What are the least and greatest numbers written in the hundredths that could round to 164.8 and explain your answer?
164.75
164.84
What can round to 164.8
To find the least and greatest numbers written in the hundredths place that could round to 164.8, we need to understand how rounding works.
When we round a number to a specific decimal place, we look at the digit immediately to the right of that decimal place. If this digit is 5 or greater, we round up by adding 1 to the digit in the rounding position. If the digit is 4 or less, we round down by leaving the digit in the rounding position as it is.
In this case, we want to round to the tenths place (one decimal place to the right). The digit immediately to the right of the tenths place is the hundredths place.
To find the least number that could round to 164.8, we need to have the smallest possible value in the hundredths place that would cause rounding up. Since the digit immediately to the right of the tenths place is 8, we want the hundredths place value to be 5 or greater. The smallest number that satisfies this condition is 0.05. Adding this to 164.8 and rounding to the tenths place would give us 164.9, which rounds down to 164.8.
To find the greatest number that could round to 164.8, we need to have the largest possible value in the hundredths place that would cause rounding down. Since the digit immediately to the right of the tenths place is 8, we want the hundredths place value to be 4 or less. The largest number that satisfies this condition is 0.04. Adding this to 164.8 and rounding to the tenths place would give us 164.8, which rounds down to 164.8.
Therefore, the least number that could round to 164.8 is 164.9, and the greatest number that could round to 164.8 is 164.8, and explained how to get those answers.