Chapter 7, Problem 1ICA

Express the following values using scientific notation, engineering notation, and using an appropriate SI prefix such that there are only one, two, or three digits shown to the left of the decimal

Standard	Scientific	Engineering	With Prefix
(a) 389,589,000 joules [J]
(b) 0.0000000008 pascals [Pa]

To determine

Express the given standard value $389,589,000\text{J}$ using an appropriate scientific notation, engineering notation and SI prefix.

Answer to Problem 1ICA

The given standard value $389,589,000\text{ J}$ is expressed in appropriate scientific notation, engineering notation and with SI prefix as follows.

Standard	Scientific	Engineering	With Prefix
389,589,000 joules [J]	$3\cdot 89589\times {10}^8\text{J}$	$389.589\times {10}^6\text{J}$	$389.589\text{MJ}$

Explanation of Solution

Given data:

The standard value is $389,589,000\text{J}$.

Formula used:

Consider the general Scientific notation as,

$\#.\#\#\#\times {10}^N$ (1)

Here,

# is single digit to the left of the decimal point which is the most significant nonzero digit,

N is an integer, and

${10}^N$ is provide to locate the true position of the decimal point.

Consider the general Engineering notation as,

$\#\#\#.\#\#\#\times {10}^M$ (2)

Here,

M is an integer multiple of 3, and

# is the number of digits to the left of the decimal point which is one, two, or three as required to yield a power of 10 that is indeed a multiple of 3.

Calculation:

The given standard value in Joules is,

$\text{Standard value}=389,589,000\text{J}$

Convert the value into scientific notation using the expression in equation (1) as follows,

$\begin{array}{c}389,589,000\text{J}=3.89589000\times {10}^8\text{J}\\ =3.89589\times {10}^8\text{J}\end{array}$

Convert the value into engineering notation using expression equation (2) as follows,

$\begin{array}{c}389,589,000\text{J}=389.589000\times {10}^6\text{J}\\ =389.589\times {10}^6\text{J}\end{array}$ (3)

Consider the SI prefixes.

$1\text{Mega}=1\text{M}={10}^6$

Convert the standard value into SI prefixes using the equation (3).

$\begin{array}{c}389,589,000\text{J}=389.589\times \left(1\text{ M}\right)\text{J}\left\{\because 1\text{Mega}=1\text{M}={10}^6\right\}\\ =389.589\text{ MJ}\end{array}$

Conclusion:

Hence, the given standard value $389,589,000\text{ J}$ is expressed in the appropriate scientific notation, engineering notation and with SI prefixes as follows.

Standard	Scientific	Engineering	With Prefix
389,589,000 joules [J]	$3\cdot 89589\times {10}^8\text{J}$	$389.589\times {10}^6\text{J}$	$389.589\text{MJ}$

To determine

Express the given standard value $0.0000000008\text{Pa}$ using an appropriate scientific notation, engineering notation and SI prefix.

Answer to Problem 1ICA

The given standard value $0.0000000008\text{Pa}$ is expressed in appropriate scientific notation, engineering notation and with SI prefix as follows.

Standard	Scientific	Engineering	With Prefix
0.0000000008 pascals [Pa]	$8.0\times {10}^{-10}\text{Pa}$	$800.0\times {10}^{-12}\text{Pa}$	$800.0\text{pPa}$

Explanation of Solution

Given data:

The standard value is $0.0000000008\text{Pa}$.

Calculation:

The given standard value in Pascal is,

$\text{Standard value}=0.0000000008\text{Pa}$

Convert the value into scientific notation using the expression in equation (1) as follows,

$0.0000000008\text{Pa}=8.0\times {10}^{-10}\text{Pa}$

Convert the value into engineering notation using expression in equation (2) as follows,

$0.0000000008\text{Pa}=800.0\times {10}^{-12}\text{Pa}$ (4)

Consider the SI prefixes.

$1\text{pico}=1\text{p}={10}^{-12}$

Convert the standard value into SI prefixes using equation (4).

$\begin{array}{c}0.0000000008\text{Pa}=800.0\times {10}^{-12}\text{Pa}\\ =800.0\left(\text{1}\text{p}\right)\text{Pa }\left\{\because 1\text{pico}=1\text{p}={10}^{-12}\right\}\\ =800.0\text{pPa}\end{array}$

Conclusion:

Hence, the given standard value $0.0000000008\text{Pa}$ is expressed in the appropriate scientific notation, engineering notation and with SI prefix as follows.

Standard	Scientific	Engineering	With Prefix
0.0000000008 pascals [Pa]	$8.0\times {10}^{-10}\text{Pa}$	$800.0\times {10}^{-12}\text{Pa}$	$800.0\text{pPa}$