What is the greatest amount of money that rounds to $108.60 when rounded to the nearest dime?
What is the least amount of money that rounds to $108.60?
The Correct Answer and Explanation is :
To determine the greatest and least amounts of money that round to $108.60 when rounded to the nearest dime, we need to understand how rounding works, particularly for a specific decimal place.
Rounding to the Nearest Dime
When rounding to the nearest dime, we focus on the hundredths place (the second digit after the decimal point). The rule for rounding states:
- If the hundredths digit is 5 or greater, we round up.
- If the hundredths digit is less than 5, we round down.
For our case, rounding to $108.60 means we want amounts that, when rounded to the nearest dime, give us $108.60.
Greatest Amount
To find the greatest amount that rounds to $108.60:
- The amount must be less than $108.65, because $108.65 rounds to $108.70.
- Therefore, the largest amount that still rounds down to $108.60 is $108.649999… (which we can express as $108.649).
So, the greatest amount of money that rounds to $108.60 when rounded to the nearest dime is $108.649.
Least Amount
Next, we need to find the least amount that rounds to $108.60:
- The least amount that can round up to $108.60 must be at least $108.55, because $108.55 rounds to $108.60.
- Thus, the smallest amount that rounds to $108.60 is exactly $108.55.
Summary
In conclusion, the greatest amount of money that rounds to $108.60 when rounded to the nearest dime is $108.649, and the least amount is $108.55. Understanding rounding rules is crucial in determining these values, as it allows us to identify the range of amounts that can produce a specific rounded figure. This knowledge can be particularly useful in financial contexts, where accurate rounding can impact calculations and reporting.