Estimating

• What is the purpose of estimation in calculations?


  Estimation is used to find an approximate answer when exact calculations are impractical.
• What is the first step in estimating the value of $38.7 \times 5.8 \div 10.25$?


  Round each number to one significant figure.
• How do you round $38.7$ to one significant figure?


  Round it to $40$ because the first non-zero digit is $3$ and the next digit $8$ is five or above.
• What is the rounded value of $5.8$ to one significant figure?


  It rounds to $6$.
• What is the rounded value of $10.25$ to one significant figure?


  It rounds to $10$.
• What is the result of the calculation $40 \times 6 \div 10$?


  The result is $24$.
• What is the approximate value of $38.7 \times 5.8 \div 10.25$?


  Approximately $24$.
• How do you round 19.2\ to one significant figure?


  It rounds to $20$.
• What is the rounded value of $98$ for the purpose of estimation?


  It rounds to $100$.
• What is the square root of $100$?


  The square root of $100$ is $10$.
• How do you round $0.48$ to one significant figure?


  It rounds to $0.5$.
• What is the result of $30 \div 0.5$?


  The result is $60$.
• What is the estimated area of a rectangle with dimensions $9.25 \text{ m}$ and $4.31 \text{ m}$ rounded to one significant figure?


  The estimated area is $36 \text{ m}^2$.
• Is the estimated area of $36 \text{ m}^2$ an overestimate or an underestimate?


  It is an underestimate.
• How do you estimate the weekly pay for someone working <latex>19</text{ hours} at £9.80</text{ per hour}?


  Estimate it as <latex>£200</text{ per week}.
• Is the estimated weekly pay of <latex>£200</text{ per week} an overestimate or an underestimate?

  It is an overestimate.
• What is the estimated value of $21.7 \times 4.963 \div 0.0955$?


  Approximately $1000$.
• How do you round $32 \text{ hours} at £21.50 \text{ per hour}$ to one significant figure?


  It rounds to $30 \text{ hours} at £20 \text{ per hour}$.
• What is the estimated weekly pay for someone working <latex>30 \text{ hours} at £20 \text{ per hour}?

  It is estimated to be <latex>£600</text{ per week}.
• Is the estimated weekly pay of <latex>£600</text{ per week} an overestimate or an underestimate?

  It is an underestimate.
• What are the steps to estimate a calculation?

  1. Round each number to one significant figure.
  2. Perform the calculation using the rounded numbers.
  3. Assess whether the result is an overestimate or an underestimate.
• What is the significance of rounding numbers in estimation?

  • Simplifies calculations.
  • Reduces the need for precise calculations.
  • Helps in quickly assessing approximate values.
• What is the difference between an overestimate and an underestimate?

  • An overestimate is when the estimated value is higher than the actual value.
  • An underestimate is when the estimated value is lower than the actual value.
• What is the process of finding a value that is close enough to the correct answer called?

  Approximation
• When is approximation most useful?

  When quick estimates are needed or when precise calculations are unnecessary