Numbers - Limits of Accuracy
Choose a question
calculator Simple Total: 3 marks

A rectangle measures \(8.5\text{ cm}\) by \(10.7\text{ cm}\), both correct to \(1\) decimal place.

Calculate the upper bound of the perimeter of the rectangle.

\[ \underline{\hspace{4cm}}\text{ cm} \]
Answer
\[ P=2(l+w) \] \[ =2(10.75+8.55) \] \[ =2(19.3) \] \[ =38.6 \] \[ \boxed{38.6\text{ cm}} \]
calculator Simple Total: 1 mark

A cuboid measures \(10\text{ cm}\) by \(4\text{ cm}\) by \(6\text{ cm}\).

Each side is measured correct to the nearest centimetre.

Complete the inequality for the volume, \(V\), of this cuboid.

\[ \cdots\text{ cm}^3 \le V < \cdots\text{ cm}^3 \]
Answer
\[ 9.5 \times 3.5 \times 5.5 = 182.875 \] \[ 10.5 \times 4.5 \times 6.5 = 307.125 \] \[ \boxed{182.875\text{ cm}^3 \le V < 307.125\text{ cm}^3} \]
calculator Simple Total: 1 mark

A car travels \(14\text{ km}\), correct to the nearest kilometre.

This takes \(12\) minutes, correct to the nearest minute.

Calculate the lower bound of the speed of the car.

Give your answer in kilometres per minute.

\[ \underline{\hspace{4cm}}\text{ km/min} \]
Answer
\[ \text{Lower distance}=13.5 \] \[ \text{Upper time}=12.5 \] \[ \text{Lower speed} =\frac{13.5}{12.5} \] \[ =1.08 \] \[ \boxed{1.08\text{ km/min}} \]
calculator Simple Total: 2 marks

The length, \(l\) m, of a rope is \(18.7\text{ m}\), correct to the nearest \(10\) centimetres.

Complete this statement about the value of \(l\).

\[ \cdots \le l < \cdots \]
Answer
\[ 10\text{ cm}=0.1\text{ m} \] \[ \frac{0.1}{2}=0.05 \] \[ 18.7-0.05=18.65 \] \[ 18.7+0.05=18.75 \] \[ \boxed{18.65 \le l < 18.75} \]
calculator Medium Total: 3 marks

\[ P=2w+2h \] \(w=11\) and \(h=9.5\), both correct to \(2\) significant figures.

Find the lower bound and the upper bound for \(P\).

Lower bound = __________

Upper bound = __________

Answer
\[ 10.5 \le w < 11.5 \] \[ 9.45 \le h < 9.55 \] \[ \text{Lower bound} =2(10.5)+2(9.45) \] \[ =39.9 \] \[ \text{Upper bound} =2(11.5)+2(9.55) \] \[ =42.1 \] \[ \boxed{\text{Lower bound }=39.9} \] \[ \boxed{\text{Upper bound }=42.1} \]
calculator Medium Total: 1 mark

Virat has \(200\) metres of wire, correct to the nearest metre.

He cuts the wire into \(n\) pieces of length \(3\) metres, correct to the nearest \(20\) centimetres.

Calculate the largest possible value of \(n\).

\[ n=\underline{\hspace{3cm}} \]
Answer
\[ \text{Upper bound of wire}=200.5 \] \[ \text{Lower bound of piece length}=2.9 \] \[ n=\frac{200.5}{2.9} \] \[ =69.1379\ldots \] \[ \boxed{n=69} \]
non-calculator Simple Total: 1 mark
Ella's height is \(175\text{ cm}\), correct to the nearest \(5\text{ cm}\).

Write down the upper bound of Ella's height.
\[ \underline{\hspace{3cm}}\text{ cm} \]
Answer

Short Method:

$$ \text{Upper Bound} = \text{Given Value} + \frac{\text{Rounding Unit}}{2} $$ $$ = 175 + \frac{5}{2} $$ $$ = 175 + 2.5 $$ $$ = 177.5 $$

Answer:

$$ \boxed{177.5\text{ cm}} $$
non-calculator Simple Total: 2 marks

The sides of a square are \(15.1\text{ cm}\), correct to \(1\) decimal place.

Find the upper bound of the area of the square.

\[ \underline{\hspace{4cm}}\text{ cm}^2 \]
Answer

Method:

\[ \text{Upper bound of side} = 15.1 + 0.05 = 15.15\text{ cm} \] \[ \text{Upper bound of area} = (15.15)^2 \] \[ = 229.5225 \]

Answer:

\[ \boxed{229.5225\text{ cm}^2} \]
non-calculator Simple Total: 3 marks

The sides of an isosceles triangle are measured correct to the nearest millimetre.

One side has a length of \(8.2\text{ cm}\) and another has a length of \(9.4\text{ cm}\).

Find the largest possible value of the perimeter of this triangle.

\[ \underline{\hspace{4cm}}\text{ cm} \]
Answer
\[ 8.2 \rightarrow 8.25 \] \[ 9.4 \rightarrow 9.45 \] \[ \text{Isosceles sides }=9.45,\;9.45,\;8.25 \] \[ P=9.45+9.45+8.25 \] \[ =27.15 \] \[ \boxed{27.15\text{ cm}} \]
non-calculator Simple Total: 2 marks

Violet and Wilfred recorded their times to run \(200\text{ m}\), correct to the nearest second.

Violet took \(36\) seconds and Wilfred took \(39\) seconds.

Work out the upper bound of the difference between their times.

\[ \underline{\hspace{4cm}}\text{ s} \]
Answer
\[ \text{Violet: }35.5 \le t_V < 36.5 \] \[ \text{Wilfred: }38.5 \le t_W < 39.5 \] \[ \text{Upper bound of difference} =39.5-35.5 \] \[ =4 \] \[ \boxed{4\text{ s}} \]