1. Decimals

2. Vocabulary To Know
Place Value Tenths Period Hundredths Powers of Ten Thousandths Decimal Ten Thousandths Decimal Point Millionths Fraction Ten Thousandths Percent

3. Representing Decimals
Standard Form
Written Form
Expanded Form
Pictures
Fractions
Percent

4. Decimals
In our place value system, the value of a digit depends on its place, or position, in the number.
Each place has a value of 10 times the place to its right.
A number in standard form is separated into groups of three digits using spaces (USA uses commas). Each of these groups is called a period.
Not every number is a whole number. Our decimal system lets us write numbers of all types and sizes, using a symbol called the decimal point.
Money,

5. Place Value Chart Numbers Get Numbers Get Bigger Smaller Millions
Thousands
Units/Ones ●
Billions
Hundred Millions
Ten Millions
Hundred Thousands
Ten Thousands
Hundreds
Tens
Ones
Tenths
Hundredths
Thousandths
Ten Thousandths
Hundred Thousandths
Millionths
Numbers Get Numbers Get
Bigger Smaller

6. Decimal Place Value • Ones Decimal • Tenths Hundredths Thousandths
Ten Thousandths
Hundred Thousandths
Millionths 1 •
0.1
0.01
0.001
0.0001 10
100
1 000
10 000
102
103
104
105
106

7. 125 . 578 As you move right from the decimal point, each place
value is divided by 10.
hundreds tens ones tenths hundredths thousandths

8. Reading Decimal Numbers
Example: Read
Solution:
Step 1: Values to the left of the decimal point are greater than one.
38 means 3 tens and 8 ones.
Step 2: The word name of the decimal is determined by the place value of the digit in the last place on the right.
The last digit (5) is in the ten-thousandth place.
is read as thirty-eight and seven thousand four hundred twenty-five ten thousandths
Reading Decimal Numbers

9. decimal number as above
How to Read and Write Decimal Numbers
Millions
Thousands
Hundreds •
Hundred
Million
Ten Million
Hundred Thousand
Ten Thousand
Thousand
Ten
One
Tenths
Hundredths
Thousandths 4 5 1 2
Read the entire number first, then add the last right digit’s place value to the end
E.g “four hundred fifty one” thousandths
2. When there is a whole number too, read the whole number first then add “AND” the
decimal number as above
e.g. “ one hundred fifty AND twelve hundredths
*** Notice Decimal Number Names end in “–ths” ***

10. The value of a digit is determined by its place value.
When the decimal point of a number is not shown (for example, in whole numbers), then it is assumed to be at the end of the number on the right hand side
Example :
321 = = 4.
Number
Place Value (of underlined digit)
Value of the digit (as a decimal)
Value of the digit (as a fraction)
3 .145
Ones 3
3. 145
Tenths
0.1 1 10
3.1 45
Hundredths
0.04 4
100
3.14 5
Thousandths
0.005 5
1000

11. Reading Place Values of Decimals
A decimal number is a number that has digits before and
after a decimal point. The decimal point is placed after the
ones digit.
Example :
Each digit in a decimal number has a place value depending
on its position.
Tens
Ones
Decimal point
Tenths
Hundredths
Thousandths 3 . 1 4 5

12. Written Form of Decimals
Read the whole number before the decimal without the use of “and.”
Write that number down.
At the decimal point use the word “and”
Read the entire number after the decimal as if it were a whole number.
Add the name of the place value of the last digit on the right hand side (after the decimal of course)

13. Written Form of Decimals
Example: Write the following decimal in words
Eight thousand, two hundred forty-three AND sixty-seven hundredths

14. Standard Form of Decimals
Example: Write the following decimal number in standard form: two hundred six and fifty-four ten-thousandths .
206
__ __ __ __
0 0
5 4
The word “ten-thousandths” indicates that we need four decimal places.
When we clean it up, the answer is

15. A Few Examples of Reading & Writing Decimal Numbers
Fifty eight hundredths
0.58
0.854
Eight hundred fifty four thousandths
12.5
Twelve and five tenths
1.777
One and seven hundred seventy seven
thousandths
0.0005
Five ten thousandths
One hundred and ten hundredths
seven thousand
100.10
0.351
Three hundred fifty one thousandths
Twenty three and six tenths
23.6

16. A Few Examples of Reading & Writing Decimal Numbers
Five hundredths
0.05
Twenty three thousandths
0.023
Thirty nine and six tenths
39.6
Thirty and one ten thousandths
Seven tenths
0.7
nine thousand and one hundredth
80.541
Eighty and five hundred four one thousandths
Twenty one ten thousandths
0.0021

17. Expanded Form of Decimals
Similar to writing whole numbers in expanded form.
Write the number that appears before the decimal point in expanded form.
For decimals, place a zero in the ones place.
Also, substitute zeroes for all spaces after the decimal point that come before the digit that you are working with.

