Laura rounds a number, 𝑦, to two decimal places. The result is 2.76. What is the error interval for 𝑦?
The error interval is the set of values that round to 𝑦. This is usually written as an inequality. If we consider the number line with values 2.75, 2.76, and 2.77, our key values are
those points halfway between 2.75 and 2.76 and also halfway between 2.76 and
2.77. Anything to the right of the first arrow will round to 2.76 and anything to the left
of the second arrow will also round to 2.76. The key values in this case are 2.755 and 2.765.
𝑦 can definitely take any value between these two numbers. What happens if 𝑦 is exactly 2.755? Well, as the last number is five, we would round up. This means that 𝑦 can be greater than or equal to 2.755. As 2.765 would round up to 2.77, our value for 𝑦 must be less than 2.765.
This means that if Laura’s number is 2.76 to two decimal places, then the error
interval for 𝑦 will be greater than or equal to 2.755 and less than 2.765.