When we measure a length of an object, such as 4 cm (correct to the nearest centimetre), the actual length falls within a range. For 4 cm, this range is 4.0 ≤ 4 cm < 4.5, with 4.0 being the least possible value and 4.5 being the greatest possible value.
It’s important to remember
On a number line, the interval a < x < b represents all values of x between a and b, but not including a and b themselves.
The interval a ≤ x ≤ b represents all values of x between a and b, including a and b. On a number line, this is shown as:
It’s also important to remember to know the following intervals and how they look on a number line:
Let’s look at some examples.
To 1 decimal place, the length of a swimming pool measures 15.4 m and the width measures 8.7 m. Calculate the perimeter of the swimming pool, giving the smallest and greatest possible value.
Given that 2.50 ≤ x < 3.75 and 1.25 ≤ y < 2.50, find the maximum and minimum values of:
2. x – y
3. x² – y²
A rectangle has a length of 74 mm and a width of 47 mm, each correct to the nearest millimetre. Calculate the lower and upper bounds for:
a) the length
b) the width
c) the perimeter of the rectangle
d) the area of the rectangle
A square has a side length measured as 9.5 cm, correct to the nearest 0.1 cm. Calculate the least and greatest possible values of the square’s perimeter and area.