# Appropriate Accuracy of Measurements (Grade 10)

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## Appropriate Accuracy of Measurements

1.

Lilly has measured the height of her desk to be 1.43 meters. The tape measure she is using has tick marks every 2 cm. What is the possible range in heights that her desk could be according to this accuracy?

- 1.33 m to 1.53 m
- 1.42 m to 1.44 m
- 1.429 m to 1.431 m
- 1.4295 m to 1.4305 m

2.

A large rock is measured with a ruler which has markings every half inch. Which of the following would be the most appropriate measurement of the rock?

- [math]5.0 \ "in" pm 0.5 \ "in"[/math]
- [math]5.4 \ "in" pm 0.2\ "in"[/math]
- [math]5.41 \ "in" pm 0.05 \ "in"[/math]
- [math]5.413 \ "in" pm 0.002\ "in"[/math]

3.

Saurabh is finding the mass of a piece of iron for an experiment. He places it on a digital scale, and reads 27.4 g. Which of the following would be the most appropriate uncertainty for this measurement?

- [math]pm 5 \ "g"[/math]
- [math]pm 1 \ "g"[/math]
- [math] pm 0.5\ "g"[/math]
- [math]pm 0.1 \ "g"[/math]

4.

Bonnie is recording the air temperature for a chemistry experiment. If she is using the thermometer pictured below, what is the most appropriate measurement?

- [math]24 \ ° "C" pm 2 \ ° "C"[/math]
- [math]24 \ ° "C" pm 1 \ ° "C"[/math]
- [math]24 \ ° "C" pm 0.5 \ ° "C"[/math]
- [math]24 \ ° "C" pm 0.05 \ ° "C" [/math]

5.

If the units of the following ruler are inches, what would be the most appropriate measurement of the pencil?

- [math]5.5 \ "in" pm 0.5 \ "in"[/math]
- [math]5.5 \ "in" pm 0.2 \ "in"[/math]
- [math]5.5 \ "in" pm 0.1 \ "in"[/math]
- [math]5.5 \ "in" pm 0.05 \ "in"[/math]

6.

The following ruler is used to measure a small object. The units are centimeters. Which of the following would be the most reasonable uncertainty to use for the measurement made?

- [math]pm 5 \ "cm"[/math]
- [math]pm 0.5 \ "cm"[/math]
- [math]pm 0.05 \ "cm"[/math]
- [math]pm 0.005 \ "cm"[/math]

7.

A car was measured, and recorded to be [math]4.4 \ "m" pm 0.1 \ "m"[/math]. Which of the following are true? Choose all that apply.

- You need to add or subtract 0.1 m from the first measurement.
- The measurement could be anywhere from 4.3 m to 4.5 m.
- There is a 10 percent error in the measurement.
- The car could be 4.37 m long.

8.

Yvonne is having a concrete pad poured for a shed she will build. If the contractor tells her that the pad is 5.5 feet by 6.0 feet, give or take an inch, what would be the difference between the largest possible area and the smallest possible area of the pad?

- 2.3 feet squared
- 1.8 feet squared
- 1.2 feet squared
- 0.9 feet squared

9.

Jerry is measuring some milk for a cake he is making. This happens to be an extremely finicky cake that requires very exact measurements. The measuring cup he has measures volume in mL. If he measures the volume as [math]250 \ "mL" pm 2%,[/math] what does this mean?

- The measurement is off by at least two percent.
- There is a two percent chance the measurement is correct.
- The actual measurement could be anywhere between 245 mL and 255 mL.
- This is incorrect, since the uncertainty must have units.

10.

Which measurement would be more accurate and why: measuring the length of a driveway, about 20 m long, with a tape measure whose smallest unit is 1/10 of a meter, or measuring the height of a fish tank, about 25 cm tall, with a ruler whose smallest unit is a centimeter? Choose all correct answers.

- The height of the fish tank will be more accurate, since the absolute uncertainty of the measurement will be [math]pm 0.5 \ "cm"[/math], while the absolute uncertainty in the driveway measurement will be [math]pm 5 \ "cm"[/math].
- The length of the driveway will be more accurate, since the relative uncertainty of the driveway will be about [math]pm 0.3%[/math], while the relative uncertainty of the fish tank's height will only be about [math]pm 2%[/math].
- The height of the fish tank will be more accurate, since the absolute uncertainty of this measurement will be [math]pm 0.05 \ "cm"[/math], while the absolute uncertainty of the driveway will be [math]pm 5 \ "cm"[/math].
- The length of the driveway will be more accurate, since the relative uncertainty of this measurement will be about [math]pm 1%[/math], while the relative uncertainty of the fish tank measurement will only be about [math]pm 2%[/math].

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