Our Number System

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

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, …

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

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

Numbers and the Decimal System

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

Numbers Digits Numerals Ten Different Numerals (Symbols)

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

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

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

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

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

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

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

Naming Numbers Naming Numbers Three thousand fifteen

Naming Numbers Take a number … 78448936482 Start at the right

Naming Numbers 3 2 1 78448936482 count three over

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

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

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

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

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

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

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

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

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

Naming Numbers Application writing checks

Writing Numbers in Expanded Form

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

Expanded Form 2,678 Two thousand,six hundred seventy eight 2 x 1000 + 6 x 100 + 7 x 10 + 8 x 1

Expanded Form 2,678 Two thousand,six hundred seventy eight 2 x 1000 + 6 x 100 + 7 x 10 + 8 Expanded form!

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 1000 + 1 x 100 + 2 x 10 + 3

Application Expanded form is the basis of scientific notation

Equal, Greater, Less Less than, Equal to, Greater than < <

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

< 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

> 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

Equal, Greater, Less Quick Quiz

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

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

Rounding Numbers Rounding Numbers 42

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.

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

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

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

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

48,936,482 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

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

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

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

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

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

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

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

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

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

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

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

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