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MGF1106

MGF1106. Unit Two Ex. 3.1 Number Bases And Counting Between Number Bases Objectives 1-6. Ex. 3.1. Objective 1. To convert from a base other than ten to base ten. The numbers used to carry our day-by-day tasks are called base ______ numbers. ten.

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MGF1106

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  1. MGF1106 Unit Two Ex. 3.1 Number Bases And Counting Between Number Bases Objectives 1-6

  2. Ex. 3.1 Objective 1 To convert from a base other than ten to base ten.

  3. The numbers used to carry our day-by-day tasks are called base ______ numbers. ten There are _____ digits that may be used to determine such numbers. 10 These digits are: 0, 1, 2, 3, 4,5,6,7,8,9 Base ten numbers can be written in expanded notation by using powers of 10.

  4. Base Name Number of Digits Digits 0,1,2,3,4,5,6,7,8,9 10 10 8 8 0,1,2,3,4,5,6,7 0,1,2 3 3 0,1,2,3,4,5,6,7,8,9,T,E 12 12

  5. List the first 20 numbers in base 5. 1 ,2 ,3 ,4 ,10 ,11 ,12 ,13 ,14 ,20 ,21 ,22 ,23 24 ,30 ,31 ,32 ,33 ,34 ,40 List the first 15 in base 12. 1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,T ,E ,10 ,11 ,12 ,13

  6. To write a number in expanded notation always use powers of the given base.

  7. 500 + 3 + 0.4 + 0.006 =

  8. To write a base 5 number in expanded notation use powers of 5, to write a base 2 number in expanded notation use powers of 2, to write a base 12 number in expanded notation use powers of 12, etc. Write 1145 in expanded notation. The subscript indicates the base. 1 x 5 2 + 1 x 51 + 4 x 50 To write a number in expanded notation always use powers of the given base.

  9. Write 11011112 in expanded notation. 26 1 1 0 1 1 1 1 25 24 21 20 22 23 1x26 + 1x25 + 0x24 + 1x23 + 1x22 +1x21 + 1x20 1 1 0 1 1 1 1 26 25 24 23 22 21 20

  10. To convert a number in another base to base ten: 1. Write the expanded form of the number. 2. Simplify the expression found in step 1. Convert each number to base 10. 1 1 4 1) 1145 = = 1(25) + 1(5) + 4(1) 25 5 1 = 25 + 5 + 4 = 34

  11. 2 0 1 6 2) 20168 = 8 512 64 1 = 2(512) + 0(64) + 1(8) + 6(1) = 1024 + 0 + 8 + 6 = 1038

  12. T E 2 3) 2TE12 = 144 12 1 = 2(144) + 10(12) + 11(1) = 288 + 120 + 11 = 419

  13. Ex. 3.1 Objective 2 To convert a number in base 10 to a base other than 10

  14. To convert a number in base 10 to another base: Step 1: Write down the powers of the base until one is found that is larger than the number being changed. Step 2: Decide the number of digits the number will have. Write blanks for the digits.

  15. Step 3: Divide the number by the largest power of the base. Step 4: Write the quotient in the first blank. Step 5: Find the product of the quotient and the place value and subtract from the number. This is the first remainder.

  16. Step 6: Divide the remainder by the next power of the base, write the quotient in the second blank. Step 7: Continue until the remainder is less than the base.

  17. 3 digits Convert 309 to base 8. 309 = 4658 Step 1: 1, 8, 64, 512 4 6 5 Step 2: Step 3: 309 divided by 64 = 4 Step 4: Write 4 in the first blank Step 5: 4(64) = 256, 309 - 256 = 53 Step 6: 53  8 = 6 with remainder of 5

  18. Convert 25 to base 2. 25 = 110012 1,2,4,8,16,32 5 digits are needed 1 1 0 0 1 25 ÷ 16 = 1, remainder is 9 9 ÷ 8 = 1, remainder is 1 Since 1 is less than 4 and 2, 0 will be placed in 3rd and 4th blanks and 1 in the last blank.

  19. Ex. 3.1 Objective 3 To convert between bases other than 10

  20. Convert 4056 to base 7. First convert 4056 to base 10. 0 5 4 = 4(36) + 0(6) + 5(1) 36 6 1 = 144 + 0 + 5 = 149

  21. Now change 149 to base 7. 1,7,49,343 3 0 2 Need 3 digits. 149 ÷ 49 = 3 with a remainder of 2 2 ÷ 7 = 0 with a remainder of 2 4056 = 149 = 3027

  22. Ex. 3.1 Objective 4 To determine the place value of any specified digit in the base 10 numeration system

  23. Select the place value associated with the underlined digit. 1. 2.168 B 2. 4136.13 C

  24. Ex. 3.1 Objective 5 To write the correct expanded notation of a numeral

  25. The expanded notation for 5468 is: First write it in expanded notation without powers of ten. 5000 + 400 + 60 + 8 Now write it with powers of 10. 5 × 103 + 4 × 102 + 6 × 101 + 8 × 100

  26. Write the expanded form of 89.475. Select the numeral for each of the following: 60000 + 500 + 40 + 6 = 60546

  27. Select the expanded notation for 50080.004 B

  28. Ex. 3.1 Objective 6 To write the standard numeral when given a base 10 numeral in expanded notation

  29. Select the numeral for: D A. 62.4 B. 602.4 C. 6002.4 D. 60020.4

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