Question

period 1 2 3 4 5 6 date_____
measurement: estimating one place beyond
the accuracy of measurement is limited by the tools we use. if a clock doesnt have a second hand, we can estimate the number of seconds past the minute by looking at the minute hand. if a clock doesnt even have a minute hand, we can estimate time in hours and minutes, but certainly not seconds!!
directions: based on the diagrams below, make the best estimate for each of the measurements indicated by the arrows.

1. estimate the number of centimeters indicated by each of the arrows below.

diagram of a centimeter ruler with arrows at a, b, c, d, e

1. a __________

b __________
c __________
d __________
e __________

1. estimate the number of centimeters indicated by each of the arrows below.

diagram of a centimeter ruler with arrows at a, b, c, d, e

1. a __________

b __________
c __________
d __________
e __________

1. estimate the number of millimeters and the number of centimeters indicated by each of the arrows below.

diagram of a millimeter ruler with arrows at a, b, c

1. a __________ mm

__________ cm
b __________ mm
__________ cm
c __________ mm
__________ cm

1. estimate the number of milliliters indicated by each of the arrows below.

diagram of a milliliter measuring device with arrows at c, f, a, e, b, d

1. a __________

b __________
c __________
d __________
e __________
f __________

Explanation:

Step1: Estimate ruler 1 marks

Each major mark = 1 cm. Estimate 1 decimal place:
[a] Arrow at halfway between 0 and 1: $\frac{0+1}{2}=0.5$ cm
[b] Arrow at exactly 4: $4.0$ cm
[c] Arrow at halfway between 6 and 7: $\frac{6+7}{2}=6.5$ cm
[d] Arrow at exactly 8: $8.0$ cm
[e] Arrow at exactly 12: $12.0$ cm

Step2: Estimate ruler 2 marks

Each major mark = 1 cm, 10 sub-marks = 0.1 cm each:
[a] Arrow at 0.8 cm: $0.8$ cm
[b] Arrow at 1.5 cm: $1.5$ cm
[c] Arrow at 2.3 cm: $2.3$ cm
[d] Arrow at 3.4 cm: $3.4$ cm
[e] Arrow at 4.1 cm: $4.1$ cm

Step3: Estimate ruler 3 marks

Major marks = 10 mm = 1 cm, 10 sub-marks = 1 mm each:
[a] Arrow at 40 mm: $40$ mm = $\frac{40}{10}=4.0$ cm
[b] Arrow at 105 mm: $105$ mm = $\frac{105}{10}=10.5$ cm
[c] Arrow at 115 mm: $115$ mm = $\frac{115}{10}=11.5$ cm

Step4: Estimate graduated cylinder marks

Major marks = 1 mL, 10 sub-marks = 0.1 mL each:
[a] Arrow at 7.2 mL: $7.2$ mL
[b] Arrow at 7.8 mL: $7.8$ mL
[c] Arrow at 8.4 mL: $8.4$ mL
[d] Arrow at 8.9 mL: $8.9$ mL
[e] Arrow at 9.3 mL: $9.3$ mL
[f] Arrow at 9.7 mL: $9.7$ mL

Answer:

1. [a] 0.5 cm

[b] 4.0 cm
[c] 6.5 cm
[d] 8.0 cm
[e] 12.0 cm

1. [a] 0.8 cm

[b] 1.5 cm
[c] 2.3 cm
[d] 3.4 cm
[e] 4.1 cm

1. [a] 40 mm, 4.0 cm

[b] 105 mm, 10.5 cm
[c] 115 mm, 11.5 cm

1. [a] 7.2 mL

[b] 7.8 mL
[c] 8.4 mL
[d] 8.9 mL
[e] 9.3 mL
[f] 9.7 mL