Expert: Lynn Houston - 1/15/2009

Question
The following questions reflect situations which could be encountered in any workshop or home. Show all working.

2.1 Leticia has to calculate, correct to one decimal place, the area of a rectangular piece of material, which is 5,46m by 6.35cm. She rounds off both numbers first, getting 5,5 x 6,4. This gives an answer of 35,2m ^2. What is wrong with this method?

2.2 A large indoor fishpond has to be kept at a temperature of 20 degrees C. The length of the pond is 10metres, and it contains 5 x 10^5 liters of water. The smallest fish is 5cm long, the biggest has a mass of 10kg. These details need to be relayed to the USA, where imperial measurements are used. Convert the figures given into the appropriate Imperial measurements, rounded off to whole numbers.
Conversion information:
1cm= 0, 39 in (inches)
1m= 1, 09 yd (yards)
1kg= 2, 2 Ib. (pounds)
1 litre= 0,264 gallons
Temperature conversion equation: F=(9C/5 + 32 degrees

2.3 Three equal lengths have to be cut from a single plank of wood, 5 metres long. An ordinary hand saw is used for the cutting. Give the most accurate length possible for each piece of wood .


Answer
2.1, 1) she's rounding both up (if she rounded one up and one down, she'd be a lot closer to the actual area) and 2), by rounding up, she's "squaring" her error.

2.2 In order to solve these, take the number in cms and multiply by the equivalent Imperial number.  For ex 5 cm = 5 x .39 = 1.95in.  For the temp, it's F = 9(20)/5 + 32 = 69 F

2.3  Depends on the width of the handsaw blade.  The length of wood would be 5 minus the 2 times the width of the saw, divided by 3.  SO, if the saw is 3mm wide, 5m = 500cm, so 5000-6/3 = 1664.666mm.  Convert back to meters = 1.66 meters per board.  If your teacher isn't concerned about the saw width, then just divide 5/3. (basically the same answer)