SME
Grade 10 Science · Chemistry
Measurement, significant figures and dimensional analysis
Use this for “How many centimeters are in 2.5 km?” with a chain of conversion factors.
Diagram
Struck through: km, m, each on a top and a bottom, so they cancel.
The unit left is cm.
Each factor is 1 (its top and bottom are the same amount), so the amount does not change.
This is an example. Type your own values to start a new problem.
d
km
×
1,000
m
1
km
×
100
cm
1
m
=
c
cm
Formulas
c
=
d
×
1,000
×
100
2.5 ×
10
5
=
2.5
×
1,000
×
100
Assumptions
•
A conversion factor equals 1, so multiplying by it changes the unit, not the amount.
•
Put the unit you want to cancel on the bottom of the factor.
•
Exact defined factors (1000 m in 1 km) never limit significant figures.
Step-by-step
WE KNOW
d = 2.5 km
FIND
distance in centimeters (c)
Step 1 · Find distance in centimeters (c)
Use c = d × 1,000 × 100
Multiply by 1000 m per km, then by 100 cm per m: km and m cancel.
c
=
2.5
×
1,000
×
100
c
=
2,500
×
100
c
=
2.5 ×
10
5
cm
Check
Put the numbers back in. Both sides should match.
2.5 ×
10
5
=
2.5
×
1,000
×
100
✓
Topic check
See what you know: 5 questions on this topic
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