1 Decimal Place Value
1 Place Value in Three Digit Whole Numbers
2 Groups of Three Place Value for Multidigit Decimals
3 More on Groups of 3 Multi-Digit Place Value
4 Groups of 3 Place Value in Decimal Fractions
5 More on Groups of 3 Place Value in Decimal Fractions
6 Groups of 3 Place Value in Mixed Decimal Fractions
7 More on Groups of 3 Place Value in Mixed Decimal Fractions
8 Review Lesson 1 2 4 and 6 - All in One
9 Place Value Review - Decimal form of Avogrados number included
10 Names for Big Numbers and Powers of Ten Expansion
11 Place Value SI Standard International way
Notes
Food for thought. The SI lesson below would be
sufficient for upper secondary schools in many countries , and
independent of the use of local naming systems for big and small
numbers and measures.
The exercise of reading decimal aloud with several places before and
after the decimal point is not a practical skill. It is a skill which can
provide comic relief in a mathematics class while developing and
reinforcing place value comprehension. A possible modification of the
following lessons to favour UK-terms meaning of billions and trillions is
indicated below.
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Place Value in Three Digit Whole Numbers describes the ones,
tens and hundreds place value of the digits and, more importantly,
says how 3 digit number aloud, digit by digit.
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Groups of Three Place Value for Multidigit Decimals gives a
single example to introduce or review the ones, thousand,
millions, billions, trillions and quadrillions place value of
groups of three in multidigit decimals. Here place value is
determined by reading a number backwards (from right to left) while
the normal way of reading identifies the groups of three and their
place value from left to right.
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More on Groups of 3 Multi-Digit Place Value gives more
examples to example to introduce or review the ones, thousand,
millions, billions, trillions, quadrillions and quintillions
place value of groups of three in multidigit decimals. Here again
place value is determined by reading a number backwards (from right
to left) while the normal way of reading identifies the groups of
three and their place value from left to right. Recognizing place in
groups of three backwards has to be done before the number is read
aloud.
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Groups of 3 Place Value in Decimal Fractions gives a single
example to introduce or review the thousandths, millionths,
billionths, trillionths and quadrillionthss place value of groups
of three in multidigit decimal fractions. Here place value is
determined by reading a number forwards(from left to right and can be
done while the decimal fraction is read aloud.
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More on Groups of 3 Place Value in Decimal Fractions gives a
more examples to introduce or review the thousandths, millionths,
billionths, trillionths, quadrillionths and quintrilionth place
value of groups of three in multidigit decimal fractions. As just
said, place value is determined by reading a number forwards(from
left to right and can be done while the decimal fraction is read
aloud.
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Groups of 3 Place Value in Mixed Decimal Fractions gives a
single example in which place value of groups of three in a mixed
decimal number or fraction is based on place value of groups of three
determined backwards, that is, contrary to the normal direction of
reading in English from a decimal point while place value of groups
of three after the decimal point is determined in accordance with the
normal reading direction.
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More on Groups of 3 Place Value in Mixed Decimal Fractions
gives more examples of the appearance of place value from
quintillions to quintillionths in a multidigit decimals that included
a decimal point.
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Review Lesson 1 2 4 and 6 - All in One present four examples,
one from each lesson.
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Place Value Review - Decimal form of Avogrados number
included. Students in science courses may appreciate the order of
magnitude of Avogrado's number after this stand-alone extension of
the previous lessons introduces them to 602 septrillions.
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Names for Big Numbers and Powers of 1000 Expansion goes from
the power of ten expansion of multidigt decimals to powers of 1000 =
103 groups of three expansion of multidigit decimals with
digits before and after a decimal point. A reference is given.
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Place Value SI Standard International way. The SI (System
International) systems of units and measures provides "standard
names" for big and small numbers from yota to yocto for powers of
103 and it reciprocal 10-3 that can occur in
discussing group of three place value in multidigit decimals. The
alternative names are given along side dare-we-say common US-style
names for numbers, big and small. A reference is given. for
Modification for UK big and small number naming.
In the UK, a billion is not a thousand million, is it is a million
million. Further, a trillion is not a thousand million, it is a million
billions. That suggests a variation of the foregoing in which multidigit
decimals may be read aloud in full or partial groups of six, where each
group of six consists of two groups of three. Thus
56 789 345 230 456 678 . 560 678 999 12
might be read aloud as
56 thousand and 789 billions
345 thousand and 230 millions
456 thousand and 678 ones or units,
560 thousand and 678 millionths, and
999 thousand and 120 billionths
That being said, some variation of this ideas may work better. Again, the
skill of reading multidigit decimals aloud in groups of three or six is
not a practical. It is a skill aimed at developing and re-enforcing place
value.
Is this better? For reading in full or partial groups of three
digits, UK instructors might emphasize the use of SI terms yota to yocto
for powers of 103 and it reciprocal 10-3 because
groups of three are easier to digest than groups of six, and groups of
three may lead to better comprehension of the SI naming system for large
and small numbers and measure.
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