B1.6 Describe relationships and show equivalences among fractions and decimal numbers up to thousandths, using appropriate tools and drawings, in various contexts.
Skill: Describing Relationships and Representing Equivalences Among Fractions, Decimal Numbers to Thousandths, and Percents, Using Appropriate Tools and Diagrams, in a Variety of Contexts
Students should understand that since decimal notation is just another way of representing a decimal fraction, then it is possible to establish an equality relationship between the two notations (for example,
Example

Students who do not understand this association are sometimes inclined to represent a fraction such as
Conceptual Understanding of Numbers
Number: 0.3
Observable behaviours:
- The student reads it as three tenths.
- The student can write the number in fractional notation as
. - The student can represent the number using concrete materials or visuals.
Example

Number:
Observable behaviours:
- The student reads it as sixteen hundredths.
- The student can write the number in decimal notation as 0.16.
- The student can represent the number using concrete materials or visuals.
Example

Number:
Observable behaviours:
- The student reads it as two sevenths.
- The student knows that the fraction
is not represented by 0.2 since they know that 0.2 = .
To establish the equality relationship between a fraction whose denominator is not a power of ten (for example,

They then partition the tenths into ten equal parts, thus creating one hundred equal parts, or hundredths of the whole, and recognize that

Since
Fraction | Equivalent Decimal Fraction | Decimal Number |
---|---|---|
0.5 | ||
0.75 | ||
0.4 | ||
0.35 |
Note: Some fractions (for example,
Source: translated from Guide d’enseignement efficace des mathématiques de la 4e à la 6e année, Numération et sens du nombre, Fascicule 3, Nombres décimaux et pourcentages, p 46-48.