# 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 **bound**ary (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.__8__**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))

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

5__3__ Underline the digit (in this case 3)

5__3__.**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

5__3__00 Underline the digit (in this case 3)

5__3__**0**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))

5350 Upper boundary

5250 Lower boundary

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

# 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 **bound**ary (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.__8__**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))

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

5__3__ Underline the digit (in this case 3)

5__3__.**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

5__3__00 Underline the digit (in this case 3)

5__3__**0**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))

5350 Upper boundary

5250 Lower boundary

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