Question

measuring length

1. a. ____ cm ____ mm

b. ____ ____
c. ____ ____
d. ____ ____

1. record the measurement for d in meters. ________
2. record the measurement for a in meters. ________
3. ______ mm
4. ______ cm
5. ______ mm

percent error

1. a student measured the volume of a liquid to be 215.5 ml. the correct value of the volume is 205.5 ml. what is the student’s percent error?
2. a student calculated the density of aluminum to be 2.95 g/cm³. the actual density of aluminum is 2.70 g/cm³. what is the student’s percent error?

Explanation:

Step1: Read thermometer - 15

Read the first thermometer. Each small - scale division is 1°C. The mercury level is at 15°C.
15°C

Step2: Read thermometer - 16

Read the second thermometer. The mercury level is at 18°C.
18°C

Step3: Read thermometer - 17

Read the third thermometer. The mercury level is at - 4°C.

• 4°C

Step4: Read length - 18A

For the length measurement at A, the reading is 1.4 cm or 14 mm.
1.4 cm; 14 mm

Step5: Read length - 18B

For the length measurement at B, the reading is 4.0 cm or 40 mm.
4.0 cm; 40 mm

Step6: Read length - 18C

For the length measurement at C, the reading is 6.4 cm or 64 mm.
6.4 cm; 64 mm

Step7: Read length - 18D

For the length measurement at D, the reading is 7.4 cm or 74 mm.
7.4 cm; 74 mm

Step8: Convert length D to meters - 19

Convert 7.4 cm to meters. Since 1 m = 100 cm, 7.4 cm=7.4÷100 = 0.074 m.
0.074 m

Step9: Convert length A to meters - 20

Convert 1.4 cm to meters. Since 1 m = 100 cm, 1.4 cm = 1.4÷100=0.014 m.
0.014 m

Step10: Read length - 21

For the length from 25 cm to 27 cm, the length is 27 - 25 = 2 cm = 20 mm.
20 mm

Step11: Read length - 22

For the length from 0 cm to 2 cm, the length is 2 cm.
2 cm

Step12: Convert length - 23

2 cm = 20 mm.
20 mm

Step13: Calculate percent error - 24

The percent - error formula is $\text{Percent Error}=\frac{\vert\text{Measured Value}-\text{True Value}\vert}{\text{True Value}}\times100\%$. Measured value = 215.5 mL, True value = 205.5 mL. $\text{Percent Error}=\frac{\vert215.5 - 205.5\vert}{205.5}\times100\%=\frac{10}{205.5}\times100\%\approx4.87\%$.
4.87%

Step14: Calculate percent error - 25

Measured density = 2.95 g/cm³, True density = 2.70 g/cm³. $\text{Percent Error}=\frac{\vert2.95 - 2.70\vert}{2.70}\times100\%=\frac{0.25}{2.70}\times100\%\approx9.26\%$.
9.26%

Answer:

1. 15°C
2. 18°C
3. - 4°C
4. A. 1.4 cm; 14 mm

B. 4.0 cm; 40 mm
C. 6.4 cm; 64 mm
D. 7.4 cm; 74 mm

1. 0.074 m
2. 0.014 m
3. 20 mm
4. 2 cm
5. 20 mm
6. 4.87%
7. 9.26%