Mammoth Memory

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.

Upper and lower boundary walls around a castle  mnemonic helps you remember upper boundary is largest value and lower boundary is smallest value

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

0 + 5                  Five or more, raise the score

0 – 5                  Four or less, just ignore (minus 5 because the interval can be between (key word) +5 and -5 (i.e. -4.99999))

 

743.85              Upper boundary

743.75              Lower boundary

Answer: The upper and lower boundaries are 743.85 and 743.75 respectively.

 

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

0 + 5                   Five or more, raise the score

0 – 5                   Four or less, just ignore (minus 5 because the interval can be between (key word) +5 and -5 (i.e. -4.99999))

 

53.5                    Upper boundary

52.5                    Lower boundary

Answer: The upper and lower boundaries are 53.5 and 52.5 respectively.

 

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

0 + 5                   Five or more, raise the score

0 – 5                   Four or less, just ignore (minus 5 because the interval can be between (key word) +5 and -5 (i.e. -4.99999))

 

5350                   Upper boundary

5250                   Lower boundary

Answer: The upper and lower boundaries are 5350 and 5250 respectively.

More Info