A satisfactory alternative calculator is Google itself. I wrote the below material overten years ago before I hadever heard of NVDA. So, the material below references JAWS. Sorry!

I never published any of this material.

Chapter 24: Google As Calculator And Conversion Tool

 

By Michael R. Cross M. S. Mathematics

 

Most people only use Google to hunt for information and links to interesting sites, but they are missing some of its most powerful features. Google has many uses which don’t send you on a hunt through a long list of web sites. It is truly a many-faceted reference tool.

 

24.1 Calculations

 

Sooner or later, everyone needs a calculator if only for a short calculation and occasionally, for a longer one. The Start Menu contains a calculator under “Programs” (Windows 2000) and under “All Programs” (Windows XP. However, it only permits you to perform one arithmetic operation at a time. It would be nice to type more complicated expressions such as (87.2 +17283/7)*(21- 3/17). So, you might prefer to use something else. There is good news! You can use Google’s “Search edit:” box to evaluate such expressions.

 

24.1.1 Addition, Subtraction, Multiplication, Division, and Exponents

 

Addition, subtraction, multiplication, and division are represented respectively by ‘+’, ‘-‘, ‘*’, and ‘/’. Mathematics texts denote exponents by superscripted numbers, however, Google expects you to put a carrot in front of an exponent. A carrot is the symbol ‘^’.    An example would be “3^2” which means 3 squared.

 

24.1.2 Functions Recognized by Google Search

 

Google search recognizes several functions such as the square root function, the logarithm function (both common and natural) and their inverses, the trigonometric function and their inverses, and modulo arithmetic. You can include these functions in an expression you want Google to evaluate. It also recognizes some operators such as “% of”.

 

24.1.2.1 Square Root

 

One function that occurs frequently in calculations is the square root function. It is designated by “sqrt” followed by the number whose square root is being computed. The function name “sqrt” and the number are enclosed in parentheses “()”. An example would be “(sqrt 64)” which means “the square root of 64”.

Example:   Take the square root of 64, add 1 to the result, and then raise that to the exponent 3. To do this, put focus on the “Google Search edit:” box on the Google web site. When the browser connects to the Google web site, focus will usually be on the “Search edit:” box. Press the ENTER key to turn on forms mode. Now you can type the expression. You should type “(1 + (sqrt 64))^3”. Next press NumPad + to exit forms mode and tab once to the “Search” button.  Ordinarily pressing the SPACEBAR starts a search, but in this case, it causes Google to perform the calculation. The name of the current web page after you pressed the SPACEBAR is “(1 + (sqrt 64))^3 Google Search”, the mathematical expression being evaluated. Verify it with the JFW keystroke command INSERT+T. If the title bar isn’t the expression you want evaluated, there is something wrong with the expression as you typed it. It might be only a typing error. However, if the title bar is the expression you typed, then you got an answer.

If you arrow down, you will find the following twelve lines, and you will find your answer in the ninth one down. The eleventh line down is a link that invites you to learn more about calculator.

 

“

Advanced Search

Preferences

 

Web

 

Table with 3 columns and 2 rows

  

(1 + sqrt(64))^3 = 729

   

More about calculator.

table end”

 

Note that rather than writing “(sqrt 64)”, you can write “sqrt(64)”. Google still understands your intent and calculates the correct result 729.  A scientist or mathematician would have probably written it this way.

In this example, I showed twelve lines of the result, but in future examples, I will only show the answer.

Example: Determine the return on an initial investment of $50,000 at 6% over 30 years. In the Google “Search edit:” box, type “50000*(1.06^30)”.

Tab once to the “Search” button and press the SPACEBAR.

The title of the web page containing your answer is “50000*(1.06^30)”. Your answer on the result page is the following line.

“50 000 * (1.06^30) = 287 174.559”

   The above expression you typed is a geometric progression (remember high school algebra). Each year, 6% gets added to the original 100% giving 106%. That’s where you get the 1.06. For each of the 30 years, the amount gets multiplied (or grows) by 1.06 (106%), thus the exponent 30.

If you put a dollar sign or a comma in the “Search edit:” box, you won’t get an answer.

