Precision and Greatest Possible Error
For Use With Lesson 9-3
No measurement is exact. The precision of a measurement is the degree to
which a measurement is accurate. A measurement can be no more precise
than the accuracy of the instrument used to make the measurement.
When comparing measurements, the measurement that uses the smaller
units is more precise. To show precision, you do not express fractional
measurements in simplest form.
1
Comparing Precision in Measurements
EXAMPLE
Choose the more precise measurement.
a. 2 28 in., 2 14 in.
Since eighth inches are smaller than quarter inches, 2 28 in. is
the more precise measurement.
b. 26 L, 260 mL
Since milliliters are smaller than liters, 260 mL is the more
precise measurement.
Any calculations with measurements will only be as accurate as
the least precise measurement. Round your answer to match the
precision of the least precise measurement.
2
Adding or Subtracting With Precision
EXAMPLE
Compute. Round your answer to match the less precise measurement.
a. 20.08 km + 5.2 km
20.08 + 5.2 = 25.28
< 25.3 km
d Add.
d Since 5.2 is less precise than 20.08, round to the nearest tenth.
b. 36 g - 12.3 g
36 - 12.3 = 23.7
< 24 g
d Subtract.
d Since 36 is less precise than 12.3, round to the nearest whole unit.
To the nearest half inch, the line segment at the right measures
112 inches. When a measurement is rounded to the nearest half
inch, it can vary from the actual length by as much as one fourth
inch. We say that one fourth inch is the greatest possible error
of measurement.
486
Investigation Precision and Greatest Possible Error
inches
The greatest possible error of a measurement is half the unit of measure to
which the measurement has been rounded.
3
Finding Greatest Possible Error
EXAMPLE
Find the greatest possible error for each measurement.
a. 28.3 L
The measurement is rounded to the nearest tenth of a liter.
Since 21 ? 0.1 = 0.05, the greatest possible error is 0.05 L.
b. 2 14 ft
The measurement is rounded to the nearest quarter foot.
Since 12 ? 14 = 18, the greatest possible error is 81 ft.
c. 800 kg
The measurement is rounded to the nearest hundred kilogram.
Since 12 ? 100 = 50, the greatest possible error is 50 kg.
EXERCISES
Choose the more precise measurement.
1. 3 mi, 2.8 mi
2. 16 tons, 17 12 tons
3. 4 34 in., 4 12
16 in.
4. 3.2 g, 3.02 g
5. ounce, pound
6. meter, centimeter
Compute. Round your answer to match the less precise measurement.
7. 34 ft + 16.9 ft
8. 60 s - 22.80 s
10. 33 58 in. + 4 14 in.
11. 42.00 m 2 - 21.0 m 2
9. 1.1 cm + 1.01 cm
12. 13.9 g - 4.0 g
Find the greatest possible error for each measurement.
13. 12 qt
14. 15.5 mL
15. 4.27 km
16. 255 ft
17. 2.1 mm
18. 1 14 c
19. 15.38 gal
20. 18 21 oz
21. 35.375 mg
22. 6 87 in.
Determine the precision possible with each scale shown.
23.
26. Writing in Math How does the precision of a measurement relate to
the greatest possible error of a measurement? Give examples.
Investigation Precision and Greatest Possible Error
487