Q. 2.50 - An Introduction to General, Organic, and Biological Chemistry

Question

Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following:
a. The Daily Value (DV) for iodine is $150 mcg$
b. Gold jewelry contains $58\%$ gold by mass.
c. The price of a liter of milk is $\$1.65$
d. A metric ton is $1000kg$

Step-by-Step Solution

Answer

Part(a) The equality and conversation factors are$1DV=150 mcg$ ,$\frac{1DV}{150 mcg}$and $\frac{150 mcg}{1DV}$There are two significant and one exact numbers.

Part(b) The equality and conversation factors are$58=100$ ,$\frac{58}{100}$and $\frac{100}{58}$There are two significant and one exact numbers. 

Part(c) The equality and conversation factors are $1L=\$1.65$,$\frac{1L}{\$1.65}$and $\frac{\$1.65}{1L}$There are three significant and one exact numbers.

Part(d) The equality and conversation factors are$1 meteric ton = 1000kg$ ,$\frac{1 meteric ton}{1000kg}$and $\frac{1000kg}{1 meteric ton}$There are one significant and one exact numbers. 

Part(a) Step 1 : Given information

We are given that the Daily Value (DV) for iodine is $150 mcg$

Part(a) Step 2 : Simplify

According to given information

Equality is $1DV=150 mcg$

Two conversion factors are $\frac{1DV}{150 mcg}, \frac{150 mcg}{1DV}$

There are two significant and one exact numbers.

Part(b) Step 1 : Given information

We are given that Gold jewelry contains $58\%$ gold by mass.

Part(b) Step 2 : Simplify

According to given information

Equality is $100 gold jewelry=58 gold$

Two conversion factors are $\frac{58}{100}, \frac{100}{58}$

There are two significant and one exact numbers.

Part(c) Step 1 : Given information

We are given that The price of a liter of milk is $\$1.65$

Part(c) Step 2 : Simplify

According to given information

Equality is $1L=\$1.65$

Two conversion factors are $\frac{1L}{\$1.65}, \frac{\$1.65}{1L}$

There are three significant and one exact numbers.

Part(d) Step 1 : Given information

We are given that a metric ton is $1000kg$

Part(d) Step 2 : Simplify

According to given information

Equality is $1 metric ton=1000 kg$

Two conversion factors are $\frac{1metric ton}{1000 kg}, \frac{1000 kg}{1metric ton}$

There are one significant and one exact numbers.