Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Standard Units of Measurement: In ancient times, people used handspans, cubits, or foot lengths, but these varied from person to person. To maintain uniformity, the International System of Units (SI units) was adopted. The SI unit of length is the ().
Measuring Length Correctly: The scale should be placed in contact with the object along its length. If the zero mark is broken or not clear, any other full mark (like ) can be used as the starting point.
Parallax Error: To get an accurate reading, the eye must be placed exactly vertically above the point where the measurement is to be taken. Looking from an angle leads to errors.
Measuring Curved Lines: A straight ruler cannot measure a curved path directly. A thread is used to trace the curved line from one end to the other. The length of the thread is then measured using a standard scale.
Unit Hierarchy: For very long distances, we use (). For small lengths, we use () or ().
📐Formulae
💡Examples
Problem 1:
The distance between two points on a curved line measured using a thread is found to correspond to the distance between the mark and the mark on a ruler. What is the length of the curved line?
Solution:
Length
Explanation:
When the zero mark is not used, the actual length is the difference between the final reading and the initial reading on the scale.
Problem 2:
Convert a distance of into and .
Solution:
In metres: . In centimetres: .
Explanation:
Since , we multiply by to convert to metres. Then, since , we multiply the result by .