Topicm00977827723ade96_1528449000663_0Topic

Conversion of multiples and submultiples of units

Levelm00977827723ade96_1528449084556_0Level

Second

Core curriculumm00977827723ade96_1528449076687_0Core curriculum

II. Solving problems using physical laws and physical dependencies.

I. Cross‑sectional requirements. Student:

7) converts multiples and submultiples (micro-, milli-, cent-, hecto-, kilo-, mega-).

Timingm00977827723ade96_1528449068082_0Timing

45 minutes

General learning objectivesm00977827723ade96_1528449523725_0General learning objectives

Familiarization with the multiples and submultiples of units.

Specific objectivesm00977827723ade96_1528449552113_0Specific objectives

1. Recognising the multiples and submultiples of units.

2. Determining the interdependence between multiples and submultiples.

Operational (detailed) goalsm00977827723ade96_1528450430307_0Operational (detailed) goals

The student:

- converts the multiples and submultiples of units.

Methodsm00977827723ade96_1528449534267_0Methods

1. Learning through observation.

Forms of workm00977827723ade96_1528449514617_0Forms of work

1. Individual work.
2. Work with the whole class.

Lesson stages

Introductionm00977827723ade96_1528450127855_0Introduction

Task 1

Familiarize yourself with the table showing the unit prefixes used in the SI system for the names of additional units and symbols of the multiples of units and the submultiples of basic units.m00977827723ade96_1527752263647_0Familiarize yourself with the table showing the unit prefixes used in the SI system for the names of additional units and symbols of the multiples of units and the submultiples of basic units.

[Table 1]

Conclusion:

The multiples and submultiples of basic units available in the SI system enable the recording of measurement results and the values of the measured quantities in such a way that this value is closest to the real value of the measured quantity.

All physical quantities recorded in basic units can be converted into multiples and submultiples of a given unit. The prefixes of these quantities are the same to all units.

Procedurem00977827723ade96_1528446435040_0Procedure

Task 2

Answer the following questions:

a) What is the similarity between the kilogram and the kilometre?

b) How many meters does a kilometre have and how many grams does a kilogram have?

Answer:

a) the common prefix is kilo (1000).

b) 1 km = 1000 m; 1 g = 0,001 kg.

Task 3

Read the values of the following data using their names and the names of units listed below:

N - newton; Pa - pascal; V - volt, W - watt;

e.g. 1 mA - one milliamper.

a) 1 kW
b) 6 MN
c) 20 TV
d) 1 hPa
e) 5 mV
f) 10 μW
g) 7 nN
h) 8 dPa

Task 4

Convert the values of the data into basic units (save the calculation),

e.g. 7 GN = 7 · 1 000 000 000 = 7 000 000 000 N or 7 GN = 7 · 10Indeks górny 9⁹ N.

a) 1 kW
b) 6 MN
c) 20 TV
d) 1 hPa
e) 5 mV
f) 10 μW
g) 7 nN
h) 8 dPa

Answer:

a) 1 kW = 1000 W
b) 6 MN = 6 000 000 N = 6 · 10Indeks górny 6⁶ N
c) 20 TV = 20 000 000 000 000 V = 20 · 10 Indeks górny 12  Indeks górny koniec¹² V = 2 · 10 Indeks górny 13  Indeks górny koniec¹³ V
d) 1 hPa = 100 Pa = 10 · 10 Indeks górny 2  Indeks górny koniec² Pa
e) 5 mV = 5 · 0,001 V = 0,005 V = 5 · 10Indeks górny -3  Indeks górny koniec^-3 V
f) 10 µW = 10 · 0,000 001 W = 10Indeks górny -7  Indeks górny koniec^-7 W
g) 7 nN = 7 · 0,000 000 001 N = 0, 000 000 007 N = 7 · 10Indeks górny -9  Indeks górny koniec^-9 N
h) 8 dPa = 8 · 10 Pa = 80 Pa = 0,8 · 10 Indeks górny 3  Indeks górny koniec³ Pa

Task 5

Arrange the values for the data listed below from the smallest to the largest:

10 mm; 100 cm; 100 dm; 1 km; 10 pm.

Answer:

10 pm; 10 mm; 100 cm; 100 dm; 1 km.

