1. DECIMAL FRACTIONS

2. Introduction to Decimal Numbers
A number written in decimal notation has 3 parts:
Whole # part
The decimal comma
Decimal part
The position of the digit in the decimal number determines the digit’s value.

3. Place Value Chart Whole number part Decimal part Decimal comma , 103
102
101
100
10-1
10-2
10-3
10-4
10-5
tens
ones
tenths
thousands
hundreds
hundredths
thousandths
ten-thousandths
Hundred-thousandths
Whole number part
Decimal part
Decimal comma

4. Writing a Decimal Number in Words
Write the whole number part
The decimal comma is written “and”
Write the decimal part as if it were a whole number
Write the place value of the last non-zero digit
Ex: Write 6,32 in words
Six
and
thirty-two
hundredths

5. Ex: Write 0,276 in words
Zero
and
two hundred seventy-six
thousandths
Or two hundred seventy-six thousandths
Ex: Write 10,0304 in words
Ten
and
three hundred four
Ten-thousandths

6. Writing Decimal Number Standard Form
Write the whole number part
Replace “and” with a decimal comma
Write the decimal part so that the last non-zero digit is in the identified decimal place value
Note: if there is no “and”, then the number has no whole number part.

7. Ex: Write in standard form “seven hundred sixty-two thousandths”
Ex: Write in standard form “eight and three hundred four ten-thousandths” 8 ,
Ex: Write in standard form “seven hundred sixty-two thousandths”
Note: no “and”  no whole part
0 ,

8. To write a decimal as a fraction, write the fraction as you would say the decimal
Hundredths
Ten-thousandths
tenths
0,12345
Hundred-thousandths
Thousandths

9. Converting Decimal to Fractions
To convert a decimal number to a fraction, read the decimal number correctly. Simplify, if necessary.
Ex: Write 0,4 as a fraction
0,4 is read “four tenths” 
Ex: Write 0.05 as a fraction
0,05 is read “five hundredths” 

10. 0,007 is read “seven thousandths” 
Ex: Write 0,007 as a fraction
0,007 is read “seven thousandths” 
Note: the number of decimal places is the same as the number of zeros in the power of ten denominator
Ex: Write 4,2 as a fractional number
Note: there’s a whole and decimal part 
Mixed number
4,2 is read “four and two tenths”  4

11. Examples Continue: Convert decimal to base 10 fractions and simplify.
0,35 is read “thirty-five hundredths” 
0,8 is read “eight tenths” 
7,28 is read “seven and twenty-eight hundredths” 
0,375 is read “three hundred seventy-five thousandths” 

12. Your turn to try a few

13. Converting Fractions to Decimal Numbers (base 10 denominator)
When the fraction has a power of 10 in the denominator, we read the fraction correctly to write it as a decimal number
Ex: Write as a decimal number
The fraction is read “three tenths”
Note: no “and”  no whole part = 0, 3

14. , Ex: Write as a decimal number
The fraction is read “twenty-seven hundredths”
Note: no “and”  no whole part
0 ,
Ex: Write as a decimal number
The mixed number is read “five and thirty-three thousandths” , 5
3 3

15. 1 25 , = = 4 100 Ex: Write as a decimal number
Setup an equivalent fraction with a denominator in closest powers of ten
x 25 1 25 , 2 5 = = 4
100
x 25
Check to see how you would convert the denominator to the closest power of 10 – 100 (102).

16. 3 6 , = = 5 10 Ex: Write as a decimal number
Setup an equivalent fraction with a denominator in closest powers of ten
x 2 3 6 , 6 = = 5 10
x 2
Check to see how you would convert the denominator to the closest power of 10 – 10 (101).

17. 3 375 , = = 8 1000 Ex: Write as a decimal number
Setup an equivalent fraction with a denominator in closest powers of ten
x 125 3
375 , 3 7 5 = = 8
1000
x 125
Check to see how you would convert the denominator to the closest power of 10 – 1000 (103).

18. Denominator goes outside
Using Long Division
Converting fractions to decimals, take the numerator and divide by the denominator.
If the fraction is a mixed number, put the whole number before the decimal.
Rewrite as long division.
Denominator goes outside
Numerator goes inside

19. Ex: Write as a decimal number, 3 7 5
Begin Long Division 8 3
, 0
- 2 , 4
Add decimal and zeros as needed 6
- 5 6
Align decimal and divide 4
- 4 0
Answer will Terminate or repeat
= 0,375

20. Ex: Write as a decimal number, 7 5
Begin Long Division 4 3
, 0
- 2 , 8
Add decimal and zeros as needed 2
- 2 0
Align decimal and divide
Answer will Terminate or repeat
= 0,75

21. 3 75 , = = 100 4 Ex: Write as a decimal number
Create equivalent fraction on the fraction part with a denominator in closest powers of ten
x 25 3 75 , 7 5 = = 4
100
x 25
Check to see how you would convert the denominator to the closest power of 10 – 1000 (103).

22. Ex: Write as a decimal number, 8 3 3 6 5
, 0
Place a bar over the part that repeats.
- 4 , 8 2
- 1 8
= 0,83 2
- 1 8 2
Is there an echo?
This will repeat
 repeating decimal number

23. Examples:
A Terminating decimal
The division problem goes on forever….
Repeating decimal

24. Repeating Decimals A single digit might repeat…. 0,3333….
Or a group of digits might repeat…
0, ….

25. Show repeating decimals by placing a line over the digit or group of digits that repeats
0,33333…. Becomes 0,3
And
0,275275….becomes 0,275

26. Ex: Convert to a decimal
Notice the mixed number – whole & fraction part 
The decimal number will have a whole & decimal part
The whole part is 2  2 . ________
Now convert the fraction 5/8 to determine the decimal part: , 6 2 5
= 2.625 8 5
, 0
- 4 , 8 2
- 1 6 4
- 4 0

27. 5 625 , 2 = = 8 1000 Ex: Write as a decimal number
Create equivalent fraction on the fraction part with a denominator in closest powers of ten
x 125 5
625 , 2 2 6 2 5 = = 8
1000
x 125
Check to see how you would convert the denominator to the closest power of 10 – 1000 (103).

