1. Our
Number
System

2. When you finish this unit, you will be able to:
Preview
When you finish this unit, you will be able to:
count using decimal numbers
given a number, write its name
given the name of a number, write its numerical value

3. When you finish this unit, you will be able to:
Preview
When you finish this unit, you will be able to:
expand a number to show its composition in units, tens, hundreds, thousands, …

4. When you finish this unit, you will be able to:
Preview
When you finish this unit, you will be able to:
determine whether a number is greater than, equal to, or less than another number

5. When you finish this unit, you will be able to:
Preview
When you finish this unit, you will be able to:
round a number to a given amount

6. Numbers and the Decimal System

7. Ten Different Symbols Counting Decimal System 1 6 2 5 9 4 7 3 8
Numbers
Counting 1
Decimal System 6 2 5 9 4 7 3 8
Ten Different Symbols

8. Numbers
Digits
Numerals
Ten Different Numerals (Symbols)

9. a combination of digits (numerals) that represents a quantity
Numbers
Number
a combination of digits (numerals) that represents a quantity
2004 is a number

10. Numbers
Whole Numbers
1,2,3,4,5,6,7…
Numbers you can count

11. Binary (Computer) System
Numbers
Binary (Computer) System 1
2 SYMBOLS
9 decimal = 1001 binary

12. 16 SYMBOLS D C 3 4 5 E 6 B 2 F A 7 9 8 1 1234 decimal = 4D2 hex
Numbers
Hexadecimal System D C 3 4 5 E 6 B 2 F A 7 9 8 1
16 SYMBOLS
1234 decimal = 4D2 hex

13. Numbers 1
Decimal System 6 2 5 9 4 7 3 8
Ten Different Symbols

14. 2175029 9 ones 2 tens 0 hundreds 5 thousands 7 ten thousands
Numbers
2 millions
1 hundred thousands
7 ten thousands
5 thousands
0 hundreds
2 tens
9 ones

15. 3829650 0 ones 5 tens 6 hundreds 9 thousands 2 ten thousands
Numbers
0 ones
3 millions
8 hundred thousands
2 ten thousands
9 thousands
6 hundreds
5 tens

16. Naming Numbers
Naming Numbers
Three thousand fifteen

17. Naming Numbers
Take a number …
Start at the right

18. Naming Numbers 3 2 1
count three over

19. , 78448936 482 count three over put in a comma 1-2-3 comma
Naming Numbers
1-2-3 comma ,
count three over
put in a comma

20. 78448,936,482 count three over put in a comma 1-2-3 comma
Naming Numbers
1-2-3 comma
78448,936,482
count three over
put in a comma

21. 78,448,936,482 count three over put in a comma 1-2-3 comma
Naming Numbers
1-2-3 comma
78,448,936,482
count three over
put in a comma

22. Naming Numbers
The “ones”
78,448,936,482
Hundreds
Tens
Ones

23. 78,448,936,482 The “thousands” Thousands Ten thousands
Naming Numbers
The “thousands”
78,448,936,482
Thousands
Hundred thousands
Ten thousands

24. 78,448,936,482 The “millions” Millions Ten millions Hundred millions
Naming Numbers
The “millions”
78,448,936,482
Ten millions
Millions
Hundred millions

25. Naming Numbers
The “billions”
78,448,936,482
Ten Billions
Billions

26. Naming Numbers
78,448,936,482
seventy eight billion,
four hundred forty eight million,
nine hundred thirty six thousand,
four hundred eighty two

27. 5,028,305 Five million, twenty eight thousand, three hundred and five
Naming Numbers
5,028,305
five million
no hundred twenty eight thousand
three hundred no teens five
Five million,
twenty eight thousand,
three hundred and five

28. Naming Numbers
Application
writing checks

29. Writing Numbers in Expanded Form

30. 2,678 two thousands and six hundreds and seven tens and eight
Expanded Form
2,678
Two thousand,six hundred seventy eight
two thousands and
six hundreds and
seven tens and
eight

