Chapter 1, Problem 1.135QP

Convert;

1. a 5.91 kg of chrome yellow to milligrams
2. b 753 mg of vitamin A to micrograms
3. c 90.1 MHz (megahertz), the wavelength of an FM signal, to kilohertz
4. d 498 mJ (the joule, J, is a unit of energy) to kilojoules

Interpretation Introduction

Interpretation:

The mass in kilogram has to be converted to milligrams.

Concept Introduction:

Conversion-factor method is the one which can be used to convert one metric unit into another.  With this, any unit can be converted to another unit by means of ratio.  The ratio that is used to convert unit is known as conversion-factor.  For example, one kilogram can be converted into gram by multiplying with 1000.

Answer to Problem 1.135QP

The given mass in kilogram is converted to milligrams as $\text{5}\text{.91 }\text{×}{\text{10}}^{\text{6}}\text{mg}$.

Explanation of Solution

Given mass in problem statement is $\text{5}\text{.91 kg}$.

Since, $\text{1}\text{kg}\text{=}{\text{10}}^{\text{3}}\text{g}$ and $\text{1}\text{mg}\text{=}{\text{10}}^{\text{-3}}\text{g}$, we can use this to convert the above unit in micrograms,

$\text{5}\text{.91 kg × }\frac{{\text{10}}^3\text{ g}}{\text{1 kg}}\text{ × }\frac{\text{1 mg}}{{\text{10}}^{\text{-3}}\text{ g}}\text{=}\text{5}\text{.91}\text{×}{\text{10}}^{\text{6}}\text{mg}$

The given mass was converted into milligrams as shown above.

Interpretation Introduction

Interpretation:

The mass in milligram has to be converted to micrograms.

Concept Introduction:

Conversion-factor method is the one which can be used to convert one metric unit into another.  With this, any unit can be converted to another unit by means of ratio.  The ratio that is used to convert unit is known as conversion-factor.  For example, one kilogram can be converted into gram by multiplying with 1000.

Answer to Problem 1.135QP

The given mass in milligram is converted to micrograms as $\text{7}\text{.53 }\text{×}{\text{10}}^{\text{5}}\text{μg}$.

Explanation of Solution

Given mass in problem statement is $\text{753 mg}$.

Since, $\text{1}\text{mg}\text{=}{\text{10}}^{\text{-3}}\text{g}$ and $\text{1}\text{μg}\text{=}{\text{10}}^{\text{-6}}\text{g}$, we can use this to convert the above unit in micrograms,

$\text{753 mg × }\frac{{\text{10}}^{\text{-3}}\text{ g}}{\text{1 mg}}\text{ × }\frac{\text{1 μg}}{{\text{10}}^{\text{-6}}\text{ g}}\text{=}7.53\times {10}^5\text{μg}$

The given mass was converted into micrograms as shown above.

Interpretation Introduction

Interpretation:

The frequency in Megahertz has to be converted to kilohertz.

Concept Introduction:

Conversion-factor method is the one which can be used to convert one metric unit into another.  With this, any unit can be converted to another unit by means of ratio.  The ratio that is used to convert unit is known as conversion-factor.  For example, one kilogram can be converted into gram by multiplying with 1000.

Answer to Problem 1.135QP

The given megahertz is converted to kilohertz as $\text{9}\text{.01 }\times {\text{ 10}}^{\text{4}}\text{ kHz}$.

Explanation of Solution

Given frequency in problem statement is $\text{90}\text{.1 MHz}$.

Since, $\text{1}\text{MHz}\text{=}{\text{10}}^6\text{Hz}$ and $\text{1 kHz}\text{=}{\text{10}}^3\text{Hz}$, we can use this to convert the above unit in kilohertz,

$\text{90}\text{.1 MHz × }\frac{{\text{10}}^6\text{ Hz}}{\text{1 MHz}}\text{ × }\frac{\text{1 kHz}}{{\text{10}}^3\text{ Hz}}\text{=}\text{9}\text{.01 }\times {\text{ 10}}^{\text{4}}\text{ kHz}$

The given frequency was converted into kilohertz as shown above.

Interpretation Introduction

Interpretation:

The energy in millijoule has to be converted to kilojoule.

Concept Introduction:

Conversion-factor method is the one which can be used to convert one metric unit into another.  With this, any unit can be converted to another unit by means of ratio.  The ratio that is used to convert unit is known as conversion-factor.  For example, one kilogram can be converted into gram by multiplying with 1000.

Answer to Problem 1.135QP

The given millijoule is converted to kilojoule as $\text{4}{\text{.98 × 10}}^{\text{-4}}\text{ kJ}$.

Explanation of Solution

Given energy in problem statement is $\text{498 mJ}$.

Since, $\text{1}\text{mJ}\text{=}{\text{10}}^{\text{-3}}\text{J}$ and $\text{1}\text{kJ}\text{=}{\text{10}}^{\text{3}}\text{J}$, we can use this to convert the above unit in kilojoules,

$\text{498 mJ × }\frac{{\text{10}}^{\text{-3}}\text{ J}}{\text{1 mJ}}\text{ × }\frac{\text{1 kJ}}{{\text{10}}^{\text{3}}\text{ J}}\text{=}\text{4}{\text{.98 × 10}}^{\text{-4}}\text{ kJ}$

The given energy was converted into kilojoules as shown above.