SME
Grade 9 Math · Problem type
A product to the right significant figures
Use this for “A table is 4.25 m by 3.1 m. Give its area to the right number of significant figures.”
Diagram
This is an example. Type your own values to start a new problem.
l (m)
×
w (m)
=
P (m²)
n₁
Significant figures in l
example
n₂
Significant figures in w
example
n
Significant figures in the answer
worked out (not typed)
A
Area, rounded
worked out (not typed) · m²
Formulas
P
=
l
×
w
13.175 = 4.25 × 3.1
n
=
the
smaller
of
n₁
and
n₂
2 = the smaller of 3 and 2
A
=
P
rounded
to
n
significant
figures
13 = 13.175 rounded to 2 significant figures
Assumptions
•
A product is no more precise than its least precise factor.
•
Count the significant figures in each measurement; round the answer to the fewer.
•
Type the counts yourself: 3.10 has 3 significant figures, though its box shows 3.1.
Step-by-step
WE KNOW
l = 4.25 m, w = 3.1 m, n₁ = 3, n₂ = 2
FIND
area as calculated (P), significant figures in the answer (n), area, rounded (A)
Step 1 · Find area as calculated (P)
Use P = l × w
Multiply the measurements as they are.
P
=
4.25
×
3.1
P
=
13.175
m²
Step 2 · Find significant figures in the answer (n)
Use n = the smaller of n₁ and n₂
The answer keeps as many significant figures as the less precise measurement.
n
=
the
smaller
of
3
and
2
n
=
2
Step 3 · Find area, rounded (A)
Use A = P rounded to n significant figures
Round
the
calculated
area;
the
digits
past
n
are
not
known
from
these
measurements.
A
=
13.175
rounded
to
2
significant
figures
A
=
13
m²
Check
Put the numbers back in. Both sides should match.
13.175 = 4.25 × 3.1 ✓
2 = the smaller of 3 and 2 ✓
13 = 13.175 rounded to 2 significant figures ✓
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Precision: least and greatest possible area
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Choosing a level of accuracy
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