PLACE VALUEWhat do we mean by place value? Key words – units digits tenths hundredths tens hundreds thousands thousandths decimal fractions biggest smallest.

Place valuePlace ValueThe 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.

As we move left, each position is 10 times bigger! Example: hundreds are 10 times bigger than tens.

... and ...

……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 pointwe 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 smallLarge and SmallSo, 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 awhole number (17 for example) .

As we move further left, every place gets 10 times bigger.

The first digit on the right meanstenths (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, etcYou 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 3/10So, 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" positionSo, 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 fractionsSo 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.

Integers

IntegersIntegers are like whole numbers, but they also include negative numbers ... but still no fractions allowed!

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 numbersWhat do we mean by ordering numbers?

List words that order numbers

Ascending – climb a mountain

Ascending descending highest lowest biggest smallest

To put numbers in order, place them from lowest (first) to highest (last). This is called "Ascending Order" (think of ascending a mountain

From lowest to the highest

Descending – go down the mountain

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")

From highest to the lowest

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 decimalsOrdering 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 leftIf 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 Decimal

Point Tenths Hundredths Thousandths

1 . 5 0 6

1 . 5 6  

0 . 8    

Fill in the empty squares with zeros:

Units Decimal

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