5 decimals, arithmetic of decimals

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  1. 1. Decimals Back to AlgebraReady Review Content.
  2. 2. Decimals In order to track smaller and smaller quantities we include base-10 fractions to the whole number-system.
  3. 3. $100s $1s$10s Decimals In order to track smaller and smaller quantities we include base-10 fractions to the whole number-system. Lets demonstrate this with a cash register that holds $1s, $10s, $100s, ...etc. *
  4. 4. $100s $1s$10s Decimals In order to track smaller and smaller quantities we include base-10 fractions to the whole number-system. Lets demonstrate this with a cash register that holds $1s, $10s, $100s, ...etc. For a moment lets assume that US Treasury not only makes * (dime), 10 1$ (penny), 100 1$ , a itty, and 1000 1 $ , a bitty, etc... 10000 1$ but also makes smaller value coins of
  5. 5. $100s $1s$10s Decimals In order to track smaller and smaller quantities we include base-10 fractions to the whole number-system. Lets demonstrate this with a cash register that holds $1s, $10s, $100s, ...etc. For a moment lets assume that US Treasury not only makes * dimes 10 1 $ pennies itties 100 1 $ 1000 1 $ (dime), 10 1$ (penny), 100 1$ , a itty, and 1000 1 $ , a bitty, etc... 10000 1$ but also makes smaller value coins 10000 1 $ of bitties *
  6. 6. $100s $1s$10s Decimals In order to track smaller and smaller quantities we include base-10 fractions to the whole number-system. Lets demonstrate this with a cash register that holds $1s, $10s, $100s, ...etc. For a moment lets assume that US Treasury not only makes * 10 1 $ 100 1 $ 1000 1 $ (dime), 10 1$ (penny), 100 1$ , a itty, and 1000 1 $ , a bitty, etc... 10000 1$ but also makes smaller value coins 10000 1 $ of Note that 10 itties = 1 penny and 10 bitties = 1 itty, etc... * dimes pennies itties bitties
  7. 7. $100s $1s$10s Decimals In order to track smaller and smaller quantities we include base-10 fractions to the whole number-system. Lets demonstrate this with a cash register that holds $1s, $10s, $100s, ...etc. For a moment lets assume that US Treasury not only makes * 10 1 $ 100 1 $ 1000 1 $ (dime), 10 1$ (penny), 100 1$ , a itty, and 1000 1 $ , a bitty, etc... 10000 1$ but also makes smaller value coins Lets further assume each slot only hold up to 9 bills or coins so we may record the money stored in the register 10000 1 $ of Note that 10 itties = 1 penny and 10 bitties = 1 itty, etc... * dimes pennies itties bitties
  8. 8. $100s $1s$10s Decimals In order to track smaller and smaller quantities we include base-10 fractions to the whole number-system. Lets demonstrate this with a cash register that holds $1s, $10s, $100s, ...etc. For a moment lets assume that US Treasury not only makes * 10 1 $ 100 1 $ 1000 1 $ (dime), 10 1$ (penny), 100 1$ , a itty, and 1000 1 $ , a bitty, etc... 10000 1$ # # # # ## but also makes smaller value coins Lets further assume each slot only hold up to 9 bills or coins so we may record the money stored in the register 10000 1 $ of Note that 10 itties = 1 penny and 10 bitties = 1 itty, etc... # * dimes pennies itties bitties
  9. 9. $100s $1s$10s Arithmetic of Decimals In order to track smaller and smaller quantities we include base-10 fractions to the whole number-system. Lets demonstrate this with a cash register that holds $1s, $10s, $100s, ...etc. For a moment lets assume that US Treasury not only makes * 10 1 $ 100 1 $ 1000 1 $ (dime), 10 1$ (penny), 100 1$ , a itty, and 1000 1 $ , a bitty, etc... 10000 1$ # # # # ## simply as . # # # # where the #s = 0,1,.., or 9.# # # The decimal point (the divider) but also makes smaller value coins Lets further assume each slot only hold up to 9 bills or coins so we may record the money stored in the register 10000 1 $ of Note that 10 itties = 1 penny and 10 bitties = 1 itty, etc... # * dimes pennies itties bitties .
