Understanding Decimals and Fractional Relationships
Explore the fascinating connection between decimals and fractions, including converting decimals to fractions, the significance of denominators as powers of ten, and the correlation between place value, fractions, and decimals. Learn how to read decimals aloud effectively and understand the relationship between different numerical representations.
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Presentation Transcript
Decimals: Fractionally more interesting.
A fraction where the denominator (the bottom number) is a power of ten (such as 10, 100, 1000, etc). or more or more correctly correctly Decimal Decimal Fractions Fractions https://www.mathsisfun.com/definitions/decimal-fraction.html
5 ... NUMERATOR VINCULUM 10 10 DENOMINATOR
5 10= 5 10 = 0.5 3 10= 3 10 = 0.3
Does the pattern work for all tenths? 7 10 4 10 8 10 6 10 1 10
What happens when we divide other numerators by their denominator? 1 2 2 5 8 20 6 12 5 10 Which fractions make the same decimals? Why do you think that happens? Can you find other fractions that are the same?
What happens when we divide other numerators by their denominator? 1 4 3 4 12 16 6 24 6 8 These fractions are converted into hundredths.
We can convert decimals back into fractions by remembering that decimals are actually decimal fractions and the denominator is also a multiple of 10. If there is only one digit after the decimal point, we read it as a tenth: 0.3 is the same as ? ?? (three tenths)
0.75 is the same as ?? ??? (seventy-five hundredths)
Reading Decimals 10 Be sure to read decimals aloud in a way that emphasises the tie between decimals and fractions. For example, read 24.09 as 9 24.09 twenty-four and nine hundredths , not as ... twenty-four point oh nine 24 100 Reys, Lindquist, Lambdin & Smith, 2009
11 Appropriate language can reinforce the relationships between place value, common fractions and decimals Tracy, 2012
Decimal Comparison Tests 12 This is an printable test made available through the University of Melbourne Includes instructions on how to use, mark and analyse the test Search Decimal Comparison Test in Google Source: Steinle, V., Stacey, K. & Chambers, D. (1999). Using Decimal Comparison Tests. Retrieved from https://extranet.education.unimelb.edu.au/SME/TNMY/Decimals/Decimals/tests/comptest.htm
Activity Sticky Decimal Numbers 13 Decimal numbers are recorded on sticky labels Labels are placed on student s back without them seeing their number Students go around the class and must ask clues to guess their number Students may only ask each person one question Each question can only be answered with a yes or no 0.342 Taken from Department of Education Victoria Fractions and Decimals On-line interview Classroom Activities https://www.education.vic.gov.au maths continuum fracdecactivities.pdf pg 24/25
