Homework: Exploring the Google Calculator

Part I Google has a built-in calculator. Go to www.google.com and try typing in "4+5" (without the double quotes) into the search box and hit the return key (which is the same as clicking "search") Now try "(2+8)*7". Now for powers, try 2^3. The google calculator can also handle many conversions. Search for "2 feet in inches" and you'll be told 2 feet equal 24 inches. Now search for:

  1. "4 inch in centimeters"
  2. "1 mile in kilometers"
  3. "234 meters in kilometers"
  4. What happens if you type in "1 barrel in gallons"?
  5. How about "1 barrel of oil in gallons"? Why might this be?
  6. "the speed of light in miles per second"
  7. 23 acres in square miles
  8. 23 liters in cubic feet
  9. "0.00002 light years in miles"

Warning #1: The answer will be "the speed of light = 299 792 458 m / s" Notice the spaces. The reason is that while we write 1.5 to mean "one and a half", in other parts of the world, they write "1,5" for one and a half. And while we write "1,200" for one thousand two hundred, in other parts of the world they write 1.200 for the same number. Very confusing! This is probably why, Google uses a space (instead of commas) to separate the every group of three digits. So here in the U.S. "299 792 458 m / s" is something we'd write as: "299,792,458" meters per second. Now let's ask Google to convert this answer in meters-per-second into an answer in miles per second. But wait:

Warning #2: While google uses spaces in its output, it doesn't accept them in the input (after all how could Google know if "1 123" is part of a search for two numbers next to each other, or for "1,123"?). So do not type "299 792 458 m / s in miles per second" into the search. Rather type in: "299,792,458 m / s in miles per second" You will get: "186 282.397 miles per second" by which Google means "186,282.397 miles per second"

Experiment and see what else you can learn about the built-in Google Calculator; see

http://www.google.com/intl/en/help/features.html#calculator
Which for fuller details points you to http://www.google.com/help/calculator.html

Part II Next, type in "0.002 light years in miles" Google will answer, "1.17569996 × 1010 miles. We will review Scientific Notation more in class (a shorter or longer review depending on how many requests there are) but briefly, recall that 10k just means 10 multiplied by itself k times. Thus 1010 (which is sometimes written "10^10" when we have only plaint-text displays) equals 1 followed by 10 zeros, which is 10000000000 which equals 10,000,000,000. Thus 1.17569996 × 1010 equals 11,756,999,600 (just move the decimal in "1.17569996" ten times to the right; after 8 moves we get "117569996" and still need to multiply by 10 two more times, so we add two more zeros. Email me if you need help)

Suppose you want to compare the distance between the Earth and the Sun to the size of the Sun. At wikipedia.org/wiki/Sun you find out that the mean diameter of the sun is "1.392×109 m" (here m stands for meters).

Use your mouse to copy this figures and paste it into the google search box. do not hit return or 'search' yet since your paste will look like "1.392W109 m" or as "1.392x109 m" (this is due to special characters and superscripts/exponents not being handled by the plain-text copy/paste) Replace the W by * if necessary, and do replace "109" by "10^9" then add the words "in miles" so your search is for " 1.392*10^9 meters in miles." The Sun's mean diameter in miles is: __________.

At the top of the Wikipedia entry for the Sun (in the gray right-hand column) you will find the Mean distance from Earth to be also given in meters as 1.496×1011. Typing the search phrase "1.496 * 10^11 meters in miles" (or equivalently, "1.496 * 10^11 m in miles" since google recognizes m to stand for meters) into the google search box tells you that the median distance between the earth and the sun is _________ miles.

Now, how much farther apart are the Earth and the Sun than the diameter of the Sun? (In other words, how many "Suns" could one fit between the Earth and the sun)? You type _______________________ into google calculator and find the answer is ______.

Suppose we use a model for the Sun that was 10 centimeters (about 4 inches) in diameter. How far away would the Earth be in meters? ______ meters (include decimals) away, or about _____ feet away. In this model, how large would the earth be? ______.

Bonus question: The Wikipedia entry for the Sun, next to "Mean distance from Earth" says "8.31 min at light speed" meaning that it takes light 8.31 minutes to travel the huge distance from the sun to the earth.

Given that you found our earlier that the speed of light is "186,282.397 miles per second" (which Google would understand if we used "186282.397 miles per second" -- no commas and no spaces) how can you check if the figure of "8.31 minutes" in Wikipedia is correct? Use "8.31" in a search query in which you ask google to multiply speed times times to get a distance, so the answer should come out to equal distance between the Earth and the Sun. The search to type into the Google Calculator would be:

______________________________ (hint: using "min" does not work use "minutes")

Did you know?
We saw that the speed of light is a little over 186,000 miles per second. Since the moon is about 240,000 miles from earth, it takes even something as fast as light a bit over a second to reach here. The moon you "see" at night is actually not the moon as it exists that instant; it is an image of what the Moon looked like just over a second earlier. And, when we safely look at the sun, we're actually seeing what the sun looked like some 8 minutes ago, since it takes light several minutes to travel from the Sun to the Earth. If the Sun magically stopped existing one instant during your day, the sky would look normal, and you'd still see an image of the Sun in the sky for the next 8 minutes and change!

Below are some answers to some of the bonus questions: don't peek until you've tried the exercise!)
To answer the last questions above, you can type
"(186282.397 miles per second) * 8.31 minutes" into google

and google will spit back out:
"(186 282.397 (miles per second)) * 8.31 minutes = 149 476 520 kilometers"
So, it appears that (if google has the correct speed of light) the distance from Earth to Sun would be 1.49476.. times 10^11 meters which rounds to 1.495 * 10^11 meters rather than the "1.496×10^11 m" Wikipedia gives. Close enough in this case.

Another approach is to use both Wikipedia's Earth-to-Sun distance and its "8.31 minutes" to see whether the speed this implies, matches the correct speed of light:
(1.49600 * ((10^11) meters)) / (8.31 minutes)
to which Google replies with:
(1.49600 * ((10^11) meters)) / (8.31 minutes) = 300 040 112 m / s
     (an answer in "m/s" or in "meters per second")

Now type "300040112 m / s in miles per second"
and you'll get back from google:
"300 040 112 (m / s) = 186 436.282 miles per second"
Again, mentally put in the commas: Google means "186, 436.282 miles per second" Thus due to rounding, the numbers Wikipedia gives for "distance from Earth to Sun" and "how long it takes light to arrive" would mean a speed of 186,436.282 miles per second, while the correct figure, according to both Google Calculator and the "Speed_of_light" entry in Wikipedia, is 186,282.397 miles per second. So there is some rounding. If we work with an example that needs more accuracy, we may need to look up something more accurate (with even more digits than Wikipedia gives) for the Earth-to-Sun distance, or find something more accurate than "8.31 minutes" for the time it takes light to travel this distance.