Upper and lower bound – Boundary possible values
If a number has been rounded it is important to realise what possible values the exact value might have been.
You want a boundary (bound) wall – What are your limits?
Upper boundary – The largest value that a number can be (in this boundary).
Lower boundary – The smallest value that a number can be (in this boundary).
Remember:
Underline the digit
Look next door
Five or more raise the score
Four or less just ignore
Example 1
What are the upper and lower bounds of the following number, which has been rounded to one decimal place? 743.8
Use the following process to solve:
743.8 To one decimal place
743.8 Underline the digit (in this case 8)
743.80 Look next door
743.80 and lower boundary - Five or more, would raise the score
If it was 743.75 the "Five or more, raise the score" would still raise this to 743.8 so the lower boundary is 743.75.
743.80 and upper boundary - Four or less, just ignore
If it was 743.84999 the "Four or less, just ignore" would reduce this to 743.8 so the upper boundary is 743.84999, but unbelievably mathematicians still call this 743.85 to simplify the answer.
Answer: The upper and lower boundaries are 743.85 and 743.75 respectively.
Notice this could have been achieved simply by adding and subtracting 0.05.
So 743.8 upper and lower boundary is
`743.8+0.05=743.85` Upper boundary
`743.8-0.05=743.75` Lower boundary
Example 2
53 mph has been rounded to the nearest mile per hour. What are the upper and lower boundaries?
53 Rounded to the nearest mile per hour
53 Underline the digit (in this case 3)
53.0 Look next door
53.0 and lower boundary - Five or more, would raise the score
If it were 52.5 the "Five or more, raise the score" would still raise this to 53.0 so the lower boundary is 52.5.
53.0 and upper boundary - Four or less, just ignore
If it were 53.4999 the "Four or less, just ignore" would reduce this to 53.0 so the upper boundary is 53.4999, but unbelievably mathematicians still call this 53.5 to simplify the answer.
Answer: The upper and lower boundaries are 53.5 and 52.5 respectively.
Notice this could have been achieved simply by adding and subtracting 0.05.
So 53 upper and lower boundary is
`53+0.5=53.5` Upper boundary
`53-0.5=52.5` Lower boundary
Example 3
5300 has been rounded to two significant figures. What are the upper and lower boundaries?
5300 Rounded to two significant figures
5300 Underline the digit (in this case 3)
5300 Look next door
`5300+50=5350` Upper boundary
`5300-50=5250` Lower boundary
Answer: The upper and lower boundaries are 5350 and 5250 respectively.
