Approximation

• What is an approximation?


  Anything similar but not exactly equal to something else
• How can a number be approximated?


  By rounding
• What are the steps for rounding to the nearest 10, 100, and 1000?


  • Nearest 10: Look at the number in the 10 column
  • Nearest 100: Look at the number in the 100 column
  • Nearest 1000: Look at the number in the 1000 column
• What is 4853 rounded to the nearest 10?


  4850
• What is 4853 rounded to the nearest 100?


  4900
• What is 4853 rounded to the nearest 1000?


  5000
• What are the steps for rounding decimals?

  1. For 1 decimal place (dp), look at the first digit after the decimal
  2. For 2 decimal places (dp), look at the second digit after the decimal
  3. If the next digit is 5 or more, increase by 1
  4. If it is 4 or less, keep the same
  5. Remove any trailing zeros
• What is 248.561 rounded to 1 decimal place?


  248.6
• What is 0.9583 rounded to 1 decimal place?


  1. 0
• What are the steps for rounding significant figures?


  1. Identify the first non-zero digit
  2. Find the required digit
  3. Look at the number next to it
  4. If 5 or more, round up by 1
  5. If 4 or less, keep the same
  6. Fill any numbers to the right with zeros
• What is 53.879 rounded to 2 significant figures?


  54,000
• What is truncation?


  • Finding an estimated number without rounding
  • Miss off all digits after the decimal point
• What is 3.784 truncated to 1 decimal place?


  1. 7
• What is 63854 truncated to 3 significant figures?


  63800
• How do you estimate calculations?

  • Round numbers to 1 significant figure
  • Use the symbol ≈ to indicate approximation
• What is the estimated value of 23 x 67 when rounded?


  1400
• What are upper and lower bounds?

  • Upper bound: Smallest value that could round up to the estimated value
  • Lower bound: Smallest value that could round down to the estimated value
• How do you find the upper and lower bounds for a measured value of 62 kg rounded to the nearest kg?


  Upper: 62.5 kg, Lower: 61.5 kg
• How do you find the upper and lower bounds for a measured value of 390 grams rounded to the nearest gram?


  Upper: 390.5 g, Lower: 389.5 g
• What is the process for finding the largest and smallest possible answers using upper and lower bounds?


  1. Work out the upper and lower bounds of the number
  2. Use these bounds to finish calculations
• What is the upper bound for 10 bags of flour if each bag has a mass of 1600g rounded to the nearest 10g?


  15,050 g (15.05 kg)
• How do you calculate the maximum and minimum area using upper and lower bounds?


  • Maximum area: Multiply two upper bounds
  • Minimum area: Multiply two lower bounds
• What is the maximum area for dimensions 21.1 cm by 29.7 cm rounded to the nearest 0.1 cm?


  629.2125 cm² (624.2 cm²)
• What is the minimum area for dimensions 21.1 cm by 29.7 cm rounded to the nearest 0.1 cm?


  624.1325 cm² (624.1 cm²)
• What are the rules for adding and subtracting upper and lower bounds?


  • Adding: Upper + Upper, Lower + Lower
  • Subtracting: Upper - Lower, Lower - Upper
• What are the rules for multiplying and dividing upper and lower bounds?

  • Multiplying: Upper x Upper, Lower x Lower
  • Dividing: Upper / Lower, Lower / Upper