Chapter 6.4, Problem 17Q

a.

To determine

To calculate: How many times larger is a kilogram than a nanogram?

Unit of mass	Kilogram	hectogram	dekagram	decigram	centigram	milligram	microgram	nanogram
Mass (in grams)	${10}^3$	${10}^2$	${10}^1$	${10}^{-1}$	${10}^{-2}$	${10}^{-3}$	${10}^{-6}$	${10}^{-9}$

Answer to Problem 17Q

Kilogram is ${10}^{12}$ times larger than nanogram.

Explanation of Solution

Given information: Use the table for the given values.

Calculation: To find how many times a quantity is larger than another, find their ratios.

Hence, $\frac{kilogram}{nanogram}=\frac{{10}^3}{{10}^{-9}}$

  $\frac{kilogram}{nanogram}={10}^{3+9}$

  $\frac{kilogram}{nanogram}={10}^{12}$

  $kilogram={10}^{12}*nanogram$

Therefore, a kilogram is ${10}^{12}$ times larger than nanogram.

b.

To determine

To calculate: How many times smaller is a milligram than a hectogram? Write your answer using only positive exponents.

Unit of mass	Kilogram	hectogram	dekagram	decigram	Centigram	milligram	microgram	nanogram
Mass (in grams)	${10}^3$	${10}^2$	${10}^1$	${10}^{-1}$	${10}^{-2}$	${10}^{-3}$	${10}^{-6}$	${10}^{-9}$

Answer to Problem 17Q

  $milligram={10}^{-5}*hectogram$

Explanation of Solution

Given information: Use the table for values.

Calculation: To find how many times a quantity is smaller than another, find their ratios.

Hence, $\frac{milligram}{hectogram}=\frac{{10}^{-3}}{{10}^2}$

  $\frac{milligram}{hectogram}={10}^{-3-2}$

  $\frac{milligram}{hectogram}={10}^{-5}$

  $milligram={10}^{-5}*hectogram$

Therefore, a milligram is ${10}^{-5}$ times smaller than hectogram.

c.

To determine

To calculate: Which is greater, 10,000 milligrams or 1000 decigrams? Explain your reasoning.

Unit of mass	Kilogram	hectogram	dekagram	decigram	Centigram	milligram	microgram	nanogram
Mass (in grams)	${10}^3$	${10}^2$	${10}^1$	${10}^{-1}$	${10}^{-2}$	${10}^{-3}$	${10}^{-6}$	${10}^{-9}$

Answer to Problem 17Q

1000 decigram is greater than 10,000 milligram.

Explanation of Solution

Given information: Use table for the values

Calculation: Both units are different so we cannot compare them, so convert both units into grams

Converting milligram to gram

  $1milligram={10}^{-3}$

Multiplying above equation both sides by 10,000, we get

  $10,000milligram={10}^{-3}*10,000$

  $10,000milligram=10gram$

Converting decigram to gram

  $1decigram={10}^{-1}$

Multiplying above equation both sides by 1,000, we get

  $1000decigram={10}^{-1}*1000gram$

  $1000decigram=100gram$

Hence, 1000 decigram is greater than 10,000 milligram because 100 gram is greater than 10 grams