To compare data in different units, first convert so that like quantities share one unit, then compare changes as percentages of their own starting values. Percentages carry no unit, so they let you rank a change in length against a change in mass.
This skill sits at the heart of cross-science data interpretation and appears in biology, chemistry and physics questions alike. All data in this lesson is invented for practice.
Why can’t I compare 3 cm with 3 g?
A centimetre measures length and a gram measures mass. The two numbers answer different questions, so “3 is the same as 3” says nothing. A change only becomes comparable once you ask how big it is compared with where it started.
There are two separate jobs here. If both values are the same quantity in different units (km and m, L and mL, kg and g), you convert. If the values are different quantities, you use percentage change.
Step by step
- List each quantity with its unit.
- Convert like quantities to a single unit before comparing. Write the conversion line, for example 1 kg = 1000 g.
- Find the change: final value minus starting value.
- Divide by the starting value and multiply by 100 to get a percentage change.
- Compare the percentages, and state the answer in a sentence that names the quantities.
Worked example
A class grows bean seedlings in a window (invented data). After one week the average height rose from 12 cm to 15 cm.
The average dry mass rose from 0.80 g to 0.92 g. Which quantity increased by the larger proportion?
Height: change = 15 − 12 = 3 cm. Percentage change = 3 ÷ 12 × 100 = 25%.
Dry mass: change = 0.92 − 0.80 = 0.12 g. Percentage change = 0.12 ÷ 0.80 × 100 = 15%.
Conclusion: the height increased by a larger proportion (25%) than the dry mass (15%). Notice that the raw change 3 looks far bigger than 0.12, yet the units made that comparison meaningless.
A second case needs only conversion. A fuel burner is weighed at 0.35 kg and a second one at 280 g. Convert 0.35 kg to 350 g, so the first burner is heavier by 70 g.
The mistake to watch for
Mistaken answer: “Height changed by 3 and mass changed by 0.12, so height changed more.”
The student compared raw numbers from different units. The correction is to convert each change into a percentage of its own start first.
Here the conclusion happens to survive, but with a different data set it would not. For example, a mass rising from 0.50 g to 0.80 g has a raw change of only 0.3, yet that is a 60% increase.
Check yourself
1. A beaker holds 450 mL of liquid and another holds 0.5 L. Which holds more, and by how much?
Show answer
Convert 0.5 L to 500 mL. The second beaker holds more, by 500 − 450 = 50 mL.
2. A student’s mass rose from 40 g to 46 g while pulse rate rose from 70 to 84 beats per minute. Which rose by the larger percentage?
Show answer
Mass: 6 ÷ 40 × 100 = 15%. Pulse: 14 ÷ 70 × 100 = 20%. The pulse rate rose by the larger percentage.
3. Why is a 25% rise from 20 °C to 25 °C not a meaningful statement?
Show answer
Zero on the Celsius scale is not a true zero, so a percentage of a Celsius value changes if you switch scale. Report the rise as 5 °C instead.
Where this leads next
Next, learn to select a graph type for a mixed investigation, then test yourself on the cross-science practice set. The scientific investigation critic helps you check whether your comparison is fair.
Some students follow each conversion yet still choose the wrong quantity to compare. That is the kind of pattern a teacher can spot in online one-to-one Combined Science tuition.