Topicm3534050d605873fa_1528449000663_0Topic

Decimal expansion of a common fraction - exercises

Levelm3534050d605873fa_1528449084556_0Level

Second

Core curriculumm3534050d605873fa_1528449076687_0Core curriculum

IV. Common and decimal fractions. The student:

9) converts common fractions whose denominators are divisors of numbers 10, 100, 1000 etc into finite decimals using any method (extension or simplification of decimal fractions, dividing the numerator by the denominatordenominatordenominator mentally, using the long method or using the calculator);

10) writes common fractions of denominators different than those listed in point 9 in the form of infinite decimals (using the ellipsis after the last digit), obtained as a result of dividing the numerator by the denominator mentally, using the long method or using the calculator.

Timingm3534050d605873fa_1528449068082_0Timing

45 minutes

General objectivem3534050d605873fa_1528449523725_0General objective

Doing simple calculations mentally or using the long method in more difficult examples, using these abilities in practical situations.

Specific objectivesm3534050d605873fa_1528449552113_0Specific objectives

1. Developing skills of converting common fractionswhose denominators are divisors of numbers 10, 100, 1000 etc into finite decimals by extension or simplification.

2. Developing skills of converting common fractions into decimals by division of the numerator by the denominator.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesm3534050d605873fa_1528450430307_0Learning outcomes

The student:

- develops skills of converting common fractions whose denominators are divisors of numbers 10, 100, 1000 etc into finite decimals by extension or simplification,

- develops skills of converting common fractions into decimals by division of the numerator by the denominatordenominatordenominator.

Methodsm3534050d605873fa_1528449534267_0Methods

1. Situational analysis.

2. Task tables.

Forms of workm3534050d605873fa_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm3534050d605873fa_1528450127855_0Introduction

Students revise information about decimal expansion of common fractions.

Procedurem3534050d605873fa_1528446435040_0Procedure

Students work individually using computers. Their task is to get to know the interactive illustration memorise information about decimal expansions of common fractions.

[Interactive illustration]

Students work using the task tables method. In groups they do exercises prepared by the teacher. Each group gets point for correct solutions and for the time of solving the exercise. The group that collects the most points gets grades from class activity.

Task 1

Fill in the table according to examples.

[Table 1]

Task 2

Using the calculator, find decimal expansion of fractions. Write the period of the fraction in parentheses.m3534050d605873fa_1527752263647_0Using the calculator, find decimal expansion of fractions. Write the period of the fraction in parentheses.

a) $\frac{15}{35}$

b) $\frac{7}{102}$

c) $1\frac{5}{17}$

d) $3\frac{7}{33}$

Task 3

Fill in the sentences.
a) Fifth digit after the coma in the number 0,(24), is ……………
b) Seventh digit after the coma in the number2,(125), is ……………
c) Fourteenth digit after the coma in the number12,(7896), is ……………
d) Tenth digit after the coma in the number5,(852), is ……………m3534050d605873fa_1527752256679_0Fill in the sentences.
a) Fifth digit after the coma in the number 0,(24), is ……………
b) Seventh digit after the coma in the number2,(125), is ……………
c) Fourteenth digit after the coma in the number12,(7896), is ……………
d) Tenth digit after the coma in the number5,(852), is ……………

Task 4

Arrange numbers on cards in non‑decreasing order.

[Table 2]

The teacher sums up and evaluates students’ work and clarifies doubts.

An extra task:

Give an example of number a that satisfies the condition: 0,(4) < a < 0,(5).

Lesson summarym3534050d605873fa_1528450119332_0Lesson summary

Students do the revision exercises. Then together they sum‑up the classes, by formulating the conclusions to memorise.

Common, simplified fraction has decimal expansion:

- finite, if the only divisors of its denominatordenominatordenominator are numbers 2 or 5,
- infinite if the denominator can be divided by a prime number different than 2 or 5.

A recurring set of digits in the infinite decimal expansioninfinite decimal expansioninfinite decimal expansion is called its period. To simplify such expansion, we write it in parentheses.

Selected words and expressions used in the lesson plan

common simplified fractioncommon simplified fractioncommon simplified fraction

decimal fractiondecimal fractiondecimal fraction

denominatordenominatordenominator

finite decimal expansionfinite decimal expansionfinite decimal expansion

infinite decimal expansioninfinite decimal expansioninfinite decimal expansion

period of an infinite decimalperiod of an infinite decimalperiod of an infinite decimal