18. For Example: Write the following decimal 13.361 in expanded form.
Expanded Form of Decimals
For Example: Write the following decimal in expanded form.
There are two ways to write in expanded form.
1. Use the decimals =
2. Use the fractions =

19. Decimals In Pictures
Decimal numbers can also be represented by pictures using the base 10 blocks
Unit = 1
How many small boxes make up the whole grid? (100) Read more on TeacherVision:
Rod = 10
Cube = 1000
Flat = 100

20. Decimals In Pictures There are 100 units in this flat 50 are grey
Using the following pictures write a fraction and decimal for the grey area.
There are 100 units in this flat
50 are grey
So the fraction is 50
100
and the decimal is 0.5

21. Decimals In Pictures There are 100 units in this flat 50 are coloured
Using the following pictures write a fraction and decimal for the coloured area.
There are 100 units in this flat
50 are coloured
So the fraction is 75
100
and the decimal is 0.75

22. Decimals In Pictures There are 100 units in this flat 6 are coloured
Using the following pictures write a fraction and decimal for the coloured area.
There are 100 units in this flat
6 are coloured
So the fraction is 6
100
and the decimal is 0.06

23. Equivalent Decimals Basic Rules:
Add as many zeros LEFT of digits that are BEFORE a decimal.
Add as many zeros as you want RIGHT of the digits AFTER the decimal.
Equivalent Decimals
Examples:
0.5 = 0.50 = =
2.4 = 02.40 = 2.400 = 
034 is the same as 34. The number still has no hundredths, 3 tens and 4 ones.
1.5 is the same as The number still has 1 one, 5 tenths, and no hundredths.
  = = =
These all have 3 tens,, 2 ones, 4 tenths, 5 hundredths and 6 thousandths.

24. Comparing Numbers < (less than) > (greater than) = (equals)
≤ (less than or equal to) ≥ (greater than or equal to)
Basic Steps
Compare the whole number parts first.
Start and move LEFT TO RIGHT
Compare the next most significant digit of each number in the same place.
If they are equal, move onto the next place to the right.
** Think of it as PAC –MAN, his mouth is ALWAYS open towards the LARGER number.
Examples:
a). Compare 1123 and < 1126
b). Compare 567 and > 497
c). Compare 1 and > 0.002
d). Compare and 0.412, < 0.412
e). Compare and >
f). Compare and >

25. Rounding Numbers BASIC RULES
If the number to the RIGHT of the Rounding Number is 5 or more (5, 6, 7 8 or 9) then the LEFT (Rounding Number) number goes UP by ONE place.
2. If the number to the RIGHT of the Rounding Number is 4 or less (4, 3, 2, 1 or 0) then the LEFT (Rounding Number) number remains the SAME.
3. Every number AFTER the Rounding Number becomes 0.
4. Everything BEFORE the Rounding Number remains the same.
5. If the Rounding Number is a 9 and it goes up by one, then a 0 is placed in the Rounding Number Place and 1 is moved to the next place to the LEFT. (same as carrying in adding)
Examples
Because ...
rounded to hundredths is 3.14
... the next digit (1) is less than 5
rounded to tenths is 1.3
... the next digit (6) is 5 or more
rounded to 3 decimal places is 1.264
... the next digit (5) is 5 or more
134.9 rounded to tens is 130
... the next digit (4) is less than 5
12,690 rounded to thousands is 13,000
1.239 rounded to units is 1
... the next digit (2) is less than 5

26. Adding Decimals Basic Steps: First, line up the decimal points
When one number has more decimal places than another, use 0's as place holders to give them the same number of decimal places.
Add.
Example #1:  + 51.37
1) Line up the decimal points:
2). Then add.
Example #2 :  + 3.6
Line up the decimal points:   3.600
2) Then add.   

27. Subtracting Decimals Basic Steps:
1). Line up the decimal points on all the numbers
2). When one number has more decimal places than another, use 0's as place holders to give them the same number of decimal places
3). Subtract.
Example:  - 6.008
1) Line up the decimal points.
18.2      6.008
2) Add extra 0's, using the fact that 18.2 =
  6.008
3) Subtract.  

28. Multiplying Decimal Numbers
Basic Steps.
Line up the NUMBERS, not the decimals.
Multiply the same way as you would with whole numbers.
After multiplying, add the numbers of digits to the RIGHT of the decimal point in both factors.
This is how many places the decimal will move to the LEFT of the last right digit.
Example 1: Example 2:
1. Multiply  ×  Multiply  × 9.063
2. Line up Numbers Line up Numbers
x x 9.063
3. Multiply Multiply
x x 9.063
4044
4. Count the Number of Decimal Places
in both Numbers
The decimal moves 3 digits from the right:
4.032
x Count the Number of Decimal Places
in both Numbers.
The decimal moves 5 digits from the right:
6.74
x 9.063

29. Dividing A Decimal by A Whole Number
Basic Steps.
When dividing the decimal goes STRAIGHT UP from where it is in the dividend.
Divide the same way as whole numbers.
Example 1: Example 2:
Divide ÷ Divide ÷ 22
______ ______ | | 241.8
3. Place the decimal straight up Place the decimal straight up from the dividend from the dividend
4. Solve Solve
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30. Dividing A Decimal by A Decimal
Basic Steps.
First, it is easier to make the Divisor a whole number.
Move the decimal in the Divisor as many places to the RIGHT as to create a whole Number.
Move the decimal in the Dividend the same number of places to the RIGHT.
Next, the decimal goes STRAIGHT UP from where it is in the dividend.
Divide the same way as whole numbers.
Example 1: Example 2:
Divide ÷ Divide ÷ 0.25
______ ______ | |
Move the Decimal in the Divisor Move the Decimal in the Divisor and the Dividend 1 places to and the Dividend 2 places to the RIGHT to make the Divisor the RIGHT to make the Divisor a Whole Number a Whole Number
The decimal goes straight up now The decimal goes straight up now
Solve Solve
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