Combine unit conversion with magnification calculations
Make the two lengths comparable before using the ratio.
Section B2.2 · Size of specimens
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
- Recall the distinction between plant, animal and bacterial cells. Read the supplied evidence before drawing a conclusion.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is 75 μm expressed in mm?
What you will learn
- Convert mixed length units before calculating.
- Detect a thousand-fold magnification error.
Convert before dividing
An image length of 30 mm and actual specimen length 75 μm must not be divided as 30 ÷ 75 without conversion. Convert 75 μm to 0.075 mm, then 30 ÷ 0.075 = 400, giving ×400. Alternatively convert 30 mm to 30 000 μm and divide by 75 μm.
Both conversion routes must agree. Magnification remains dimensionless. Write the conversion step so the origin of a factor of 1000 is visible rather than treating it as an unexplained adjustment after the answer.
Keep actual-size units explicit
An image length of 48 mm at ×1200 gives actual length 48 ÷ 1200 = 0.04 mm, which is 40 μm. The first result is correct in mm; converting to μm changes the number but not the physical length.
If a result says ×0.4 for the first enlarged image, substituting shows a unit mismatch or reversed interpretation. A scale bar may supply an actual μm length; compare its measured image length with the specimen on the same copy before converting.
Sources for this lesson
Pause and explain
A 30 mm image represents 75 μm actual length. Why is ×0.4 wrong?
Worked example
A 30 mm image represents an actual length of 75 μm. Calculate magnification.
Show the worked solution
- 75 μm ÷ 1000 = 0.075 mm.
- 30 ÷ 0.075 = 400.
- Or 30 000 μm ÷ 75 μm = 400.
Answer ×400.
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.
An image is 18 mm; actual length is 60 μm. Find magnification.
Give me a hint
Convert 60 μm to mm.
Compare my reasoning
- 60 μm = 0.06 mm.
- 18 ÷ 0.06 = 300.
×300.
Look for these in your work
- Correct conversion.
- Dimensionless result.
A 56 mm image is ×1400. Find actual length in μm.
Give me a hint
First calculate mm, then convert.
Compare my reasoning
- 56 ÷ 1400 = 0.04 mm.
- 0.04 × 1000 = 40 μm.
40 μm.
Look for these in your work
- Correct division.
- Correct unit conversion.
A 20 mm drawn bar represents 25 μm actual length. A cell measures 64 mm on the same copy. Find actual cell length and state the scaling assumption.
Give me a hint
Use cell-to-bar image ratio.
Compare my reasoning
- 64 ÷ 20 = 3.2 bar lengths.
- 3.2 × 25 = 80 μm.
- Both dimensions and the bar must share the same proportional scale.
80 μm, assuming a common proportional scale.
Look for these in your work
- Ratio and conversion meaning.
- State the same-copy scaling assumption.
Common mistakes
- A mm-to-μm mismatch can produce a thousand-fold error.
- State units at the conversion step.
What can you explain now?
What must be done before dividing image length in mm by actual length in μm?
Compare with the explanation
Express both lengths in the same unit.
The units must cancel in the ratio.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Solve the same magnification once in mm and once in μm and compare.
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.