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Table 1-7 shows some old measures of liquid volume. To complete the table, what numbers (to three significant figures) should be entered in (a) the wey column, (b) the chaldron column, (c) the bag column, (d) the pottle column, and (e) the gill column, starting from the top down? (f) The volume of 1 bag is equal to 0.1091 m3. If an old story has a witch cooking up some vile liquid in a cauldron of volume 1.5 chaldrons, what is the volume in cubic meters?

Short Answer

Expert verified

1way=109Chaldron=403Bag=640Pottle=120240

The volume of 1 bag=0.1091m3

Step by step solution

01

Given data

1way=109Chaldron=403Bag=640Pottle=120240

The volume of 1 bag=0.1091m3

02

Understanding the unit conversion

Unit conversion is the conversion between different units of measure for the same quantity, usually through multiplier conversion factors.

03

(a) Determination of values in way column

Use the relationship between wey and chaldron to calculate the first value in first column.

1wey=109Chaldron1×910wey=1Chaldron1Chaldron=910wey=0.900way

Use the relationship between wey and bag to calculate the next value.

1wey=403bag1×340wey=1bag1bag=7.50×10-2wey

Thus, 1bagis equal to 7.50×10-2wey

1way=640pottle1pottle=1.56×10-3way

Therefore, 1pottleis equal to 1.56×10-3way.

Use the relationship between wey and pottle to calculate the next value.

1way=120240gill1gill=8.32×10-6way

Therefore, 1gillis equal tolocalid="1654605291666" 8.32×10-6way.

04

(b) Determination of values in chaldron column

As the conversion is from chaldron to chaldron, it will be 1.00.

Use the relationship between bag and chaldron to calculate the next value.

1way=109chaldron=403Bag

Therefore,

109chaldron=403Bag1bag=10×39×40Chaldron=8.33×10-2Chaldron

Therefore, 1bagis equal to8.33×10-2Chaldron.

Use the relationship between pottle and chaldron to calculate the next value.

1way=109chaldron=640pottle

Therefore,

localid="1654604729304" 109chaldron=640pottle1pottle=109×640chaldron=1.74×10-3chaldron

Use the relationship between gill and chaldron to calculate the next value.

1way=109chaldron=120240gill

Therefore

localid="1654605089506" 109chaldron=120240gill1gill=109×120240chaldron=9.24×10-6chaldron

Thus, 1gillis equal to localid="1654605354518" 9.24×10-6chaldron.

05

(c) Determination of values in bag column

Use the relationship between chaldron and bag to calculate the next value.

1way=403Bag=109chaldron

Therefore,

403Bag=109chaldron1chaldron=40×93×10bag=12.0bag

Therefore, 1chaldronis equal to12.0bag.

As the conversion is from bag to bag, the next value will be 1.00

To calculate the next value, use the relationship between pottle and bag.

1way=403bag=640pottle

Therefore,

403bag=640pottle1pottle=403×640bag=2.08×10-2bag

Therefore, 1pottleis equal to 2.08×10-2bag.

Use the relationship between gill and bag, to calculate the next value.

1way=403bag=120240gill

Therefore,

403bag=120240gill1gill=403×120240bag=1.11×10-4bag

06

(d) Determination of values in pottle column

To calculate the next value, use the relation between chaldron and pottle.

1way=640pottle=109chaldron

Then,

640pottle=109chaldron1chaldron=640×910pottle=576pottle

Therefore, 1chaldronis equal to 576pottle.

Use the relation between bag and pottle to calculate the next value.

1way=640pottle=403bag

Then,

role="math" localid="1654607184405" 640pottle=403bag1bag=640×340pottle=48.0pottle

48.0pottle.Thus, 1bagis equal to

As the conversion is from pottle to pottle, it will be 1.00.

To calculate the next value, use the relation between gill and pottle.

1way=640pottle=120240gill

Then,

640pottle=120240gill1gill=640120240pottle=5.32×10-3pottle

Therefore, 1gillis equal to 5.32×10-3pottle.

07

(e) Determination of values in gill column

Use the relation between chaldron and gill to find the next value.

1way=120240gill=109childron

Then,

120240gill=109childron1chaldron=120240×910gill=1.08×105gill

Therefore, 1childronis equal to 1.08×105gill

Use the relationship between bag and gill to find the next value.

1way=120240gill=403bag

Then,

1bag=120240×340gill=9.02×103gill

Therefore, 1bagis equal to 9.02×103gill.

Use the relation between pottle and gill to calculate the next value.

1way=120240gill=640pottle

Then,

120240gill=640pottle1pottle=120240640gill=187.87gill=188gill

Therefore, 1pottleis equal to 188gill.

As the conversion is from gill to gill, it will be 1.00.

08

(f) Determination of the volume in cubic meter

It is given that,

1bag=0.1091m3

from part (c), 1chaldron=12.0bag

Therefore,

1.5chaldron=1.5×12.0bag=18bag

Each bag is 0.1091m3

1.5childron=18×0.1091m3=196m3

Therefore, the volume of 1.5chaldron is 1.96m3.

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