Perimeter, area and statistics

Question

1.       The length and width of a rectangle are 16.343cm and 9.37cm respectively.

a)      Calculate the perimeter of the rectangle correct to 2 decimal places

b)      Calculate the perimeter of the rectangle correct to 3 significant figures.

c)       Calculate the area of the rectangle correct to 3 decimal places

d)      Calculate the area of the rectangle correct to 1 decimal place.

e)      Round the dimensions off to 1 decimal place. Recalculate the area to 1 decimal place.

f)       Normally we wouldn’t round at the start of a calculation, doing it as the last stage. Why is this so?

 

2.       Using 2005 estimates, Australia and New Zealand can be compared on a number of issues

Australia:                                                                  New Zealand:

Population: 20 090 437                                         Population: 4 035 461

Area: 7 636 233km^2                                             Area: 270 534km^2

Highest Mountain: 2228m                                   Highest Mountain: 3754m

Number of sheep: 106 000 000                          Number of sheep: 40 000 000

 

a)      Calculate the number of sheep per person in each country to 2 decimal places.

b)      Calculate the number of sheep per square kilometre for each country to 2 decimal places.

c)       (i) The population of New Zealand in 1991 was 3 434 950. What was the actual increase from 1991 to 2005?

(ii) What percentage of the 1991 population is this increase? Express answer to 1 decimal place.

d)      Express the following in standard form:  (i)    106 000 000   (ii)  20 090 437

e)      Using standard form, for New Zealand calculate the number of sheep per km^2 of area(round to 2 decimal places).

Answer 1

1) Length of a rectangle = 16.343cm

Width of a rectangle =  9.37cm

Perimeter of the rectangle is 2(l+b) = 2(16.343+9.37)

= 51.426

a) Perimeter of the rectangle correct to 2 decimal places is 51.43

b) Perimeter of the rectangle correct to 3 significant figures is 51.5

c) Area of the rectangle is 16.343*9.37 = 153.13391

Area of the rectangle correct to 3 decimal places is 153.134

d)Area of the rectangle correct to 1 decimal place s 153.1

e)Round the dimensions off to 1 decimal place of rectangle is 16.3 and 9.3

Area of the rectangle is 16.3*9.3 = 151.59 = 151.6

f) Normally we would round at the last stage of a calculation,why because division property is part of given caliculation,

But some times we didn't finish our long division , we stopped after we reached the thousands place value.

In this case we are going to round the answer to the hundreds place value.,making our answer.

Answer 2

2)a) Number of sheep per person in Australia = Number of sheep/Population

= 106 000 000/20 090 437

= 5.2761420

Number of sheep per person in Australia to 2 decimal places is 5.28

Number of sheep per person in New Zealand = Number of sheep/Population

= 40 000 000/4 035 461

= 9.91226

Number of sheep per person in New Zealand to 2 decimal places is 9.91

b) Number of sheeps per squre kilometre in Australia = number of sheeps/area

= 106000000/7636233

= 13.881189

Number of sheeps per square kilometre in Australia to 2 decimal places is 13.89

Number of sheeps per squre kilometre in New Zeland = number of sheeps/area

= 40000000/270534

= 147.8557

Number of sheeps per squre kiilometre in New Zeland to 2 decmals is 147.86

Answer 3

c) (i) The population of New Zealand in 1991 = 3 434 950

The population of New Zealand in 2005 = 4 035 461

The population of New Zealand increase from 1991 to 2005 = 4 035 461-3 434 950 = 600 511

(ii) percentage of the 1991 population increase is (600 511/4 035 461)*100

= 14.88085

To express it 1 decimal place is 14.9

Answer 4

d)106 000 000 is expressed in sandard form is 1.06*10^8

20 090 437 is expressed in sandard form is 2.0090437*10^8

e) Number of sheeps in NewZeland = 40 000 000

Area = 270534

Number of sheep per km^2 of area = 40 000 000/270534

Which is expressed in standard form

= 400*10^5/2.70534*10^5

= 400/2.70534

= 147.85572

(round to 2 decimal places)is = 147.86