31. Expanded Form
2,678
Two thousand,six hundred seventy eight
2 x
6 x 100 +
7 x 10 +
8 x 1

32. Expanded Form
2,678
Two thousand,six hundred seventy eight
2 x x x
Expanded form!

33. 304,123 Three hundred four thousand, one hundred twenty three
Expanded Form
304,123
Three hundred four thousand,
one hundred twenty three
3 x 100,000 +
0 x 10,000 +
4 x
1 x 100 +
2 x 10 + 3

34. Application Expanded form is the basis of scientific notation

35. Equal, Greater, Less
Less than, Equal to,
Greater than
<
<

36. Equal, Greater, Less
Equal Sign =
Mathematical quantities on either side are exactly the same
Equation
12 = 12
z = 12 (algebra)
(BALANCE)

37. < 12 6 6 < 12 Inequalities 6 is less than 12 “less than”
Equal, Greater, Less
Inequalities 12 6
“less than”
< 6
is less than 12
6 < 12

38. > 23 23 > 15 Inequalities 15 “greater than” 23 is greater than
Equal, Greater, Less
Inequalities
“greater than”
> 15 23
is greater than 15 23
23 > 15

39. Equal, Greater, Less
Quick Quiz

40. Equal, Greater, Less
True or false?
23 = 24
1,243 > 1,235
120 < 12
15 = 15 T
1,243 > 1,235 F
23 = 24 F
120 < 12 T
15 = 15

41. Equal, Greater, Less
True or false? T
1,234,567,890 > 1,234,547,890
1,234,567,890 > 1,234,547,890 F
7,203,124,908 > 7,203,124,908
7,203,124,908 > 7,203,124,908 T
5,678 > 5,658
5,678 > 5,658

42. Rounding Numbers
Rounding Numbers 42

43. Sometimes we need to do a quick calculation
Rounding Numbers
463 ft
Sometimes we need to do a quick calculation
where an exact answer is not important.

44. 463 ft round off we can Rounding Numbers
If calculating with 463 feet takes too long,
round off
we can

45. 463ft 460 ft to nearest 10 463ft 500 ft to nearest 100 463 ft
Rounding Numbers
463 ft
463ft ft to nearest 10
463ft ft to nearest 100

46. 113º 120º 110 º 113 º is closer to 110 ºthan to 120 º - round to 110 º
Rounding Numbers
113 º is closer to 110 ºthan to 120 º
- round to 110 º
120º
110 º
113º
Another example

47. 48,936,482 Rule to round a number to a given place Rounding Numbers
count from right to place indicated
put marker (finger, pencil) there
48,936,482

48. 48,936,482 48,940,000 Rule continued Rounding Numbers
If number to right is equal to or greater than 5:
add 1 to marked number
fill to right with zeros
48,936,482
48,940,000

49. 48,932,482 48,930,000 Rule continued Rounding Numbers
If number to right is less than 5:
keep marked number
fill to right with zeros
48,932,482
48,930,000

50. Rounding Numbers
48,936,482
to the nearest:
ten
48,936,480

51. Rounding Numbers
48,936,482
to the nearest:
hundred
48,936,500

52. Rounding Numbers
48,936,482
to the nearest:
thousand
48,936,000

53. Rounding Numbers
48,936,482
to the nearest:
ten thousand
48,940,000

54. Rounding Numbers
48,936,482
to the nearest:
million
49,000,000

55. Review We have seen that:
our numbering system, the DECIMAL system, uses 10 different symbols
Ten Different Symbols

56. Review We have seen that:
the value of a number depends on the particular digit and its position

57. Review We have seen that:
numbers are named by the digits and the name of the position of the digits

58. Review We have seen that:
numbers can be expanded to show how they are composed

59. Review We have seen that:
sometimes it is useful to approximate the value of a number

60. Next…