Decimals to Fractions - Lesson Plans

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					Calculating in Construction - Decimals to Fractions




                             Decimals to Fractions
Lesson Focus
This lesson is to help learners understand the relationship between decimals and
fractions and to be able to convert a decimal into a fraction.

Lesson Plan includes:
       Lesson instruction for trainers
       Worksheet and answers

Knowledge of the following numeracy skills:
       Ability to use a calculator for basic operations
       Ability to read decimals and understand the place value of the digits

How this calculating skill can be reinforced on the job:
An understanding of the basic number concepts of fractions and decimals is
beneficial across General Construction, Plumbing, Civil Construction and Furnishing,
such as when converting metric measurements, when reading plans, when
calculating and estimating quantities, when using formulae and when working with
customer invoices.

Lesson time:
       Approximately 30 minutes

Materials needed for this lesson:
       Worksheets 1 and 2 for each learner
       Calculator for each learner
       Whiteboard

Lesson breakdown:
Suggested delivery strategy:


Step                       Trainer / Learner Activity


           1               Introduction or explanation of the term “decimal”


           2               Changing one decimal place to a fraction


           3               Changing a number with two decimal places to a fraction.


           4               Changing a number with three decimal places to a fraction.


           5               Learners complete worksheets 1 and 2 with trainer support
                           and answers available.


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Calculating in Construction - Decimals to Fractions




1.          Introduction or explanation of the term “decimal”


Most learners will understand what a decimal is and how it is written, but as an
introduction to this lesson it would be beneficial to have a brief discussion of what
decimals are.

          Our number system is based on 10. So in any number the individual digits take
           on different values depending on the location as shown below –



                    Hundreds         Tens      Units    .   Tenths       Hundredths   Thousandths


    13.6
    1 ten
            means
                                        1         3     .       6
    3 units
    and
    6 tenths


    8.24 means
    8 units and
                                                  8     .       2               4
    2 tenths
    and 4
    hundredths


    947.065
    means
    9 hundreds
    4 tens
    7 units               9             4         7     .       0               6          5
    and 6
    hundredths
    and 5
    thousandths


          Point out to learners how the decimal point separates the whole numbers from
           the parts of whole numbers.

          A copy of this reference page is attached at the end of the lesson plan if
           trainers wish to distribute to learners.




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Calculating in Construction - Decimals to Fractions




2.      Changing one decimal place to a fraction


       Discuss the following case on the whiteboard with the learners.

Case1 – one decimal place

       Explain that in a decimal number, the first decimal place represents tenths. So
        if a decimal number has only one decimal place, it is written as a fraction with a
        denominator of 10. Then you simplify the fraction if possible.

                                                       3
Example 1                     0.3 is written as              This fraction cannot be simplified.
                                                      10



                                                       6
Example 2                     0.6 is written as              This can be simplified by dividing by 2.
                                                      10

                                                       6 3
                                                        
                                                      10 5



3.      Changing a number with two decimal places to a fraction.


       Discuss the following with learners.

Case 2 – two decimal places

       Explain that the first decimal place represents tenths and the second decimal
        place is for hundredths. So any decimal number with two decimal places is
        written as a fraction with a denominator of 100. The fraction is then simplified if
        possible.

                                                        73
Example 1                     0.73 is written as
                                                       100

               This fraction cannot be simplified as there is no number that divides into
                73 and 100 evenly.


                                                        45
Example 2                     0.45 is written as
                                                       100


               This can be simplified by dividing top and bottom by 5.

                                                       45   9
                                                          
                                                      100 20



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Calculating in Construction - Decimals to Fractions




4.      Changing a number with three decimal places to a fraction.


       Discuss the following with learners

Case 3 – three decimal places

       Explain that the third decimal place is for thousandths. Any decimal number
        with three decimal places can be written as a fraction with a denominator of
        1000, and simplified if possible.

                                                         359
Example 1                     0.359 is written as                 This fraction cannot be simplified.
                                                        1000


                                                         462
Example 2                     0.462 is written as
                                                        1000


               This can be simplified by dividing top and bottom by 2.

                                                       462 231
                                                          
                                                      1000 500


       Point out to learners that if a decimal number has more than 3 decimal places,
        then the number of places determines the number of zeros in the denominator
        of the fraction. For example, 5 decimal places would have a fraction with
        denominator of 100000.




5.      Learners complete worksheets 1 and 2 with trainer support and
        answers available.




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Calculating in Construction - Decimals to Fractions




           Decimals to Fractions Worksheet 1
Express these decimals as fractions. Simplify where possible.



                                                      Fraction          Simplified


1.                       0.2


2.                       0.3


3.                       0.8


4.                      0.16


5.                      0.71


6.                      0.28


7.                      0.74


8.                     0.607


9.                     0.688


10.                    0.246




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Calculating in Construction - Decimals to Fractions




           Decimals to Fractions Worksheet 1
                        Answers
Express these decimals as fractions. Simplify where possible.



                                                      Fraction          Simplified

                                                         2                       1
1.                       0.2                            10                       5

                                                         3
2.                       0.3                            10                       -

                                                         8                       4
3.                       0.8                            10                       5

                                                        16                      4
4.                      0.16                            100                     25

                                                         71
5.                      0.71                            100                      -

                                                         28                     7
6.                      0.28                            100                     25

                                                         74                     37
7.                      0.74                            100                     50

                                                        607
8.                     0.607                           1000                      -

                                                        688                      86
9.                     0.688                           1000                     125

                                                        246                     123
10.                    0.246                           1000                     500




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Calculating in Construction - Decimals to Fractions




           Decimals to Fractions Worksheet 2
1. A job requires 0.32kg of sand. Express this amount as a simplified fraction




                                                                      3
2. Drill bits can come in imperial sizes, for example                   of an inch. Change the
                                                                     16
      following sizes into fractions of an inch

(a)     0.25 of an inch =



                                                                                         inches

(b)     0.375 of an inch =



                                                                                         inches

(c)     0.875 of an inch =



                                                                                         inches

(d)     0.0625 of an inch =




                                                                                         inches


3. A section of road which is 0.48 km long needs repairing. What is this as a fraction
   of a kilometre?




                                                                                         of a km

4. At a particular work site, there are three types of employees, 0.4 are permanent,
   0.45 are casual and 0.15 are contractors.
   Express these as fractions of the total workers




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Calculating in Construction - Decimals to Fractions




Decimals to Fractions Worksheet 2 Answers




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 Calculating in Construction - Decimals to Fractions




                                                 Reference
Our number system is based on 10. So in any number the individual digits take
on different values depending on the location as shown below.



                   Hundreds          Tens      Units       Tenths      Hundredths   Thousandths


 13.6    means                                         
                                       1          3             6
 1 ten
 3 units
 and
 6 tenths


 8.24 means                                            
                                                  8             2                4
 8 units and
 2 tenths
 and 4
 hundredths


 947.065
 means
 9 hundreds
 4 tens
 7 units                 9             4          7            0                6        5
 and 6
 hundredths
 and 5
 thousandths




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