Practicing scientific notation and all that

[Here's a pdf of this page if it doesn't show up right in your browser].

A.) Convert to scientific notation: E.g. 20,000,000=$2\times 10^7$

  1. 1.) 0.003=$3\times10^{-3}$ ________
  2. 2.) 100,000=$10^5$_______
  3. 3.) 0.210=$2.1\times10^{-1}$ _______
  4. 4.) 7,800=$7.8\times10^{3}$_______

 

B.) Convert from scientific notation: E.g. $3.4\times 10^{-3}=0.0034$

  1. 1.) $5\times 10^4$=$50,000$________
  2. 2.) $6\times 10^{-2}$=$0.06$_______
  3. 3.) $6.58\times10^{5}$=$658,000$_______

 

C.) Carry out the multiplication or division E.g. $3\times 10^{-3}\times.2=3\times 10^{-3}\times 2\times10^{-1}=(3\times 2)\times(10^{-3}\times10^{-1})=6\times 10^{-4}$

  1. $1\times10^4\ \times\ 3 \times 10^2$=$3\times10^6$

  2. $2\times10^{-2}\ \times\ 4.4\times10^3$=$8.8\times10^1=88$


  3. $10^{-3} / 10^{-6}=$$10^3=1000$

  4. $3.2\times 10^2 / 0.08=$$4000$

D.) Convert metric quantities

  1. 2.5 meters -> $2,500$millimeters

  2. 68 grams -> $0.068$kilograms

  3. $3\times 10^4$ meters -> $=30\times10^3\text{ meters}=30$kilometers

You should be able to do all these problems without a calculator. Make sure you can! But by all means check your results on a calculator or use wolframalpha.com .

On both sites, you use e notation. Essentially e means *10^. For example:

$2.3\times10^5\equiv$2.3e5;
$6\times 10^{-4}\equiv$6e-4

Here's how you would enter $2.3\times10^5\ \times\ 1.9\times 10^{-4}$ on wolfram alpha (WA):

Here's how you would enter $2.3\times10^5\ \times\ 1.9\times 10^{-4}$ in any Google search box.

 

and a number like $10^{-3}=1\times 10^{-3}$ gets entered as 1e-3.

Many calculators have a key labelled EE which does the same thing as e on WA.