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PLACE VALUE
What do we mean by place value?
Key words – units digits tenths hundredths
tens hundreds thousands thousandths decimal
fractions biggest smallest.
Place value
Place Value
The value of where digits is in the number, such as units, tens
hundreds, etc.
Example: in 352, the place value of the 5 is tens.
Example: in 17.591, the place of 9 is hundredths.
327
In the number 327:
the "7" is in the Units position,
meaning just 7 (or 7 "1"s),
the "2" is in the Tens position
meaning 2 tens (or twenty),
and the "3" is in the Hundreds
position, meaning 3 hundreds.... and ...
As we move left, each position is 10
times bigger! Example: hundreds are 10
times bigger than tens.
……and…..
As we move right, each position is 10
times smaller - from hundreds tens
and units.
But what if we continue past Units?
What is 10 times smaller than Units?
1/
10 ths (Tenths) are!
Decimal point
we must first write a decimal point,
so we know exactly where the Units
position is:
Three hundred twenty seven and four tenths – and that is
a Decimal Number! - But we usually say three hundred
twenty seven point four.
Decimal point
We can continue with smaller and smaller values, from tenths, to
hundredths, and so on, like in this example:
Large and small
Large and Small
So, our Decimal System lets us write
numbers as large or as small as we want,
using the decimal point. Digits can be
placed to the left or right of a decimal
point, to indicate values greater than one
or less than one.
The decimal point is the most important
part of a Decimal Number. Without it,
we would be lost ... and not know what
each position meant.
17.591
On the left of the decimal point is a
whole number (17 for example) .
As we move further left,
every place gets 10 times bigger.
The first digit on the right means
tenths (1/10).
As we move further right,
every place gets 10 times smaller
(one tenth as big).
See decimals on a number line
Ways to think about decimals
Ways to think about Decimal
Numbers ...
... as a Whole Number Plus
Tenths, Hundredths, etc
You could think of a decimal
number as a whole number plus
tenths, hundredths, etc:
Example 1: What is 2.3 ?
On the left side is "2",
that is the whole number
part.
The 3 is in the "tenths"
position, meaning "3
tenths", or 3/10
So, 2.3 is "2 and 3 tenths
Example 2: What is 13.76 ?
On the left side is "13", that
is the whole number part.
There are two digits on the
right side, the 7 is in the
"tenths" position, and the 6 is
the "hundredths" position
So, 13.76 is "13 and 7 tenths
and 6 hundredths"
... as a Decimal Fraction
Or, you could think of a
decimal number as a Decimal
Fraction.
A Decimal Fraction is a
fraction where the
denominator (the bottom
number) is a number such as
10, 100, 1000, etc. (in other
words a power of ten.
Decimal as a fractions
So 2.3 would look like this
23
10
And 13.76 would look like this
1376
100
... as a Whole Number and Decimal
Fraction
Or, you could think of a decimal number as a Whole
Number plus a Decimal Fraction.
So 2.3 would look like
2 and 3
10
And 13.76
13 and 76
100
Numbers
Key words- counting zero
negative positive integer
natural numbers
……………..so what are numbers?
Whole Numbers are simply the
numbers 0, 1, 2, 3, 4, 5, ...
(and so on)
No Fractions!
Counting numbers
Counting Numbers are Whole
Numbers, but without the
zero.
So they are 1, 2, 3, 4, 5, ... (and so on).
Natural numbers
"Natural Numbers" can mean
either "Counting Numbers" {1,
2, 3, ...}, or "Whole Numbers"
{0, 1, 2, 3, ...}, depending on
the subject.
allowed!
Integers
Integers
Integers are like whole
numbers, but they also include
negative numbers ... but still
no fractions allowed!
allowed!
So, integers can be negative {-1, -2,-3, -4, -5, ... },
positive {1, 2, 3, 4, 5, ... }, or zero {0}
We can put that all together like this:
Integers = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }
(But numbers like ½, 1.1 and 3.5 are not
integers)
Recap on numbers….
Name
Numbers
Examples
Whole Numbers
{ 0, 1, 2, 3, 4, 5, ... }
0, 27, 398, 2345
Counting Numbers
{ 1, 2, 3, 4, 5, ... }
1, 18, 27, 2061
Integers
{ ... -5, -4, -3, -2, -1, 0, 1,
2, 3, 4, 5, ... }
-15, 0, 27, 1102
Ordering numbers
What do we mean by ordering numbers?
List words that order numbers
Ascending – climb a mountain
Ascending descending highest lowest biggest smallest
From lowest to the highest
To put numbers in order, place
them from lowest (first) to
highest (last). This is called
"Ascending Order" (think of
ascending a mountain
Descending – go down the mountain
From highest to the lowest
Sometimes you want the
numbers to go the other way,
from highest down to lowest,
this is called "Descending
Order" (think of a "steep
descent")
Descending order
Place 3, 18, 35, 9, 81, 33, 14, 77, 89, 36 in
descending order.
Ascending order
Place 12, 1, 11, 19, 6, 7, 14, 8 and 2 in
ascending order.
Ordering decimals
Ordering decimals can be tricky.
Because often we look at 0.42 and 0.402
and say that 0.402 must be bigger
because there are more digits. But no!
We can use this method to see which
decimals are bigger:
Set up a table with the decimal point in
the same place for each number.
Put in each number.
Fill in the empty squares with zeros.
Compare using the first column on the
left
If the digits are equal move to the next
column to the right until one number
wins.
Have a go at ascending – climbing up
Example: Put the following decimals in
ascending order:
1.506, 1.56, 0.8
Ascending 1.506, 1.56, 0.8
Units
Deci
mal
Point
Tenths
Hundredths
Thousandths
1
.
5
0
6
1
.
5
6
0
.
8
Fill in the empty squares with zeros:
Units
Deci
mal
Point
Tenths
Hundredths
Thousandths
1
.
5
0
6
1
.
5
6
0
0
.
8
0
0
Smallest first
So 0.8 is the smallest – lowest in order to climb up to
the highest
Why do you need to know any of this?
Sometimes we need to find values or
answers to calculations. In order to do
this we need to recognise that numbers
need to placed in some sort of order to
solve problems and find the answers. We
might need to add or subtract (take away)
multiply and divide. We might need to find
the highest or lowest of something for a
specific task or job.
What other words could we use?
Increase
decrease