# Length Discete Continuous Data Dimension

```Length
1 foot = 12 inches
 1 yard =3 feet
 1 mile = 1760 yards
Converting to metric length
 1 inch = 2.5 cm
 1 foot = 30.5 cm
 1 m = 39 inches
 1 mile = 1.6 km or 5 miles = 8 km

Converting metric and Imperial
Measures in Length
Convert 40cm into inches.
1 inch = 2.5 cm
40/2.5 = 16 inches
 Tim is 6 feet 2 inches tall. Estimate Tims height in cm.
1 foot = 12 inches
6 feet =6 x 12 = 72 inches
Total height = 72 + 2 = 74 inches
1 inch = 2.5 cm
74 x 2.5 = 185 cm

Conversions on length
How far is 32 km in miles?
1 mile = 1.6 km
32/1.6 = 20 miles

Mass
1 pound = 16 ounces
 14 pounds = 1 stone
 240 pounds = 1 ton
Converting to metric length
 1 kg = 2.2 pounds

Converting Imperial to Metric Mass
Change 5 kg to pounds.
1 kg = 2.2 pounds
5 kg = 5 x 2.2 = 11 pounds
 James weighs 10 stones 6 pounds. Estimate his weight
in kilograms.
1 stone = 14 pounds
10 stones = 10 x 14 = 140 pounds
Total weight in pounds = 140 + 6 = 146 pounds
1 kg = 2.2 pounds
146 pounds/2.2 = 66 kg

Capacity and Volume

1 gallon = 8 pints
Converting to metric units
 1 litre = 1.75 pints
 1 litre = 0.2 gallons
Conversions on mass
How many pints are there in a 4 litre carton of
milk?
1 litre = 1.75 pints
4 x 1.75 = 7 pints
 The capacity of a cars petrol tank is 12 gallons.
How much does the petrol tank hold in litres?
1 litre = 0.2 gallons
12/0.2 = 60 litres

Discrete and Continuous Measures
Discrete Measures
 Can only take particular measures
 The number of people on the bus is 42.
 My shoe size is 4 &frac12;.
Continuous Measures
 Measures that can lie within a range of possible values
 Height of a mountain
 Weight
 Age
Continuous Measures Examples
Jane is 160 cm tall to the nearest 10 cm.
What are the limits between which her
true height lies?
The smallest value is 155 cm
The highest value is 164.99999999999 cm
which we take as 165 cm
155cm≤ Janes height&lt;165 cm

Continuous Measures Examples
Jane is 160 cm tall to the nearest 1 cm.
What are the limits between which her
true height lies?
The smallest value is 159.5 cm
The highest value is 160.4999999999 cm
We take it as 160.5 cm.
159.5 cm≤ Janes height &lt; 160.5 cm

Dimensions and Formulae



Length (L) has a dimension of 1.
Area has dimension of Length x Length
(L&sup2;) 2-D
Volume has dimension of Length x Length
x Length (L&sup3;) 3-D
Dimensions and Formulae examples

1)
2)
3)
4)
In each of these expressions the letters a, b, and c
represent lengths. Use dimensions to check
whether the expressions could represent
perimeter, area or volume.
2a + 3b + 4c
2a&sup2;b +abc
3a&sup2; +2b(a+c)
3a + 2ab + c&sup3;
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