Question

Standard Form & Scientific Notation• 3 examples of converting from standard form to scientific notation• 3 examples of converting from scientific notation to standard form

Answer 1

Required:

We need to convert from standard form to scientific notation and also scientific notation to standard form.

Explanation:

a) Convert from standard form to scientific notation:

1) Consider the number 4,520,000.

The given number can be written as follows.

$4,520,000=452\times10000$

$=452\times10^4$

$=452\times10^4\times\frac{10^2}{10^2}$

$=452\times\frac{10^4\times10^2}{10^2}$

$=\frac{452}{100}\times10^6$

$=4.52\times10^6$

The scientific notation of s

$4.52\times10^6$

2) Consider the number

$35.98\times10^3$

Multiply and divide by 10.

$35.98\times10^3=35.98\times10^3\times\frac{10}{10}$

$=\frac{35.98}{10}\times10^3\times10$

$=3.598\times10^4$

The scientific notation is

$3.598\times10^4$

3) Consider the number.

$600.89\times10^{-8}$

Multiply and divide by 100.

$600.89\times10^{-8}=600.89\times10^{-8}\times\frac{100}{100}$

$=\frac{600.89}{100}\times10^{-8}\times10^2$

$=6.0089\times10^{-6}$

The scientific notation is

$6.0089\times10^{-6}$

b) convert from scientific notation to standard form:

1)

Consider the notation:

$6.285\times10^{-5}$$Use\text{ }10^{-5}=\frac{1}{100000}.$

$6.285\times10^{-5}=\frac{6.285}{100000}$

$=0.00006285$

The standard form is 0.00006285.

2) Consider the notation.

$7.9\times10^4$$Use\text{ }10^4=10000.$

$7.9\times10^4=7.9\times10000$

$=79000$

The standard form is 79,000.

3) Consider the notation.

$9.008\times10^5$$Use\text{ }10^5=100000.$

$9.008\times10^5=9.008\times100000$

$9.008\times10^5=900800$

The standard form is 900,800.