ED2652 Lecture Notes - Lecture 2: Decimal Mark
Mathematics 2: Number and Algebra (ED2652)
Lecture Two – Week Two
Decimal Fractions
• What is a Decimal Fraction?
o A fraction where the denominator (the bottom number) is a power of ten (such as 10, 100, 1000, etc)
o You can write decimal fractions with a decimal point (and no denominator), which make it easier to do
calculations like addition and multiplication on fractions
o Examples:
▪ 7/10 is a decimal fraction and it can be shown as 0.7
▪ 43/100 is a decimal fraction and it can be shown as 0.43
▪ 51/1000 is a decimal fraction and it can be shown as 0.051
•
• Decimal Fractions
o A connected understanding of decimals while always a key component of the school mathematics
curriculum, has increased the importance since the introduction of the metric system of measurement and the
wider use of calculators and computers
o Despite the face that common fractions are generally taught before decimal fractions, children’s estimates
were more accurate for decimal fractions than for common fractions
o One plausible explanation is that decimal fractions are more similar to while numbers in symbolic notation
• First Steps in Mathematics
o Number Key Understanding 7
▪ We can extend the patterns in the way we write whole numbers to the way we write decimals
• There are numbers between consecutive whole numbers.
• The place value system can be extended to the right of the ones place to show numbers
between two whole numbers.
• To represent a number between two consecutive whole numbers, record the smaller whole
followed by the part, separated by a decimal point (e.g. a number between 14 and 15 is
14.64)
• The digits to the right of the unit have decreasing values in powers of ten...and can
represent infinitely small numbers.
• Decimal fractions can be partitioned just as whole numbers can.
• In a number written as a whole number and a decimal fraction
o Everything to the left-hand side of the decimal point is a whole number.
o Everything to the right-hand side of the decimal point refers to parts of a whole, a fraction.
o So when we write 14.647, 14 is a whole number and .647 is a fraction of one. (it’s 647, 1000ths or 647
of 1).
• Decimal fractions can be partitioned just as whole numbers can
• Progress of Decimal Understanding – FsiM
o A decimal point is like punctuation or a decoration.
o A decimal point separates two whole numbers.
▪ (using money or measurement as a context can promote this!
o In decimals numbers on the right are different in some way.
▪ Some misconceptions which may arise before understanding develops
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
First steps in mathematics: number key understanding 7, we can extend the patterns in the way we write whole numbers to the way we write decimals. The place value system can be extended to the right of the ones place to show numbers between two whole numbers. To represent a number between two consecutive whole numbers, record the smaller whole followed by the part, separated by a decimal point (e. g. a number between 14 and 15 is. The digits to the right of the unit have decreasing values in powers of tenand can represent infinitely small numbers: decimal fractions can be partitioned just as whole numbers can. In decimals numbers on the right are different in some way: some misconceptions which may arise before understanding develops. Longer is larger: 0. 217 > 0. 37 because two hundred and seventeen is greater than thirty-seven: shorter is larger: 0. 3 is larger than 0. 567 because tenths are larger than thousandths.
