A ruler calibrated in cm measures a table length of 102.0 cm. Find A. the limit of reading, B. the absolute error as fraction, C. the relative error as fraction.

A standard ruler calibrated in centimeters (cm) typically has markings for millimeters (mm).
1 mm is equivalent to 0.1 cm.

The limit of reading (or least count) of an instrument is its smallest measurable division.
The limit of reading of a ruler calibrated in cm is 0.1 cm.

• B. the absolute error as fraction;

The absolute error for a measurement made with a ruler is generally taken as half of its least count (limit of reading).
Least count = 0.1 cm.
Absolute error = $\frac{1}{2} \times \text{Least Count}$
Absolute error = $\frac{1}{2} \times 0.1 \, \text{cm}$
Absolute error = $0.05 \, \text{cm}$

$0.05 = \frac{5}{100} = \frac{1}{20}$
The absolute error as a fraction is $\frac{1}{20} \, \text{cm}$.

• C. the relative error as a fraction;

Relative error is the ratio of the absolute error to the measured value.
Relative error = $\frac{\text{Absolute Error}}{\text{Measured Value}}$

Measured value = 102.0 cm
Absolute error = 0.05 cm (or $\frac{1}{20}$ cm)
Relative error = $\frac{0.05 \, \text{cm}}{102.0 \, \text{cm}}$

Relative error = $\frac{1/20}{102}$
Relative error = $\frac{1}{20 \times 102}$
Relative error = $\frac{1}{2040}$

Here are the answers:

• A. The limit of reading of a ruler: $\boxed{\text{0.1 cm}}$
• B. The absolute error as fraction: $\boxed{\frac{1}{20} \, \text{cm}}$
• C. The relative error as a fraction: $\boxed{\frac{1}{2040}}$