 

24.1.2.2 Common And Natural Logarithms

 

The common logarithm of a number x (denoted by log(x)) is that number which when 10 is raised to that number produces x. That is, 10^(log(x)) = x. Raising 10 to an exponent is the inverse of the common logarithm function. You may think of inverse functions as doing the reverse of each other. Specifically, the Inverse function of the function log(x) is the function 10^x. Verify to yourself that these functions really are inverses. FACT: log(1) = 0 and 10^0 = 1. See if Google gets it right.

Google also recognizes the natural log function. Denoted by ln(x), the natural log of x is similar to the common logarithm of x, except the base is not 10 as in common logarithms. It is 2.71828183 and is designated by the letter e.  Similar to the common logarithm, its inverse function is e^x.  NOTE: You might be wondering why would anyone be interested in such strange functions as ln(x) and e^x. Both these functions have some unusual properties that mathematicians and engineers find useful. Suppose a little cartoon character is on skis riding the curves (graphs) of each of these functions one at a time. For each point (x,y) on the curve ln(x), as he reaches the point (x,y) the slope of his skis is 1/x. When he is on the curve e^x, for each of its points (x,y) as he reaches it,  his skis will have slope y. His skis lie inside the tangent line to the curve at the point (x,y). I invite you to use google to get a feel for the relationship between these two functions. Find ln(10) and then raise e to whatever result you got from the previous calculation. You should find that ln(10) = 2.30258509. Does e^2.30258509 equal 10?

See if the above result is consistent with the definition of natural logarithm I just stated. Here’s the query and the result.

e^2.30258509 - Google Search

e^2.30258509 = 9.99999997

Well! The result is almost 10, close enough anyway.

Let’s find out the value of e. here are the query and the result.

Search edit: e^1

Search

e^1 = 2.71828183

 

24.1.2.3 Trigonometric And Inverse Trigonometric Functions

 

Google also recognizes the trigonometric functions and the inverse trigonometric functions. Angles are in radians. In the definitions below,  side-adjacent is the length of the leg of the right triangle bordering the angle in question. Side-opposite is the length of the other leg of the triangle. Hypotenuse is the length of the longest side of the triangle, which incidentally is the side opposite the right angle. The functions are:

Sin(angle)    sine of an angle = side-opposite/hypotenuse

Cos(angle)    cosine of an angle = side-adjacent/hypotenuse,

Tan(angle)    tangent of an angle = side-opposite/side-adjacent,

Sec(angle)     secant of an angle = hypotenuse/side-adjacent,

Csc(angle)    cosecant of an angle = hypotenuse/side-opposite, and

Cot(angle)    cotangent of an angle = side-adjacent/side-opposite.

Google also supports the inverse trigonometric functions. They are:

Arcsin(side-opposite/hypotenuse) = angle ,

Arccos(side-adjacent/ hypotenuse) = angle,

Arctan(side-opposite/side-adjacent) = angle,

Arcsec(hypotenuse/side-adjacent) = angle,

Arccsc(hypotenuse/side-opposite) = angle, and

Arccot(side-adjacent/side-opposite) = angle.

Revisiting an earlier explanation, two functions are inverses means that the inputs (abscissas) of the first function are the outputs (ordinates) of the second function, and that the outputs (ordinates) of the first function are the inputs (abscissas) of the second function. You might say that each function reverses the other. For example, if there is an angle between the hypotenuse and the side adjacent to it, then

Arcsin(sin(angle)) = angle. Also sin(arcsin(side-opposite/hypotenuse)) = side-opposite/hypotenuse.

When using trigonometric functions, “sin( 30 degrees)” is correct for angle 30 degrees whereas “sin(30)” returns the sine of 30 radians. If you typed “sin(30 degrees)” into the “Search edit” box and activated the “search” button, you would get the following result:

sine(30 degrees) = 0.5

 

24.1.3 Modulo Arithmetic

 

In elementary school when you were learning long division, before you learned to produce quotients with a decimal point, you expressed the quotient as a number followed by a capital R and a remainder. The modulo operator % produces a remainder.  The % is preceded by the dividend and followed by the divisor, and its resulting value is the remainder in that long division problem. In the “Search edit:” box type 27%5, and then activate the “Search” button. The result should be:

“27 modulo 5 = 2”

 

24.1.4 The % Of Operator

 

This operator is preceded by one number and followed by a second. To state the obvious, it returns the percentage of the second number specified by the first number.  As an example, find 7 percent of 89. In the “search edit:” box, type “7 % of 89”. Then activate the “Search” button the result should be:

“7% of 89 = 6.23”

 

24.1.5 Complex Numbers

 

Google can work with complex numbers too. The numbers that you have seen up to now are called real numbers. A complex number consists of two parts – a real number plus an imaginary part. The imaginary part is a real number times the imaginary number I which is the square root of –1.      For instance, if in the “Search edit:” box, you type “sqrt(-1)” and activate the “Search” button, the answer is “i”, the imaginary number.

