Measure lengths from two ruler readings
Read a scale at eye level and subtract the starting reading when the object does not begin at zero.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Subtract decimal numbers.
- Convert centimetres and millimetres.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How many millimetres are in 1 cm?
What you will learn
- Describe a ruler measurement with a suitable scale.
- Calculate a length from two endpoint readings.
Align the object and read the scale
Place a straight ruler alongside the length with its scale parallel to the object. View each endpoint directly above the scale so the line of sight is perpendicular to it; looking from an angle can produce parallax. Identify the value of one small division before reading. Ten equal intervals between adjacent centimetre marks represent millimetres.
An endpoint at 8.9 cm is a position on the ruler, not automatically the object's length. If the other endpoint is at 2.4 cm, the length is 8.9 − 2.4 = 6.5 cm. Using two clear marks away from a damaged ruler end can be better than assuming the physical edge is the zero mark.
Record the unit and a defensible precision
A length of 6.5 cm equals 65 mm or 0.065 m. Convert the complete length after subtracting readings in the same unit. Use the scale's resolution and the visibility of the endpoint to decide the recording precision; a millimetre scale does not justify an arbitrarily long decimal answer.
Repeat a measurement after realigning the ruler to check consistency. Repetition can reveal scatter or a placement mistake, but averaging repeated readings does not correct a systematic zero error or persistently slanted viewing. State the method that addresses the actual problem rather than claiming repetition makes a measurement exact.
Sources for this lesson
Pause and explain
A ruler object starts at 2.4 cm and ends at 8.9 cm. What is its length?
Worked example
A strip starts at 2.4 cm and ends at 8.9 cm. Find its length in millimetres.
Show the worked solution
- Subtract endpoint positions: 8.9 − 2.4 = 6.5 cm.
- Multiply centimetres by ten.
- Record the length, with its unit, as 65 mm.
Answer 65 mm.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A strip spans 2.4 cm to 8.9 cm. Calculate its length in cm and mm.
Give me a hint
Length is the difference between positions on the same scale.
Compare my reasoning
- Identify lower and upper readings.
- Subtract to obtain 6.5 cm.
- Convert to 65 mm.
6.5 cm; 65 mm.
Look for these in your work
- Subtract the initial reading.
- Use consistent units.
A rod spans 14 mm to 89 mm. Give its length in metres.
Give me a hint
Subtract first, then divide millimetres by one thousand.
Compare my reasoning
- 89 − 14 = 75 mm.
- 75 mm = 0.075 m.
- Retain the unit m with the converted value.
0.075 m.
Look for these in your work
- Use both endpoints.
- Convert mm to m.
A ruler has a damaged zero end. Describe how to measure a card accurately with its remaining clear scale.
Give me a hint
Choose two readable positions rather than trusting the physical edge.
Compare my reasoning
- Align the card between clear non-zero marks.
- Read both ends directly above the scale.
- Subtract the starting reading from the finishing reading and record the unit.
Use two clear readings and subtract, viewing perpendicular to the scale.
Look for these in your work
- Avoid the damaged zero.
- Address parallax explicitly.
Common mistakes
- The upper reading alone is not the length when the start is non-zero.
- Count scale intervals rather than printed marks.
- Repeating the same parallax error does not remove it.
What can you explain now?
An object spans 13 mm to 57 mm. How long is it?
Compare with the explanation
44 mm.
Subtract 57 − 13; both endpoint readings share the same unit.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Draw a ruler with a non-zero start, calculate the object length and explain why viewing angle matters.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.