  10. 10. $100s* $1s$10s* 10 1 $ 100 1 $ 1000 1 $ 4 5 63 For example, . Decimals dimes pennies itties bitties
  11. 11. $100s* $1s$10s* dimes 10 1 $ pennies itties 100 1 $ 1000 1 $ 4 5 63 For example, .43 5 6is written as . Decimals bitties
  12. 12. $100s* $1s$10s* dimes 10 1 $ pennies itties 100 1 $ 1000 1 $ 4 5 63 For example, .43 5 6is written as . 4 $1s 3 $10s Decimals bitties
  13. 13. $100s* $1s$10s* dimes 10 1 $ pennies itties 100 1 $ 1000 1 $ 4 5 63 For example, .43 5 6is written as . 4 $1s 3 $10s (5 dimes) (6 pennies) 10 5 100 6$ $ Decimals bitties
  14. 14. $100s* $1s$10s* dimes 10 1 $ pennies itties 100 1 $ 1000 1 $ 4 5 63 For example, .43 5 6is written as . 4 $1s 3 $10s (5 dimes) (6 pennies) 10 5 100 6$ $ $100s $1s$10s* 10 1 $ 100 1 $ 1000 1 $ 4 5 0 7 Decimals 8 10000 1$ bitties .
  15. 15. $100s* $1s$10s* dimes 10 1 $ pennies itties 100 1 $ 1000 1 $ 4 5 63 For example, .43 5 6is written as . 4 $1s 3 $10s (5 dimes) (6 pennies) 10 5 100 6$ $ $100s $1s$10s* 10 1 $ 100 1 $ 1000 1 $ 4 5 0 7 4 $1s 4is written as . Decimals 8 10000 1$ bitties .
  16. 16. $100s* $1s$10s* dimes 10 1 $ pennies itties 100 1 $ 1000 1 $ 4 5 63 For example, .43 5 6is written as . 4 $1s 3 $10s (5 dimes) (6 pennies) 10 5 100 6$ $ $100s $1s$10s* dimes 10 1 $ pennies itties 100 1 $ 1000 1 $ 4 5 0 7 4 $1s (no penny) 100 0$ (5 dimes)10 5$ 1000 7$ 4 75 0is written as . Decimals 8 10000 1$ (8 bitties) 10000 8 $ bitties . 8 (7 itties)
  17. 17. Comparing Decimal Numbers Decimals Because decimal numbers may be viewed as coins stored in a base- 10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.)
  18. 18. Comparing Decimal Numbers Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest. Decimals Because decimal numbers may be viewed as coins stored in a base- 10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.)
  19. 19. Comparing Decimal Numbers 1. line up the numbers by their decimal points, Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest. Decimals Because decimal numbers may be viewed as coins stored in a base- 10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.) Specifically, to compare multiple decimal numbers to see which is largest, we
  20. 20. Comparing Decimal Numbers 1. line up the numbers by their decimal points, Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest. Decimals Because decimal numbers may be viewed as coins stored in a base- 10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.) Specifically, to compare multiple decimal numbers to see which is largest, we 0.0098 0.010 0.00199 1. line up by the decimal points
  21. 21. Comparing Decimal Numbers 1. line up the numbers by their decimal points, 2. scan the digits, i.e. the number of coins, in the slot from left to right, Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest. Decimals Because decimal numbers may be viewed as coins stored in a base- 10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.) Specifically, to compare multiple decimal numbers to see which is largest, we 0.0098 0.010 0.00199 1. line up by the decimal points
  22. 22. Comparing Decimal Numbers 1. line up the numbers by their decimal points, 2. scan the digits, i.e. the number of coins, in the slot from left to right, Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest. Decimals Because decimal numbers may be viewed as coins stored in a base- 10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.) Specifically, to compare multiple decimal numbers to see which is largest, we 0.0098 0.010 0.00199 1. line up by the decimal points 2. scan the digits in each slot from left to right
  23. 23. Comparing Decimal Numbers 1. line up the numbers by their decimal points, 2. scan the digits, i.e. the number of coins, in the slot from left to right, 3. the one with the 1st largest digit is the largest quantity. Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest. Decimals Because decimal numbers may be viewed as coins stored in a base- 10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.) Specifically, to compare multiple decimal numbers to see which is largest, we 0.0098 0.010 0.00199 1. line up by the decimal points 2. scan the digits in each slot from left to right
  24. 24. Comparing Decimal Numbers 1. line up the numbers by their decimal points, 2. scan the digits, i.e. the number of coins, in the slot from left to right, 3. the one with the 1st largest digit is the largest quantity. Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest. Decimals Because decimal numbers may be viewed as coins stored in a base- 10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.) Specifically, to compare multiple decimal numbers to see which is largest, we 0.0098 0.010 0.00199 1. line up by the decimal points 2. scan the digits in each slot from left to right 1st largest digit, so its the largest number
  25. 25. Comparing Decimal Numbers 1. line up the numbers by their decimal points, 2. scan the digits, i.e. the number of coins, in the slot from left to right, 3. the one with the 1st largest digit is the largest quantity. Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest. Decimals Bec