The four operations addition, subtraction, multiplication, and division are  slightly different than those between real numbers. Suppose that a, b, c, and d are real numbers. Here are the definitions.

 

24.1.5.1 Complex Addition

 

(a +b i) + (c +d i) = (a + c) + (b + d)i.

Try the calculation (1 + 10i) + (2 + 20i). The result should be:

(1 + (10 * i)) + (2 + (20 * i)) = 3 + 30 i.

 

24.1.5.2 Complex Subtraction

 

Definition: (a + b i) - (c + d i) = (a – c) + (b – d)i.

Try the calculation (1 + 10i) – (3 + 30i). Your result should be:

(1 + (10 * i)) - (3 + (30 * i)) = -2 - 20 I

 

24.1.5.3 Complex Multiplication

 

Definition: (a + b i) * (c + d i) = (a*c –b*d) + (a*d + b*c) i.  Try the calculation (1 + 10i) * (2 + 20i). Your result should be:

(1 + (10 * i)) * (2 + (20 * i)) = -198 + 40 i.

This is correct because i^2 = -1. Remember I is the square root of –1.

 

24.1.5.4 Complex Division

 

Definition: (a + b i) / (c + d i) = (a*c –b*d)/(a^2 + b^2) + ((a*d + b*c)/(a^2 + b^2)) i. 

This definition seems very strange. The trick is that you trade the complex divisor in for a real number divisor. The way you do that is to multiply through by the complex conjugate of the divisor divided by itself which changes nothing since it is the same as multiplying by 1. Now, the complex conjugate is  c - d i. Notice that the sign in front of the imaginary part is reversed (the meaning of the complex conjugate of a complex number). Plus is reversed to minus and minus to plus. Regrouping some factors, the numerator becomes (a + b I)*(c – d I). The denominator becomes (c – d I)*(c – d I) which is c^2 + d^2. Therefore, the quotient is (a*c + b*d+ (b*c - a*d) I)/(c^2 + d^2).   However, this quotient does not exist if both c and d are 0.

Try the calculation (-15 + 55 I) / (7 + 9i). The result line should say:

“((-15) + (55 * i)) / (7 + (9 * i)) = 3 + 4 I”.

 

24.2 Conversions

As with the calculator above, you are going to enter into the Google “search edit:” box the conversion you want performed. Then you are going to activate the “Search” button either by hitting ENTER or tabbing once to the “Search” button and hitting the SPACEBAR.   If the Google conversion tool can perform the conversion, focus goes immediately to the “Search edit:” box. The lines shown in each example below is the result page. 

 

24.2.1 Degrees And Radians

 

This conversion is relevant to the discussion of the trigonometric functions presented earlier. How many degrees are in 1 radian? In the “Search edit:” box, type “1 radian in degrees”, and then activate the “search” button.  Your result page should look like this:

Search

 

Advanced Search

Preferences

 

Web

 

Table with 3 columns and 2 rows

  

1 radian = 57.2957795 degrees

   

More about calculator.

table end

 

24.2.2 English Versus Metric System

 

Google can convert between the English and the metric system. How many meters are in 25 miles?

In Google’s “Search edit:” box, type "25 miles in meters." Tab once to the “Search” button, and press the SPACEBAR. Beneath the line that says “Web”, you will find a line containing the answer.

 

24.2.3 Temperature Readings

 

Google can convert among Fahrenheit, Celsius, and Kelvin systems. For example, type “40 degrees Fahrenheit in Celsius” into the “Search edit:” box, and activate the “Search” button. You will see the following:

“40 degrees Fahrenheit in Celsius - Google Search

Sign in

Google

 

Web

Images

Video

News

Maps

more »

 

Search

40 degrees Fahrenheit in Celsius

Search

 

Advanced Search

Preferences

 

Web

 

Table with 3 columns and 2 rows

  

40 degrees Fahrenheit = 4.44444444 degrees Celsius

   

More about calculator.

table end “

 

24.2.4 Currency Conversion

 

Google can also convert currencies.

