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Chapter 2: Problem 189

Write two conversion factors that express the relationship between: (a) Grams and kilograms, using 1 and 1000 (b) Kilograms and grams, using 1 and \(0.001\) (c) Yards and feet (d) Meters and centimeters, using 1 and 100 (e) Meters and centimeters, using 1 and \(0.01\)

Short Answer

Expert verified
(a) Grams and kilograms: \( \frac{1000 \text{ g}}{1 \text{ kg}} \) and \( \frac{1 \text{ kg}}{1000 \text{ g}}\) (b) Kilograms and grams: \( \frac{1 \text{ g}}{0.001 \text{ kg}} \) and \( \frac{0.001 \text{ kg}}{1 \text{ g}} \) (c) Yards and feet: \( \frac{1 \text{ yd}}{3 \text{ ft}} \) and \( \frac{3 \text{ ft}}{1 \text{ yd}} \) (d) Meters and centimeters: \( \frac{1 \text{ m}}{100 \text{ cm}} \) and \( \frac{100 \text{ cm}}{1 \text{ m}}\) (e) Meters and centimeters: \( \frac{1 \text{ m}}{0.01 \text{ cm}} \) and \( \frac{0.01 \text{ cm}}{1 \text{ m}} \)

Step by step solution

01

Conversion factor 1 from grams to kilograms

For every 1000 grams, we have 1 kilogram, since 1 kilogram is equal to 1000 grams: \( \frac{1000 \text{ g}}{ 1 \text{ kg}} \)
02

Conversion factor 2 from kilograms to grams

For each kilogram, there are 1000 grams: \( \frac{1 \text{ kg}}{1000 \text{ g}}\) (b) Kilograms and grams, using 1 and \(0.001\)
03

Conversion factor 3 from grams to kilograms

For each gram, there is \(0.001\) kilogram: \( \frac{1 \text{ g}}{0.001 \text{ kg}} \)
04

Conversion factor 4 from kilograms to grams

For each kilogram, there are 1000 grams, and since \(0.001\) is the reciprocal of 1000: \( \frac{0.001 \text{ kg}}{1 \text{ g}} \) (c) Yards and feet
05

Conversion factor 5 from yards to feet

For every yard, there are 3 feet: \( \frac{1 \text{ yd}}{3 \text{ ft}} \)
06

Conversion factor 6 from feet to yards

For each foot, there is \(\frac{1}{3}\) of a yard: \( \frac{3 \text{ ft}}{1 \text{ yd}} \) (d) Meters and centimeters, using 1 and 100
07

Conversion factor 7 from meters to centimeters

For every meter, there are 100 centimeters: \( \frac{1 \text{ m}}{100 \text{ cm}} \)
08

Conversion factor 8 from centimeters to meters

For each centimeter, there are \(0.01\) meters: \( \frac{100 \text{ cm}}{1 \text{ m}}\) (e) Meters and centimeters, using 1 and \(0.01\)
09

Conversion factor 9 from meters to centimeters

For every meter, there are 100 centimeters: \( \frac{1 \text{ m}}{0.01 \text{ cm}} \)
10

Conversion factor 10 from centimeters to meters

For each centimeter, we have \(0.01\) meters: \( \frac{0.01 \text{ cm}}{1 \text{ m}} \)

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