could round to it:

1. To find the least number, we consider the digit in the thousandths place, which is 0. Since it is less than 5, we round down. So the least number that could round to 164.8 is simply 164.80.

2. To find the greatest number, we consider the digit in the thousandths place, which is 8. Since it is greater than 5, we round up. Therefore, the greatest number that could round to 164.8 is 164.81.

Thus, the least number is 164.80, and the greatest number is 164.81.