3. More on Place Value in Multi-digit Decimals
Single Digit Numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Two Digits Numbers: 10, 11, 12, 13, ..., 20, .. 30, ... 40 ,
50, 60, 70, 80, 90, ... 99. (Count by ones from 10 to
99)
Three Digit Numbers: 100, 101, ... 997, 998, 999
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I assume you know how to count from zero to thousand and how to write the
numbers from zero to are thousand in decimal notation. So you
should be able read aloud numbers like the following
- 13 thirteen
- 24 twenty-four
- 93 ninety-three
- 356 three hundred and fifty six.
- 999 nine hundred and ninety-nine
- 1000 one thousand.
We may read 356 aloud as [A] three five six digit by digit,
or as [B]three hundred and fifty-six. In reading multidigit expressions
backwards and forwards, option [B] is recommeneded.
Decimals notation is based on place value. We are going to learn or
review how to read and interpret multi-digit decimal notation in groups
of three. The exercise is informative, but tongue twisting.
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Read backwards to obtain place
value in groups of three- see down arrow. Next read forward to
read number aloud with highest value digits groups first. See
below.
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The multi-digit decimal notation
24 378 956 789 145
represents a large number. Spaces between groups of three in this
notation is optional - used to make the groups of three or less easier to
identify.
The place value of the first digit 2 and further ones are hard to
identify if we start reading from left to right. But reading backwards
from right to left gives a way to easily identify the place values of all
the digits individually or in groups of three & less.
Reading backwards, we see the multidigit decimal notation
24 378 956 789 145
means or represents
145 ones or units,
789 thousands,
956 millions
378 billions and
24 trillions
Here a billion is thousand million, and a trillion is a thousand billions
(or a million millions).
So we have found the decimal place of all the digits individually or in
groups of three. So the multidigit decimal notation
24 378 956 789 145
means or represents the number
24 trillions,
378 billions,
956 millions,
789 thousands plus
145 ones or units.
We can also write 24 trillions, 378 billions, 956
millions, 789 thousands and 145 ones or units without covering
several lines.
The leading two digits in the notation represents 24 trillion - a large
number and the leading digit 2 is in the 10 trillion decimal
position. So reading backwards from the units, thousands
and millions position for groups of three, and so on is the easiest
way to interpret the place value in a large multidigit decimal
notation for a number.
Read backwards to get place value.
Then forward to read highest
value digit first
Tongue in Cheek: Decimal notation might be best used in written
languages that read from right to left - and what is backward in
reading and writing English becomes forward.
EXERCISE: Read the following decimal representation of numbers backwards
and then forwards.
- 7 123 456 789 123 234 555
- 34 456
- 56 899 201
- 206 205 204 203 202 201
Note the following reading backwards
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Group of 3 digits
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Place Value
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Notes
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last group
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ones or units
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second to last
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thousands
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third to last
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millions
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1000 thousand =
one million
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fourth to last
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billions
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1000 million =
one billion
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fifth to last
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trillions
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1000 billion =
one billion
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sixth to last
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quadrillions
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1000 trillion=
one billion
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seventh to last
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quintillions
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1000 quadrillion=
one billion
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ANSWER to first (backwards only)
- 7 123 456 789 123 234 555 may be read backwards as 555 ones,
234 thousands, 123 millions, 789 billions, 456 trillions, 123
quadrallions and 7 quintillions.
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Teachers & Tutors: Site pages offer better or best practices for providing skills -
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Parent Center: Help your child or teen
learn:
Parent-friendly
Work Booklets for ages 3+ to 13 Use these or others to check
or build skills. Other booklets are available but these booklets
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children. The selection acquired in Canada is published in the
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the choice is theirs. But in retrospect, the selection does not
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Arithmetic
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More
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70
Calculus Starter Lessons
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They cover basic topics in ways likely to complement your
notes, your textbooks and site material. When Goldilocks
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if one or more explanations is not to liking, try another. It may
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Unsolicited Advice
Learning to do and high marks if it comes to easy is often
deceptive - light rather than deep. For that reason, students
with learning difficulties determined not to let it get in their
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if the come easy, may be deceptive - provide a too light and not
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calculus and more generally in the first year of college. Bon
Appetite.
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