Question

Esther is asked for the upper bound of 8.2, correct to the nearest tenth. She writes:

The upper bound is 8.24 because that's the biggest number that rounds down to 8.2. I know this because 8.25 would round up to 8.3.

By finding a bigger number than 8.24 that rounds down to 8.2, show that Esther is wrong.

a) 8.249

b) 8.245

c) 8.23

d) 8.26

Answer 1

Esther is incorrect because 8.245 is a larger number than 8.24 that still rounds down to 8.2, following the rounding rules when the hundredths place is a 5 and there are no non-zero digits after.

Step-by-step explanation:

To determine the upper bound for 8.2 when rounded to the nearest tenth, we need to find the largest number that would still round down to 8.2. Esther proposed 8.24, which she believes to be this upper bound. However, this is incorrect as there is a number slightly larger that will still round down to 8.2.

When rounding to the nearest tenth, any number from 8.20 up to but not including 8.25 will round down to 8.2. By looking at the choices provided:

• (a) 8.249 still rounds down to 8.2 because the digit in the hundredths place is 4, which is less than 5.
• (b) 8.245 would still round down to 8.2 because according to rounding rules, when the digit to the immediate right of the digit we are rounding to (the hundredths place in this case) is 5, and all subsequent digits are zero or there are no subsequent digits, we round down if the digit in the rounding place (the tenths place) is even.
• (c) 8.23 definitely rounds down to 8.2, as it is less than 8.24.
• (d) 8.26 rounds up to 8.3.

Therefore, the correct choice that demonstrates a larger number than 8.24 that still rounds down to 8.2 is (b) 8.245.