Example 1: How many pesos are in a U. S. dollar (USD)? In the Google “Search edit:” box, type

“1 USD in pesos”. Again, tab once to the “Search” button, and press the SPACEBAR. Focus moves into a page whose title is “1 USD in pesos”. The PC cursor will be on the “Search Edit:” box. Below it, you will find the following lines.

“

Search

 

Advanced Search

Preferences

 

Web

 

Table with 3 columns and 2 rows

  

1 U.S. dollar = 11.0304 Mexican pesos

   

Rates provided for information only -

see disclaimer.

More about currency conversion.

table end”

 

In the remaining examples, I show the result page only. 

 

Example 2: 

“Search edit: currency of Japan in Mexican money

Search

 

Advanced Search

Preferences

 

Web

 

Table with 3 columns and 2 rows

  

1 Japanese yen = 0.0907625507 Mexican pesos

   

Rates provided for information only -

see disclaimer.

More about currency conversion.

table end”

 

Example 3:

money - Google Search

Sign in

Google

 

Web

Images

Video

News

Maps

more »

 

Search

British currency in Canadian money

Search

 

Advanced Search

Preferences

 

Web

 

Table with 3 columns and 2 rows

  

1 British pound = 2.3247194 Canadian dollars

   

Rates provided for information only -

see disclaimer.

More about currency conversion.

 

Example 4:

“Search edit: 3.5 USD in GBP

Search

 

Advanced Search

Preferences

 

Web

 

Table with 3 columns and 2 rows

  

3.5 U.S. dollars = 1.77881683 British pounds

   

Rates provided for information only -

see disclaimer.

More about currency conversion.

table end”

 

Example 5:

“Search edit:  2.2 USD per gallon in INR per litre

 

 “Search edit: 2.2 USD per gallon in INR per litre

Search

 

Advanced Search

Preferences

 

Web

 

Table with 3 columns and 2 rows

  

2.2 (U.S. dollars per US gallon) = 25.6157917 Indian rupees per litre

   

More about calculator.

table end”

Example 6:

“Search edit: 1 USD in THB

Search

 

Advanced Search

Preferences

 

Web

 

Table with 3 columns and 2 rows

  

1 U.S. dollars = 31.3459971 Thai Baht

   

Rates provided for information only -

see disclaimer.

More about currency conversion.

table end”

 

Google knows some science facts too. For example, type this into the “Search edit:” box – “speed of light in miles per second”.

Arrowing down, you find the following:

Table with 3 columns and 2 rows

  

the speed of light = 186 282.397 miles per second

   

More about calculator.

table end

Or, try the following: “solar mass in tons”. Google returns the following: “1 solar mass = 2.19240901 × 1027 short tons”. A short ton is a metric ton. If you want an English system ton, change the spelling of tons to “tones”. You then get the following result: “1 solar mass = 1.98892 × 1027 tonnes”.

 

Let’s inquire about a physical constant such as the gravitational constant. The “Search edit:” box should say “universal gravitational constant”. The result is “gravitational constant = 6.67300 × 10-11 m3 kg-1 s-2”.

 

24.2.4 Miscellaneous Conversions

 

Google can also perform many other types of conversions. It can help out in the kitchen. Try these two conversions suggested by Google. 

• half a cup in teaspoons

• 160 pounds * 4000 feet in Calories

 

 

Let’s end this chapter with an example that joins together the ideas in 24.1 and 24.2. It is a calculation and a conversion packaged together. Remember the above calculation determining the return on an investment of $50000 at 6% over 30 years? I want the result in Japanese currency. Here are the Google “Search edit:” and result. It is  “50 000 * (1.06^30) Japanese yen = 2 364.16036 U.S. dollars”. . This is a puzzling result. Google took the 50000 to be in Yen. Here is a second attempt.

I typed “50000*(1.06)^30 USD in Japanese currency” and got the result

“50 000 * (1.06^30) U.S. dollars = 34.8830936 million Japanese yen”. This is the result I want.  The problem in the first search I conducted was that I didn’t specify two currencies. Assuming that USD is a default is imperial thinking.

The above is some of the things you can do with Google, but the coverage in this and the previous chapter was by no means exhaustive. So, have fun investigating Google for yourself.

 

 

©2007 Michael R. Cross