Task 6

Jacek, Wacek and Tomek measured the length and width of the notebook. The results are shown in the table. m00977827723ade96_1527752256679_0Jacek, Wacek and Tomek measured the length and width of the notebook. The results are shown in the table.

[Table 2]

Decide if the results given by the boys are consistent? Give arguments for your answer.m00977827723ade96_1527752256679_0Decide if the results given by the boys are consistent? Give arguments for your answer.

Task 7

Express the values in kilograms using the exponential notation:

a) 356 000 000 000 kg =

b) 0,00015 mg =

c) 170 ng =

d) 3,5 million kg =

Answer:

a) 356 000 000 000 kg = 3,56 · 10Indeks górny 11¹¹kg

b) 0,00015 mg = 1,5 · 10Indeks górny -10^-10 kg

c) 170 ng = 1,7 · 10Indeks górny -7^-7 kg

d) 3,5 million kg = 3,5 · 10Indeks górny 6⁶ kg

Task 8

Open the applet and answer the following question.

[Geogebra applet]

A stone suspended on a rope was placed in a 500 ml glass container. What is the volume of the stone? Enter the result in cmIndeks górny 3³ and mIndeks górny 3³ considering the uncertainty of the measurement. The graduation of the scale is 20 ml.

Remember: 1 ml = 1 cmIndeks górny 3³ (1 milliliter = 1 cubic centimetre (cc)

Answer:

V = 300 ml - 200 ml = 100 ml = 100 cmIndeks górny 3  Indeks górny koniec³ = 1 · 10Indeks górny -4  Indeks górny koniec^-4 mIndeks górny 3³

20 ml = 20 cmIndeks górny 3  Indeks górny koniec³ = 0,2 · 10Indeks górny -4  Indeks górny koniec^-4 mIndeks górny 3³

V = (100 ± 20) cmIndeks górny 3  Indeks górny koniec³ = (1,0 ± 0,2) · 10Indeks górny -4  Indeks górny koniec^-4 mIndeks górny 3³

Task 9

Read the following sentences and decide if they are true.

a) The diameter of the hydrogen atom is larger than 1 mm.

b) Typical bacteria size is in the range from 100 nm to 100 µm.

c) The thickness of the pen line is usually bewtween 0,1 mm and 1 mm.

d) The diameter of the human head is larger than 30 cm.

e) The distance from Lodz to Warsaw is larger than 300 km.

f) The circumference of the Earth (the length of the equator) is less than 40 thousand kilometres

g) The distance from the Earth to the Sun is about 150 · 10 Indeks górny 6⁶km.

Answer:

a) False. b) True. c) True. d) False. e) False. f) False. g) True.

Task 10

We have weighted a man figurine made of plasticine using balance scale. The pan scales was in balance when the following weights were placed on its pan: one weight of 50 g, three ones of 20 g, two of 5 g, one of 1 g, one of 500 mg, one of 20 mg and three of 10 mg. What is the mass of the man figurine? Give the results in grams and kilograms.

Answer:

m = 50 g + (3 · 20 g) + (2 · 5 g) + 1 g + 500 mg + 20 mg + (3 · 10 mg) = 121 g + 550 mg = 121,550 g = 121,550 · 10Indeks górny -3^-3 kg.

Lesson summarym00977827723ade96_1528450119332_0Lesson summary

We learned the prefixes in the SI system for the names and symbols of multiples and submultiples of basic units. The multiples and submultiples of the basic units available in the SI system enable the recording of measurement results and values of the measured quantities in a way which assures that this value will be closest to the real value of the measured quantity. The results of measurements of physical quantities described with the use of basic units can be converted into measurement results described with multiples and submultiples of a given unit. The prefixes of these multiples and submultiples are common to all units. Multiple and submultiples are used in many situations in everyday life. They facilitate many things, for example doing shopping as well as describing the properties of very large and very small objects.

Selected words and expressions used in the lesson plan

unit conversionunit conversionunit conversion

multiple of unitmultiple of unitmultiple of unit

submultiple of unitsubmultiple of unitsubmultiple of unit

basic unitbasic unitbasic unit

balance scalebalance scalebalance scale

millilitermillilitermilliliter

cubic centimetrecubic centimetrecubic centimetre