Question

using significant figures, what would be the best measurement of the leaf using the ruler provided?
· 5 cm
· 5.73 cm
· 5.2 cm
· 5.8 cm
· 5.24 cm

Explanation:

Step1: Understand significant figures in measurement

When measuring with a ruler, the measurement should be recorded to the nearest \(0.1\) cm (one - decimal place for centimeters when the ruler's smallest division is \(0.1\) cm). This is because we estimate one digit beyond the smallest marked division on the ruler.

Step2: Analyze each option

• \(5\) cm: It has only one significant figure. It is too approximate as it does not account for the tenths place based on the ruler's markings.
• \(5.73\) cm: The ruler's smallest division is \(0.1\) cm. Measuring to the hundredths place (\(0.01\) cm) is over - estimating as there are no \(0.01\) cm markings on the given ruler.
• \(5.2\) cm: It is only to the tenths place. But from the ruler, the leaf extends further than \(5.2\) cm.
• \(5.8\) cm: The ruler's smallest division is \(0.1\) cm. We look at the position of the end of the leaf. The leaf starts at \(0\) cm and ends close to \(5.8\) cm. Since we estimate one digit beyond the smallest marked division (which is \(0.1\) cm), this is a reasonable measurement.
• \(5.24\) cm: Similar to \(5.73\) cm, measuring to the hundredths place (\(0.01\) cm) is over - estimating as there are no \(0.01\) cm markings on the given ruler.

Answer:

\(5.8\) cm