© t madas. describing the accuracy of measurements part 1

© T Madas

Describing the Accuracy of Measurements

Part 1

© T Madas

The length of a pencil is measured as 112 ± 1 mm.What is the maximum and the minimum possible length of the pencil according to this information?

Minimum Length:

Maximum Length:

111 mm

113 mm

L≤ ≤ 113111

LowerBound

UpperBound

© T Madas

The thickness of a coin is measured as 3 ± 0.2 mm.What is the maximum and the minimum possible thickness of this coin according to this information?

Minimum Thickness:

Maximum Thickness:

2.8 mm

3.2 mm

T≤ ≤ 3.22.8

LowerBound

UpperBound

© T Madas

The thickness of an optical lens is measured as 3 ± 0.015 mm.What is the maximum and the minimum possible thickness of this lens according to this information?

Minimum Thickness:

Maximum Thickness:

2.985 mm

3.015 mm

T≤ ≤ 3.0152.985

LowerBound

UpperBound

© T Madas


Part 2

© T Madas

The weight of a chocolate bar and its packaging is 72 grams, correct to the nearest gram.What is the maximum and the minimum possible weight of this object according to this information?

Minimum Weight:Maximum Weight:

71.5 g72.5 g

W≤ < 72.571.5

68 69 70 71 72 73 74 75

gramsUpperBound

LowerBound

© T Madas

The length of a pencil is 11.8 cm correct to 1 decimal place.What is the maximum and the minimum possible length of the pencil according to this information?

Minimum Length:Maximum Length:

11.75 cm11.85 cm

L≤ < 11.8511.75

11.4 11.5 11.6 11.7 11.8 11.9 12.0 12.1

cmUpperBound

LowerBound

© T Madas

The weight of an empty can is 15.32 g correct to 2 decimal placesWhat is the maximum and the minimum possible weight of the can according to this information?


15.315 g15.325 g

W≤ < 15.32515.315

15.28 15.29 15.30 15.31 15.32 15.33 15.34 15.35

gUpperBound

LowerBound

© T Madas

The shutter time for a camera in cloudy conditions is 0.017 seconds, correct to 3 decimal places.What is the maximum and the minimum possible shutter times according to this information?


0.0165 s0.0175 s

t≤ < 0.01750.0165

0.013 0.014 0.015 0.016 0.017 0.018 0.019 0.020

secUpperBound

LowerBound

© T Madas

A specialised AC generator used in medicine is said to provide a constant voltage of 0.0475 volts, correct to 4 decimal places.What is the maximum and the minimum possible voltage that this instrument provides, according to this information?

Minimum voltage:Maximum voltage:

0.04745 V0.04755 V

V≤ < 0.047550.04745

0.0472 0.0473 0.0474 0.0475 0.0476 0.0477 0.0478 0.0479

voltsUpperBound

LowerBound

ESC

LOAD ON ON BATT BYPASS FAULT

generator

© T Madas

The length of a ladybird is 7 mm correct to the nearest mmWhat is the maximum and the minimum possible length of the ladybird according to this information?

0 10

mm

5

Minimum Length:Maximum Length:

6.5 mm7.5 mm

L≤ < 7.56.5

UpperBound

LowerBound

© T Madas

The weight of a male gorilla is measured as 285 kg, correct to the nearest 5 kg.What is the maximum and the minimum possible weight of this gorilla according to this information?

255 260 265 270 275 280 285 290 295 300 305 310

Kg


282.5 kg287.5 kg

W≤ <287.5282.5

UpperBound

LowerBound

© T Madas

The winning time of a 100 metre sprinter is 10.2 seconds correct to the nearest tenth of a second.What is the fastest and the slowest possible winning times for this particular sprint?

9.8 9.9 10.0 10.1 10.2 10.3 10.4 10.5

sec

Fastest Time:Slowest Time:

10.15 sec10.25 sec

t≤ <10.2510.15

UpperBound

LowerBound

© T Madas

The time exposure of a photographic film is measured as 0.036 seconds, correct to the nearest two thousandths of a second.What is the fastest and the slowest possible exposure times for this particular photographic film?

