Question

Problem 8

Sierra measured her sunflower to the nearest tenth of an inch and found that he
sunflower was 5.4 inches tall. To the nearest hundredth, what is the smallest and
largest possible height of Sierra's sunflower?

Answer 1

The smallest possible height of Sierra's sunflower when measured to the nearest tenth at 5.4 inches is 5.35 inches, and the largest possible height is 5.449 inches.

Step-by-step explanation:

To determine the smallest and largest possible height of Sierra's sunflower to the nearest hundredth of an inch when it's measured to the nearest tenth, we need to consider the rounding interval for tenths of an inch. When a measurement is 5.4 inches to the nearest tenth, the smallest possible value would be at the halfway point to the next lower tenth, and the largest possible value would be right before it rounds up to the next tenth.

The halfway point between 5.3 inches and 5.4 inches is 5.35 inches. So, anything equal to or greater than 5.35 inches would be rounded up to 5.4 inches. Analogously, the highest value that would still round down to 5.4 inches (and not up to 5.5 inches) is right below 5.45 inches, which we can express as 5.449 inches. Thus, the smallest possible height is 5.35 inches, and the largest possible height is 5.449 inches.

Answer 2

To find the smallest and largest possible height of Sierra's sunflower, round down to 5.40 inches and round up to 5.41 inches, respectively.

Step-by-step explanation:

To find the smallest and largest possible height of Sierra's sunflower, we need to consider the rounding rules for measuring to the nearest hundredth. If the tenth digit is 4 or less, we round down to the nearest hundredth. If the tenth digit is 5 or greater, we round up to the nearest hundredth.

Sierra measured her sunflower to be 5.4 inches tall. To find the smallest possible height, we round down to the nearest hundredth, which is 5.40 inches. To find the largest possible height, we round up to the nearest hundredth, which is 5.41 inches.