1. Decimal Numbers Geneviève Boulet, Ph.D

2. Overview of Decimals • History • Language • Extending the numeration chart • Real Numbers in Decimal Notation • Fractions to Decimals • Decimals to Fractions

3. History • Decimal notation • La Disme, published in1585 by Simon Stevin • Integration of fractions into the base-ten numeration system

4. Language • 0.5 is “five tenths” and not “zero point 5” • Misadaptation: the case of “and” • Enunciate well: “ths” (“ièmes” in French) • In SI, both the comma and the period are used: 12.345 or 12,345

5. Extendingthe Numeration chart What is 3.725? What is it counting? How many tenths in 3.725? Hundredths? Thousandths? Tens? Hundreds? Thousands?

6. Real numbers in decimal notation

7. Fractions to Decimals • Find and equivalent decimal fraction (a fraction with a denominator that is a power of 10): • If an equivalent decimal fraction cannot be found, use division 3 ÷ 4

8. Decimals to fractions • If the period is 0, express the decimal number as a decimal fraction:

9. decimals as Fractions • If the period is not zero, use the card and registry method. 0.3333... Is what fraction?