0.028 0.030 0.032 0.034 0.036 0.038 0.040 0.042

sec

Fastest Time:Slowest Time:

0.035 sec0.037 sec

t≤ <0.0370.035

UpperBound

LowerBound

© T Madas

The weight of a bean is measured as 8 grams, correct to the nearest quarter of a gram.What is the maximum and the minimum possible weights for this bean?

6.75 7.00 7.25 7.50 7.75 8.00 8.25 8.50

grams

Maximum Weight:Minimum Weight:

8.125 g7.875 g

w≤ <8.1257.875

UpperBound

LowerBound

© T Madas


Part 3

© T Madas

The population of the U.K. is estimated to be 56 000 000, correct to 2 significant figures.What is the maximum and minimum possible U.K. populations according to this information?

Minimum Population:

Maximum Population:

55 500 000

56 499 999

P≤ ≤56 499 99955 000 000

LowerBound

UpperBound

© T Madas

The speed of a rocket is measured as to be 5630 km per hour, correct to 3 significant figures.What is the maximum and minimum possible rocket speeds according to this information?

Minimum Speed:

Maximum Speed:

5625

5635

s≤ < 56355625

LowerBound

UpperBound

© T Madas

The length of a pens is measured as 15 cm, correct to the nearest whole number.What is the maximum and minimum possible lengths of this pen according to this information?

Minimum Length:

Maximum Length:

14.5 cm

15.5 cm

P≤ < 15.514.5

LowerBound

UpperBound

© T Madas

A rectangle measures 45 cm by 32 cm.These dimensions are correct to the nearest cm. 1. Calculate the minimum possible perimeter of this

rectangle 2. Calculate the maximum possible perimeter of this

rectangle3. Calculate the minimum possible area of this rectangle4. Calculate the maximum possible area of this

rectangle

44.5 – 45.5

31.5

– 32.5 Min Perimeter

31.5+ 31.5+ 44.5+ 44.5= 152 cm

Max Perimeter

32.5+ 32.5+ 45.5+ 45.5= 156 cm

Min Area

31.5x 44.5= 1401.75 cm2

Max Area

32.5x 45.5= 1478.75 cm2

© T Madas

A right angled triangle has perpendicular sides equal to 140 mm and 84 mm.These dimensions are correct to 2 significant figures. Calculate the minimum and maximum possible lengths for the hypotenuse, correct to 1 d.p.

83.5 – 84.5

135

– 145

Minimum Length

(83.5)2+ (135)2x 2 =

x

6972.25+ 18225x 2 =

25197.25x 2 =

158.7 mmx =

Maximum Length

(84.5)2+ (145)2x 2 =

7140.25+ 21025x 2 =

28165.25x 2 = 167.8 mmx =

© T Madas

The formula is used to calculate the tension T exerted by an elastic spring.The following data is given, correct to 3 significant figures: The natural length of the spring L, is 0.386 m The extension of the spring x, is 0.156 m The modulus of elasticity λ, 1.52 NFind the maximum and the minimum possible values for the tension exerted by this spring, to 3 significant figures.

xTL

=

0.38650.15651.525

0.38550.15551.515

≤ L ≤≤ x ≤≤ λ ≤

To maximise T

T = x 0.15651.5250.3855

= 0.619

© T Madas

0.38650.15651.525

0.38550.15551.515

≤ L ≤≤ x ≤≤ λ ≤

To maximise T

To minimise T

T = 1.515x 0.15550.3865

= 0.610

T = x 0.15651.5250.3855

= 0.619

The formula is used to calculate the tension T exerted by an elastic spring.The following data is given, correct to 3 significant figures: The natural length of the spring L, is 0.386 m The extension of the spring x, is 0.156 m The modulus of elasticity λ, 1.52 NFind the maximum and the minimum possible values for the tension exerted by this spring, to 3 significant figures.

