SME
Grade 10 Science · Problem type
Reading a ruler to the estimated digit
Use this to read a rod’s length from its start and end, to one digit past the smallest marks.
Diagram
The marks are 0.1 cm apart, so 7.7 cm is certain.
The rod ends about 1 tenths of the way to 7.8: the estimated digit is 1, so it reads 7.71 cm.
Length = 7.71 − 1.25 = 6.46 cm, 3 significant figures.
This is an example. Type your own values to start a new problem.
L (cm)
=
x₂ (cm)
−
x₁ (cm)
Formulas
L
=
x₂
−
x₁
6.46 = 7.71 − 1.25
Assumptions
•
The ruler is marked every 0.1 cm (every millimeter).
•
Read one digit past the smallest mark; that last digit is estimated and still significant.
•
A length such as 6.46 cm has 3 significant figures: two certain digits and one estimated.
Step-by-step
WE KNOW
x₁ = 1.25 cm, x₂ = 7.71 cm
FIND
length of the rod (L)
Step 1 · Find length of the rod (L)
Use L = x₂ − x₁
The length is the end reading minus the start reading.
L
=
7.71
−
1.25
L
=
6.46
cm
Check
Put the numbers back in. Both sides should match.
6.46 = 7.71 − 1.25 ✓
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