Aussie Maths & Science Teachers: Save your time with SmarterEd
The length and width of a rectangle are measured to be 8 cm and 5 cm respectively, to the nearest centimetre.
What are the lower and upper bounds for the area of the rectangle?
`D`
`text{Absolute error}\ = 1/2 xx text{precision}\ =0.5\ text{cm}`
`text{8 cm side: upper limit = 8.5 cm, lower limit = 7.5 cm}`
`text{5 cm side: upper limit = 5.5 cm, lower limit = 4.5 cm}`
`text{Rectangle upper limit}\ =8.5xx5.5=46.75\ text{cm}^2`
`text{Rectangle lower limit}\ =7.5xx4.5=33.75\ text{cm}^2`
`=>D`
A plant stem is measured to be 16.0 cm, correct to one decimal place.
What is the percentage error in this measurement?
`A`
`text{Absolute error} = 1/2 xx \text{precision} = 1/2 xx 0.1 = 0.05\ text{cm}`
| `% text(error)` | `= frac(0.05)(16.0) xx 100` |
| `= 0.3125%` |
`=> \ A`
A person's weight is measured as 79.3 kg.
What is the absolute error of this measurement?
`B`
♦ Mean mark 46%.
| `text(A)text(bsolute error)` | `= 1/2 xx\ text(precision)` |
| `= 1/2 xx 0.1\ text(kg)` | |
| `= 1/2 xx 100\ text(grams)` | |
| `= 50\ text(grams)` |
`=> B`
A cockroach is measured in a school science experiment and its length is recorded as 5.2 cm.
What is the upper limit of accuracy of this measurement?
`=>\ B`
`text(A)text(bsolute error = 0.05 cm)`
| `text(Upper limit)` | `= 5.2 + 0.05` |
| `= 5.25\ text(cm)` |
`=>\ B`
The length of a window is measured as 2.4 m.
Which calculation will give the percentage error for this measurement?
`A`
`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 0.1 = 0.05\ text{m}`
| `text{% error}` | `=\ frac{text{absolute error}}{text{measurement}} xx 100%` | |
| `=0.05/2.4 xx 100%` |
`=>A`
The length of a netball court is measured to be 30.50 metres, correct to the nearest centimetre.
What is the lower limit for the length of the netball court?
`C`
| `text(A)text(bsolute error)` | `= 0.5\ text(cm)` |
| `= 0.005\ text(m)` |
| `:.\ text(Lower limit)` | `= 30.50-0.005` |
| `= 30.495\ text(m)` |
`=>C`
The length of a fish was measured to be 49 cm, correct to the nearest cm.
What is the percentage error in this measurement, correct to one significant figure?
`C`
`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 1 = 0.5\ text{cm}`
| `text{% error}` | `=\ frac{text{absolute error}}{text{measurement}} xx 100%` | |
| `=0.5/49 xx 100%` | ||
| `=1.020… %` | ||
| `=1%\ \ text{(to 1 sig fig)}` |
`=>C`
The capacity of a bottle is measured as 1.25 litres correct to the nearest 10 millilitres.
What is the percentage error for this measurement? (1 mark)
`text(0.4%)`
`text(A) text(bsolute error) = 5\ text(mL)`
| `:.\ text(% error)` | `= 5/1250 xx 100` |
| `=\ text(0.4%)` |
The top of the Sydney Harbour Bridge is measured to be 138.4 m above sea level.
What is the percentage error in this measurement?
`A`
`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 0.1 = 0.05\ text{m}`
| `text{% error}` | `=\ frac{text{absolute error}}{text{measurement}} xx 100%` | |
| `=0.05/138.4 xx 100%` | ||
| `=0.036%` |
`=> A`
A rectangular wooden chopping board is advertised as being 17 cm by 25 cm, with each side measured to the nearest centimetre.
--- 2 WORK AREA LINES (style=lined) ---
--- 4 WORK AREA LINES (style=lined) ---
i. `text(Longer side) = 25\ text(cm)`
`text{Absolute error}\ =1/2 xx text{precision}\ = 1/2 xx 1 = 0.5\ text{cm}`
| `text{% error}` | `=\ frac{text{absolute error}}{text{measurement}} xx 100%` | |
| `=0.5/25 xx 100%` | ||
| `=2%` |
ii. `text(Area) = l xx b`
| `text{Area (upper)}` | `=25.5 xx 17.5` |
| `=446.25\ text{cm}^2` |
| `text{Area (lower)}` | `=24.5 xx 16.5` |
| `=404.25\ text{cm}^2` |
`:.\ text{Area is between 404.25 cm}^2\ text{and 446.25 cm}^2.`