28. Ex: Write as a decimal number5 , 1 2 5
Set Long Division on the Fraction Part 8 1
, 0
- 0 , 8
Add decimal and zeros as needed 2
- 1 6 4
Align decimal and divide
- 4 0
Place decimal in front of Decimal
= 5,125

29. Ex: Write as a decimal number12 , 6 2 5
Set Long Division on the Fraction Part 8 5
, 0
- 4 , 8
Add decimal and zeros as needed 2
- 1 6 4
Align decimal and divide
- 4 0
Place decimal in front of Decimal
= 12,625

30. Your turn to try a few

31. Rounding Decimal Numbers
Rounding decimal numbers is similar to rounding whole numbers:
Look at the digit to the right of the given place value to be rounded.
If the digit to the right is > 5, then add 1 to the digit in the given place value and zero out all the digits to the right (“hit”).
If the digit to the right is < 5, then keep the digit in the given place value and zero out all the digits to the right (“stay”).

32. Ex: Round 7,359 to the nearest tenths place
Identify the place to be rounded to:
Tenths
Look one place to the right. What number is there?
Compare the number to 5: 5 > 5  “hit” (add 1)
3 + 1 = 4 in the tenths place, zero out the rest
7,359 rounded to the nearest tenths place is
7,400 = 7,4

33. Ex: Round 22,68259 to the nearest hundredths place
Identify the place to be rounded to:
Hundredths
Look one place to the right. What number is there?
Compare the number to 5: 2 < 5  “stay” (keep)
Keep the 8 and zero out the rest
22,68259 rounded to the nearest hundredths place is 22,68000 = 22,68

34. Ex: Round 1,639 to the nearest whole number
Identify the place to be rounded to:
ones
Look one place to the right. What number is there?
Compare the number to 5: 6 > 5  “hit” (add 1)
1 + 1 = 2 in the ones place, zero out the rest
1,639 rounded to the whole number is
2,000 = 2

35. Your turn to try a few

36. Decimal Addition & Subtraction
To add and subtract decimal numbers, use a vertical arrangement lining up the decimal places (which in turn lines up the place values.)
Ex: Add 16, ,21 + 2,0036
Put in 0 place holders
16,113
15,21 +
2,0036 3 3 , 3 2 6 6

37. Put in the decimal comma - 9,6413 Put in 0 place holders 6 , 3 5 8 7
Ex: Subtract 24,024 – 19,61 1 1 3 1
Put in 0 place holders
24,024 -
19,61 4 , 4 1 4
Ex: Subtract 16 – 9,6413 1 9 9 9 5 1 16 ,
0000
Put in the decimal comma -
9,6413
Put in 0 place holders 6 , 3 5 8 7

38. Your turn to try a few

39. Decimal Multiplication Multiply by Powers of 10
When multiplying by 10, 100, 1000, …
Move the decimal in the number to the right as many times as there are zeros.
2,345 times 10, move the decimal one place to the right, 23,45

40. Ex: Multiply 1,2345 x 10
Think x 10
 x 10 =
1,2345 has 4 decimal place
10 has 0 decimal places
Therefore the product of 1,2345 and 10 will have = 4 decimal places ,
 1,2345 x 10 = 12,3450
= 12,345

41. Ex: Multiply 1,2345 x 100
Think x 100
 x 100 =
1,2345 has 4 decimal place
100 has 0 decimal places
Therefore the product of 1,2345 and 100 will have = 4 decimal places ,
 1,2345 x 100 = 123,4500
= 123,45

42. Ex: Multiply 1,2345 x 1000
Think x 1000
 x 1000 =
1,2345 has 4 decimal place
1000 has 0 decimal places
Therefore the product of 1,2345 and 1000 will have = 4 decimal places ,
 1,2345 x 1000 = 1234,5000
= 1234,5

43. So what have we seen?
1,2345 x 10 = 12,345
1 zero  move decimal comma 1 place to the right
1,2345 x 100 = 123,45
2 zeros  move decimal comma 2 places to the right
1,2345 x 1000 = 1234,5
3 zeros  move decimal comma 3 places to the right
To multiply a decimal number by a power of 10, move the decimal comma to the right the same number of places as there are zeros.

44. Ex: Multiply 34,31 x 1000
How many zeros are there in 1000? 3
 Move the decimal comma in 34,31 to the right 3 times 34 , 31 ,
 34,31 x 1000 =

45. Ex: Multiply 21 x 100
How many zeros are there in 100? 2
 Move the decimal comma in to the right 2 times 21 , ,
 21 x 100 = 2100

46. Decimal Multiplication Continued
Decimal numbers are multiplied as if they were whole numbers. The decimal comma is placed in the product so that the number of decimal places in the product is equal to the sum of the decimal places in the factors.

47. Ex: Multiply 1,2 x 0,04
Think 12 x 4
 12 x 4 = 48
1,2 has 1 decimal place
0,04 has 2 decimal places
Therefore the product of 1,2 and 0,04 will have = 3 decimal places
4 8 ,
 1,2 x 0,04 = 0,048

48. Ex: Multiply 3,1 x 1,45
Think 31 x 145
 31 x 145 =4495
3,1 has 1 decimal place
1,45 has 2 decimal places
Therefore the product of 3,1 and 1,45 will have = 3 decimal places ,
 3,1 x 1,45 = 4,495

49. Your turn to try a few