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20.1
a) 260
b) 2 600
c) 26,7
d) 267
e) 2 670
f) 26,79
g) 267,9
h) 2 679
20.2 x10: Each digit moves 1 place left / comma moves 1 to the right.
x100: Each digit moves 2 places left / comma moves 2 to the right.
x1000: Each digit moves 3 places left / comma moves 3 to the right.
20.4
| a) | 54,8 | 548 | 5480 |
| b) | 3,67 | 36,7 | 367 |
| c) | 8,9 | 89 | 890 |
| d) | 165,38 | 1653,8 | 16 538 |
| e) | 282,51 | 2825,1 | 28 251 |
20.5.1
a) 21,522
b) 46,215
c) 1,4
d) 4,64
e) 12 250
f) 2 370,6
x with number <1
20.8
a) 0,4964
b) 1,3737
c) 0,109
d) 5,53724
e) 38,57997
f) 16,78164
23.1
Each digit moves 1 place right
Each digit moves 2 place right
Each digit moves 3 places right
23.3
| 8,21 | 0,729 | 0,6 | ||||||
| 0,864 | 0,6254 | 0,0392 | 8,791 | 0,035 | 0,08 | |||
| 74,68 |
20. MULTIPLICATION OF DECIMAL FRACTIONS
20.1 Let us revise
Do the following with the help of your calculator:
| SUM | ANSWER | |
| e.g. | 2,6 x 10 | 26 |
| a) | 2,6 x 100 | ......................... |
| b) | 2,6 x 1 000 | ......................... |
| c) | 2,67 x 10 | ......................... |
| d) | 2,67 x 100 | ......................... |
| e) | 2,67 x 1 000 | ......................... |
| f) | 2,679 x 10 | ......................... |
| g) | 2,679 x 100 | ......................... |
| h) | 2,679 x 1 000 | ......................... |
20.2 Work in groups of three. Quickly formulate rules for the multiplication of decimal fractions by 10, 100 and 1 000.
20.3 Do you still remember?
10 x 1 = 10 = 101
10 x 10 = 100 = 102
10 x 10 x 10 = 1 000 = 103
10 x 10 x 10 x 10 = 10 000 = 104
10 x 10 x 10 x 10 x 10 = 100 000 = 105
10 x 10 x 10 x 10 x 10 x 10 = 1 000 000 = 106
20.4 Complete the following table:
| × | 101 | 102 | 103 | |
| e.g. | 3,2 | 32 | 320 | 3 200 |
| a) | 5,48 | ..................... | ..................... | ..................... |
| b) | 0,367 | ..................... | ..................... | ..................... |
| c) | 0,89 | ..................... | ..................... | ..................... |
| d) | 16,538 | ..................... | ..................... | ..................... |
| e) | 28,251 | ..................... | ..................... | ..................... |
20.5 More revision
20.5.1 Work with a friend. Calculate the answers without using a calculator:
a) s = 3,587 x 6
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b) f = 9,243 x 5
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c) p = 0,02 x 70
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d) r = 0,058 x 80
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e) t = 24,5 x 500
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f) h = 2,634 x 900
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20.5.2 Check your answers with a calculator.
20.6 MULTIPLYING DECIMAL FRACTIONS WITH DECIMAL FRACTIONS
20.6.1 Read the following problem and work through the different solutions with a friend:
A tortoise walks 0,8 km in 1 hour. How far will he walk in 0,6 of an hour?
a)
I convert the decimal fractions to proper fractions:
Thus he walks 0,48 km.
b) I first work out what 8 × 6 is. The answer is 48. Now I add up the amount of decimal places after each comma. There are 2. Thus, my answer must have 2 digits after the decimal comma.
The answer is thus 0,48.
20.6.2 What do you notice when you compare the answer (product) with the multiplicand?
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Can you explain this?
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20.7 REMEMBER!
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20.8 Calculate the following on your own without a calculator:
a) j = 0,146 x 3,4
b) v = 2,41 x 0,57
c) u = 0,025 x 4,36
d) g = 8,143 x 0,68
e) d = 7,293 x 5,29
f) o = 3,849 x 4,36
21. Time for self-assessment
|
Uncertain | Certain |
| I can add decimal fractions correctly. | ||
| I can subtract decimal fractions correctly from each other. | ||
| I can multiply decimal fractions by 10 correctly. | ||
| I know how to multiply decimal fractions by 100. | ||
| I can calculate the product of decimal fractions and 1 000 correctly. | ||
| I can multiply decimal fractions by whole numbers. | ||
| I can multiply decimal fractions by decimal fractions. |
22. Let us play a game.
You need a friend and a calculator for this game.
Key in any decimal number on your calculator.
Then divide it by 10, 100 or 1 000. Give the calculator to your friend. He/She must get the original number again.
e.g. Player 1 keys in : 43,674.
Player 1 divides 43,674 by 1 000 and gets 0,043674.
Player 2 must get 43,674 on the screen.
Player 2 must thus × by 1 000!
23. DIVISION BY DECIMAL FRACTIONS
Let us first revise.
23.1 Divide into groups of 3. Can you explain to each other what happens when we divide natural and decimal numbers by 10, 100 and 1 000?
…………………………………………………………………………………………..
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23.2 Take turns in saying the answers of the following to each other, out aloud.
a) 6 ÷ 10
b) 0,3 ÷ 10
c) 0,06 ÷ 100
d) 2,9 ÷ 100
e) 4 ÷ 100
f) 15,8 ÷ 100
g) 8 ÷ 1 000
h) 39,2 ÷ 100
i) 34,67 ÷ 1 000
j) 27,458 ÷ 10
23.3 Colour the answers to find the correct “path” to the house!
a) 82,1 ÷ 10
b) 86,4 ÷ 100
c) 746,8 ÷ 10
d) 625,4 ÷ 1 000
e) 39,2 ÷ 1 000
f) 72,9 ÷ 100
g) 879,1 ÷ 100
h) 6 ÷ 10
i) 35 ÷ 1 000
j) 8 ÷ 100
| BEGIN | ||||||||
| 8,21 | 0,821 | 6,254 | 39,2 | 0,729 | 879,1 | 0,6 | 35 | 0,8 |
| 0,864 | 7,468 | 0,6254 | 0,0392 | 7,29 | 8,791 | 6 | 0,035 | 0,08 |
| 8,64 | 74,68 | 62,54 | 3,92 | 729 | 87,9 | 60 | 3,5 | 80 |
Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.
Assessment Standard 1.3: We know this when the learner recognises, classifies and presents the following numbers in order to describe and compare them:
1.3.4 numbers in exponential form including squares of natural numbers to at least 122, cubes of natural numbers to at least 53, and their square and cube roots;
Assessment Standard 1.7: We know this when the learner estimates and calculates by selecting and using operations appropriate to solving problems that involve:
1.7.7 rounding off numbers to at least one decimal place;
Assessment Standard 1.9: We know this when the learner uses a range of techniques to perform calculations including:
1.9.2 using a calculator;
Assessment Standard 1.10: We know this when the learner uses a range of strategies to check solutions and judges the reasonableness of solutions.
Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.
Assessment Standard 2.3: We know this when the learner represents and uses relationships between variables in a variety of ways using:
2.3.3 tables.
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Last edited by Siyavula Uploaders on Aug 12, 2009 7:38 am GMT-5.