xTL

=

© T Madas

Write the lower & upper bounds for these measurements

2.35 g2.25 gto 1 d.p.2.3 g

3350 s3250 snearest one hundred3300 s

295 kg285 kgnearest ten290 kg

18.5 mm17.5 mmto the nearest mm18 mm

10.05 kg9.95 kgto 1 d.p.10.0 kg

0.0035 g0.0025 gto 3 d.p.0.003 g

1.2345 s1.2335 sto 3 d.p.1.234 s

4.085 m4.075 mto 2 d.p.4.08 m

45.5 g44.5 gnearest whole number45 g

175.5 m174.5 mnearest m175 m

Upper Bound

Lower Bound

AccuracyMeasureme

nt

© T Madas


10.85 s10.75 sto 1 d.p.10.8 s

7850 km7750 kmnearest one hundred7800 km


76.5 m75.5 mto the nearest metre76 m

307.5 oz302.5 ozto the nearest 5 oz305 oz

603 m601 mto the nearest 2 metres602 m

0.4565 s0.4555 sto 3 d.p.0.456 s

1.775 kg1.765 kgto 2 d.p.1.77 kg

56.5 mm55.5 mmnearest whole number56 mm

34.5 cm33.5 cmnearest cm34 cm

Upper Bound

Lower Bound

AccuracyMeasureme

nt

© T Madas


7.65 s7.55 sto 1 d.p.7.6 s

1385 km1375 kmto 3 s.f.1380 km


317.5 m312.5 mto the nearest five metres315 m

12.75 oz12.25 ozto the nearest ½ oz12.5 oz

1.375 m1.125 mto the nearest ¼ metre1.25 m

0.0245 s0.0235 sto 2 s.f.0.024 s

1.175 kg1.165 kgto 3 s.f.1.17 kg

875 mm865 mmto 2 s.f.870 mm

26.5 cm25.5 cmto 2 s.f.26 cm

Upper Bound

Lower Bound

AccuracyMeasureme

nt

© T Madas


2.35 g2.25 gto 1 d.p.2.3 g

3350 s3250 snearest one hundred3300 s


18.5 mm17.5 mmto the nearest mm18 mm

10.05 kg9.95 kgto 1 d.p.10.0 kg

0.0035 g0.0025 gto 3 d.p.0.003 g

1.2345 s1.2335 sto 3 d.p.1.234 s

4.085 m4.075 mto 2 d.p.4.08 m

45.5 g44.5 gnearest whole number45 g

175.5 m174.5 mnearest m175 m

Upper Bound

Lower Bound

AccuracyMeasureme

nt

© T Madas


10.85 s10.75 sto 1 d.p.10.8 s

7850 km7750 kmnearest one hundred7800 km


76.5 m75.5 mto the nearest metre76 m

307.5 oz302.5 ozto the nearest 5 oz305 oz

603 m601 mto the nearest 2 metres602 m

0.4565 s0.4555 sto 3 d.p.0.456 s

1.775 kg1.765 kgto 2 d.p.1.77 kg

56.5 mm55.5 mmnearest whole number56 mm

34.5 cm33.5 cmnearest cm34 cm

Upper Bound

Lower Bound

AccuracyMeasureme

nt

© T Madas


7.65 s7.55 sto 1 d.p.7.6 s

1385 km1375 kmto 3 s.f.1380 km


317.5 m312.5 mto the nearest five metres315 m

12.75 oz12.25 ozto the nearest ½ oz12.5 oz

1.375 m1.125 mto the nearest ¼ metre1.25 m

0.0245 s0.0235 sto 2 s.f.0.024 s

1.175 kg1.165 kgto 3 s.f.1.17 kg

875 mm865 mmto 2 s.f.870 mm

26.5 cm25.5 cmto 2 s.f.26 cm

Upper Bound

Lower Bound

AccuracyMeasureme

nt

© t madas. describing the accuracy of measurements part 1

Documents

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