Decimal fractions

Mathematics

Decimal fractions

Educator section

Memorandum

2.

Temperature Swimmers

Volume Athletes

Measurement Odometer

Distance Scientists

Scales Engineers

Money

3.1 a) $\frac{6}{\text{100}}$

b) $\frac{2}{\text{1000}}$

c) 200

d) $\frac{2}{\text{10}}$

e) 80

f) $\frac{9}{\text{1000}}$

g) 2 000

h) $\frac{8}{\text{100}}$

i) $\frac{5}{\text{10}}$

j) $\frac{8}{\text{1000}}$

• a) $\frac{9}{\text{10}}$

b) $\frac{3}{\text{10}}$ $\frac{8}{\text{100}}$

c) $\frac{8}{\text{10}}$ $\frac{2}{\text{100}}$ $\frac{4}{\text{1000}}$

d) $\frac{3}{\text{10}}$ $\frac{8}{\text{1000}}$

5. a) 0,12; 0,18; 0,24; 0,3; 0,36;

0,42; 0,48; 0,54; 0,6; 0,66

b) 0,018; 0,027; 0,036; 0,045;

0,054; 0,063; 0,072; 0,081; 0,09

c) 7,4; 11,1; 14,8; 18,5;

22,2; 25,9; 29,6; 33,3; 37

6. a) 0,8; 1,0; 1,2; 1,4

b) 5,5; 5; 4,5; 4

c) 0,989; 0,986; 0,983;

0,98; 0,977

d) 0,016; 0,02; 0,024;

0,028; 0,032

7. +20 +100 +0,003

+0,3

+0,07 +0,13 +0,05

+0,3

+0,007 +0,12 +0,009

8. a) 1,0

b) 3,2

c) 0,75

d) 4,2

e) 1,4

f) 2,9

g) 3,15

h) 3,42

i) 0,05

j) 4,5

k) 3,98

l) 1,02

m) 2,5

n) 15,6

o) 11,4

Leaner Section

Content

Activity: decimal fractions [lo 1.1.1, lo 1.3.2, lo 1.7.4, lo 1.10]

1. Did you know?

The decimal system was developed about 500 AD by the Hindu’s in India. Johannes Kepler, a mathematician in The Netherlands, used the decimal comma for the first time in the early 1600’s. Prior to this, mathematicians used circles or bars to show the decimal comma. John Napier, a Scot, was the first to use the decimal point in 1617. Today England and the USA still use a decimal point instead of a comma.

2. Do you still remember?

Divide into groups of four. Make a list of where we use decimal fractions in our everyday lives.

3. Let us revise

1 438,576 = 1 000 + 400 + 30 + 8 + $\frac{5}{\text{10}}$ + $\frac{7}{\text{100}}$ + $\frac{6}{1\text{000}}$

3.1 Write down the value of the underlined digit in each number below:

a) 532,1 6 8 ..................................................

b) 326,43 2 ..................................................

c) 2 91,567 ..................................................

d) 460, 2 31 ..................................................

e) 8 8 6,434 ..................................................

f) 1 467,23 9 ..................................................

g) 2 321,456 ..................................................

h) 3 641,9 8 5 ..................................................

i) 2 634, 5 27 ..................................................

j) 8 139,43 8 ..................................................

3.2 Complete the following:

e.g.. 5,3 = 5 + $\frac{3}{\text{10}}$

a) 6,9 = 6 + ....................

b) 26,38 = 26 + .................... + ....................

c) 9,824 = 9 + .................... + .................... + ....................

d) 16,308 = 16 + .................... + ....................

4. Work together with a friend. Take turns to count aloud:

a) 3,8 ; 3,9 ; 4 ; 4,1 ; . . . to 8

b) 14 ; 13,5 ; 13 ; 12,5 ; . . . to 6

c) 2,4 ; 2,6 ; 2,8 ; . . . to 7

d) 18,8 ; 18,6 ; 18,4 ; to 10

5. Can you still remember?

If we want to add the same number continuously, e.g. 0,01 (one hundredth), we programme the calculator in this way : 0,01 + + = = =

a) Programme your calculator to add on 0,06 each time and complete:

0,06 ; ................. ; ................. ; ................. ; ................. ; ................. ;

................. ; ................. ; ................. ; ................. ; .................

b) Add on 0,009 each time (programme your calculator)

0,009 ; ................. ; ................. ; ................. ; ................. ;

................. ; ................. ; ................. ; ................. ; .................

c) Add on 3,7 each time with the help of you calculator:

3,7 ; ................. ; ................. ; ................. ; ................. ;

................. ; ................. ; ................. ; ................. ; .................

6. Complete the following WITHOUT a calculator:

a) 0,2 ; 0,4 ; 0,6 ; ................. ; ................. ; ................. ; .................

b) 7 ; 6,5 ; 6 ; ................. ; ................. ; ................. ; .................

c) 0,998 ; 0,995 ; 0,992 ; ............. ; ............. ; ............ ;........... ; ...........

d) 0,004 ; 0,008 ; 0,012 ; ............. ; ............. ; ............ ;........... ; ...........

7. BRAIN-TEASER!

Complete the following flow diagram. (You may use your calculator).

8. Let us see how well you do in the first mental test. Write down only the answers:

a) 0,7 + 0,3 = .................

b) 2,4 + 0,8 = .................

c) 0,35 + 0,4 = .................

d) 5 – 0,8 = .................

e) 0,8 + 0,6 = .................

f) 3,4 – 0,5 = .................

g) 3,45 – 0,3 = .................

h) 3,45 – 0,03 = .................

i) 2,45 – 2,4 = .................

j) 2,45 + 2,05 = .................

k) 4 – 0,02 = .................

l) 0,38 + 0,64 = .................

m) 1,25 + 1,25 = .................

n) 6,9 + 8,7 = .................

o) 15 – 3,6 = .................

(15)

9. Time for self-assessment

Assessment

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 1.1 We know this when the learner counts forwards and backwards in the following ways:

1.1.1 in decimal intervals;

Assessment Standard 1.3 We know this when the learner recognises, classifies and presents the following numbers in order to describe and compare them:

1.3.2 decimal (to at least three decimal places), fractions and percentages;

Assessment Standard 1.7: We know this when the learner estimates and calculates by selecting and using operations appropriate to solving problems that involve:

1.7.4 addition, subtraction and multiplication of positive decimals to at least 2 decimal places;

Assessment Standard 1.10: We know this when the learner uses a range of strategies to check solutions and judges the reasonableness of solutions.