Rounding, estimation & bounds

• What is the first step in rounding numbers to a given place value?

  Identify the digit in the required place value and circle the number to the right.
• How does the number to the right of the circled digit affect rounding?

  This number determines whether to round up or round down.
• If you round 1294 to the nearest 100, what are the two options it could round to?

  The two nearest 100's to 1294 are 1200 and 1300.
• What should you be careful about when the digit being rounded is a 9?

  You should be careful as it may affect the higher place values.
• What happens if the circled number is 5 or more?

  You round to the bigger number.
• What happens if the circled number is less than 5?

  You round to the smaller number.
• What should you do with any following place values before the decimal when rounding?

  You put a zero in any following place values before the decimal.
• When rounding to decimal places, what should you ensure about your answer?

  You should leave your answer with the required amount of decimal places and not put unnecessary zeros.
• What is 1297 rounded to the nearest 100?

  1300
• What is 3.497 rounded to two decimal places?

  1. 50
• How is rounding to significant figures similar to rounding to place value?

  It involves identifying the relevant place value and applying the same rounding rules.
• What is the first significant figure of the number 3097?

  3
• What is the first significant figure of the number 0.006207?

  3
• When counting significant figures, do you count the following zeros?

  Yes, you do count the following zeros.
• What is the second significant figure of the number 3097?

  0
• What is the third significant figure of the number 3097?

  9
• Why do we use estimation?

  We estimate to find approximations for difficult sums or to check our answers are about the right size.
• What is the general rule for rounding numbers for estimation?

  Round numbers to 1 significant figure.
• How would you round the number 7.8 for estimation?

  8
• How would you round the number 18 for estimation?

  20
• How would you round the number 3.65 × 10^2 for estimation?

  4 × 10^2

  
• How would you round the number 1080 for estimation?

  1000
• What are exceptions to the general rule of rounding for estimation?

  It can be more sensible to round to something convenient.
• How would you round the number 16.2 for estimation?

  15
• How would you round the number 9.1 for estimation?

  10
• How would you round the number 1180 for estimation?

  1200
• When would it not make sense to round a number?

  It wouldn’t usually make sense to round a number to zero.
• How do you know if you have underestimated or overestimated in addition?

  If you round both numbers up, you will overestimate; if you round both numbers down, you will underestimate.
• How do you know if you have underestimated or overestimated in multiplication?

  If you round both numbers up, you will overestimate; if you round both numbers down, you will underestimate.

  
• Why are subtraction and division more complicated when estimating?

  You need to consider the effects of rounding each number.
• What happens when you increase 'a' and/or decrease 'b' in subtraction?

  It will increase the answer, so you will overestimate.
• What happens when you decrease 'a' and/or increase 'b' in subtraction?

  It will decrease the answer, so you will underestimate.
• What happens if both numbers in subtraction are increased or decreased?

  You cannot easily tell if it is an underestimate or overestimate.
• What happens when you increase 'a' and/or decrease 'b' in division?

  It will increase the answer, so you will overestimate.
• What happens when you decrease 'a' and/or increase 'b' in division?

  It will decrease the answer, so you will underestimate.
• What happens if both numbers in division are increased or decreased?

  You cannot easily tell if it is an underestimate or overestimate.
• What should you remember when rounding to a degree of accuracy greater than ten?

  Add the necessary zeros to ensure the place value of the number is not changed.
• What is the rounded answer for the number 5760 to the nearest hundred?

  5800
• What is an estimate for the calculation \( \frac{17.3 \times 3.81}{11.5} \)?

  8
• Why is the estimate of \( \frac{17.3 \times 3.81}{11.5} \) considered an overestimate?

  Because the numerator was rounded up and the denominator was rounded down.