Scientific notation is written in the form $\displaystyle \small a\times 10^b$.

In this equation, to go from standard to scientific notation, the decimal is shifted four places to the left.

$\displaystyle \small 74627=7.4627\times 10^4$

When calculating standard notation from scientific notation, if the exponent is negative, the decimal point must move that number of spaces to the left. If the exponent is positive, the decimal point must move that number of spaces to the right. In this problem, the exponent is negative, therefore we must move the decimal three places to the left:

$\displaystyle \small 3.14\times 10^{-3}=0.00314$

A number that is wrtiten in scientific notation includes the number with a decimal point after the first number $\displaystyle (8.34538)$ and  $\displaystyle *10^{x}$, where $\displaystyle x$ is the number of times you need to move the decimal point.

So, if you write $\displaystyle 100$ in scientific notation, it would be: $\displaystyle 1*10^{2}$, which is equivalent to $\displaystyle 1*100$. This shows that you need to move the decimal point two places to the right so it equals $\displaystyle 100$. Similarly, $\displaystyle .001$ would be $\displaystyle 1*10^{-3}$, which is equivalent $\displaystyle 1*.001$, where you move the decimal point three places to the left.

$\displaystyle 834,538$ becomes $\displaystyle 8.34538*10^{5}$, which is equivalent $\displaystyle 8.34538*100000$. You would move the decimal point five places to the right to go back to $\displaystyle 834,538$.

A number that is wrtiten in scientific notation includes the number with a decimal point after the first number $\displaystyle (2.5)$ and  $\displaystyle *10^{x}$, where $\displaystyle x$ is the number of times you need to move the decimal point.

So, if you write $\displaystyle 100$ in scientific notation, it would be: $\displaystyle 1*10^{2}$, which is equivalent to $\displaystyle 1*100$. This shows that you need to move the decimal point two places to the right so it equals $\displaystyle 100$. Similarly, $\displaystyle .001$ would be $\displaystyle 1*10^{-3}$, which is equivalent $\displaystyle 1*.001$, where you move the decimal point three places to the left.

$\displaystyle .0025$ becomes $\displaystyle 2.5*10^{-3}$, which is equivalent $\displaystyle 2.5*.001$. You would move the decimal point three places to the left to go back to $\displaystyle .0025$.

Apply the exponent properties:

$\displaystyle \left ( 4.5 \times 10 ^{7}\right ) \left (3.2 \times 10 ^{4} \right )$

$\displaystyle = 4.5 \cdot 3.2 \cdot 10 ^{7} \cdot 10 ^{4}$

$\displaystyle = 14.4 \cdot 10 ^{7+4}$

$\displaystyle = 14.4 \cdot 10 ^{11}$

$\displaystyle = 1.44\cdot 10 ^{1} \cdot 10 ^{11}$

$\displaystyle = 1.44\cdot 10 ^{1+11}$

$\displaystyle = 1.44\cdot 10 ^{12}$

or, more correctly, $\displaystyle 1.44 \times 10 ^{12}$.

This can be most easily solved by writing the expression in fraction form, then applying the rules of exponents as follows:

$\displaystyle \left ( 4.8 \times 10^{-14} \right )\div \left (8 \times 10 ^{-7} \right )$

$\displaystyle = \frac{4.8 \times 10^{-14}}{8 \times 10 ^{-7} }$

$\displaystyle = \frac{4.8 }{8 } \cdot \frac{ 10^{-14}}{ 10 ^{-7} }$

$\displaystyle =0.6 \cdot 10^{-14 -(-7)}$

$\displaystyle =0.6 \cdot 10^{-14 +7}$

$\displaystyle =0.6 \cdot 10^{- 7}$

$\displaystyle =6 \cdot 10 ^{-1} \cdot 10^{- 7}$

$\displaystyle =6 \cdot 10 ^{-1+ (-7)}$

$\displaystyle =6 \cdot 10 ^{-8}$,

or, more correctly written, $\displaystyle 6 \times 10 ^{-8}$.

This can be most easily solved by writing the expression in fraction form, then applying the rules of exponents as follows:

$\displaystyle \left ( 2.7 \times 10^{13} \right )\div \left (3 \times 10 ^{8} \right )$

$\displaystyle = \frac{ 2.7 \times 10^{13}}{3 \times 10 ^{8}}$

$\displaystyle = \frac{ 2.7 }{3 } \cdot \frac{ 10^{13}}{ 10 ^{8}}$

$\displaystyle = 0.9 \cdot 10^{13-8}$

$\displaystyle = 0.9 \cdot 10^{5}$

$\displaystyle = 9 \cdot 10 ^{-1}\cdot 10^{5}$

$\displaystyle = 9 \cdot 10^{- 1 + 5}$

$\displaystyle = 9 \cdot 10^{4}$

or $\displaystyle 9 \times10^{4}$.

When multiplying a decimal using base 10 with a negative exponent, the method is to move the decimal point to the left the amount of spaces which is indicated by the exponent.  In this example, you will move the decimal point four spaces to the left because the exponent is $\displaystyle -4$. Because there is only one decimal place to the left of the decimal indicated by the whole number 3, you will need to annex or add three zeroes to the left of the three as place holders, thus making the correct answer $\displaystyle .000378$ 

The significant figures will only count the number $\displaystyle 2.50$.  

All non-zero digits are significant figures, and the values after the decimal place are also considered as significant digits.

Do NOT expand the term to $\displaystyle 250,000$ or the significant digits will be lost.

The answer is:  $\displaystyle 3$

To convert $\displaystyle 5.7 \times 10^{-6}$ to standard notation, first note that

$\displaystyle 10^{-6} = 0.000001$

Multiply this by 5.7:

$\displaystyle 5.7 \times 10^{-6} = 5.7 \times 0.000001 = 0.0000057$,

the correct choice.