159110GRBL - Uncategorized Milan - Free user manual and instructions

USER MANUAL 159110GRBL Milan

• Press the RESET button on the back of the calculator before using it for the first time.

• Even if the calculator is operating normally, replace the battery at least once every three years. Dead battery can leak, causing damage to and malfunction of the calculator. Never leave the dead battery in the calculator.

• Avoid use and storage in areas subject to ex- treme temperatures. Very low temperatures can cause slow display response, total failure of the display, and shortening of battery life. Also avoid leaving the calculator in direct sunlight, near a window, near a heater or anywhere else it might become exposed to very high tempera- tures. Heat can cause discoloration or deforma- tion of the calculator’s case, and damage to its internal circuitry. Before

• Avoid use and storage in areas subject to humidity or dust. Never to leave the calculator where it might be splashed by water or exposed to large humidity or dust. These adverse condi- tions may damage its internal circuitry.

• Avoid any strong impact on the calculator, e.g. prevent it from dropping onto the floor.

• Never twist or bend the calculator. Avoid carry- ing the calculator in the pocket of your trousers or other tight-fitting clothing where it might be subject to twisting or bending.

• Never try to disassemble the calculator.

• Avoid pressing the keys of the calculator with a ballpoint pen or other pointed object.

• Use a soft, dry cloth to clean the exterior of the unit. If the calculator becomes very dirty, wipe it off with a cloth moistened in a week solution of water and a mild neutral household deter- gent. Bring out all excess moisture before wip- ing the calculator. Never use thinner, benzine or other volatile agents to clean the calculator. Doing so may remove printed markings and damage the case.3

Removing the Hard Case The hard case should be removed by sliding it downwards. It can then be affixed to the back of the calculator as shown below.

Turning the Calculator On and Off To turn the calculator on, press . To turn the calculator off, press ( ), that is, press and release the key, and then press (which has OFF printed in orange above it). Since the calculator has Static Memory,4

turning it off does not affect any information you have stored. To save energy, the calculator turns itself off after 10 minutes of no use. Power Supply

• This calculator is powered by two AAA batteries. Always make sure that the positive

terminals of the batteries are facing correctly when you load them into the calculator.

• Low battery power can cause any stored information to become corrupted or completely lost. Always keep written records of all impor- tant data.

• Never charge batteries, try to take batteries apart, or allow batteries to become shorted. Do not expose batteries to direct heat or dispose of them by incineration.

• Remove the batteries if you do not plan to use the calculator for a long time5

How to replace the battery?

1. Press ( ) to switch the calculator

2. Remove the screw that holds the battery

cover in place and then remove the battery cover.

3. Remove the old batteries.

4. Wipe off the sides of the new batteries with a

5. Load them into the calculator.

6. Put the battery cover back in place and secure

it in place with the screw.

7. Press to turn power on.

About the Keyboard Each key may have up to three functions: one printed on its face, a shifted function (in orange), and an ALPHA function (in blue). Press the appro- priate function key ( or ) before pressing the key for the desired function. For instance, to use the

function, press and release the key, then press . In this manual, this type of operations will be summa- rized as ( ).6

Acoustic feedback Acoustic feedback of the keyboard can be switched on and off by alternatively pressing

About the Display This calculator has a two-line display. It allows viewing both the calculation formula and its result at the same time. The first line can simultaneously display 12 cha- racters. However, entries up to 79 characters can be entered for a single calculation. In this case, entries with more than 12 characters will scroll to the left. When an entry reaches the 73

charac- ter, the cursor will change from “ ” to “ ” to let you know that only 7 more characters can be entered. ALPHA function SHIFT function

For numbers bigger or equal than 1,000 a separa- tor symbol facilitates reading the result by placing the separator “,” among every set of three digits. Cursor keys The cursor keys allow you to move around on the screen. Display Annunciators The display may show different indicators, which illustrate the current state of the calculator. Annunciator

Description The key is active. At the moment you press a key the keypad will unshift, and the8

annunciator will disappear. The key is active. At the moment you press a key the alpha mode will be exited, and the annunciator will disap- pear. The independent memory is storing a value.

The calculator is waiting for the user to input a variable name. Then a value will be assigned to this variable. This annuncia- tor appears after keying in

The calculator is waiting for the user to input a variable name to recall the variable’s value. This annunciator appears after pressing . The calculator is in the “statis- tical” mode. The default angle unit is set to degrees. The default angle unit is set to radians. The default angle unit is set to grads. A fixed number of decimal places has been set.

A fixed number of significant9

digits has been set.

Calculation history memory data is available. This allows browsing over previous for- mulas and replay them. The display is showing an intermediate result in a multi- statement calculation.

Calculator Modes It is important to enter the correct mode before start a calculation. The table below details the available modes. Type of calculation Key operations to switch to the correct mode Selected mode Basic arithmetic calculations COMP Statistical calculations

Regression calculations REG Pressing the key more than once sequen- tially displays additional setup screens. In all the sections below, the main title of each section is preceded by the required mode to perform the described calculations. Important note! If you want to restore the initial default calcula- tor mode, press

Decimal Point Character Dot Making Corrections during Input One of the first things you need to know is how to correct numbers and delete or insert characters. Key Description and Move the cursor to the desired location11

Erase the character immediately to the left of "_". If the cursor is placed at on top of a character, it deletes the number or function at the current cursor position.

The first time it is pressed, it changes to an insert cursor . Inputting something when the insert cursor is on the display insert the input at the insert cursor position. Pressing ( ) or when the insert cursor is “on” returns the cursor to its default behavior. Replay a Calculation When you press a calculation is performed, and the calculation formula is stored in the replay memory. You may know that there is something in the replay memory because the annunciator appears in the LCD. When you key in , the previous formula and result is displayed. Pressing again back steps sequentially from the newest to the oldest calculations. If you are viewing a replay memory calculation, pressing or makes the display change into editing mode. On the other hand, if you press12

the or key immediately after you finish a calculation, the editing screen for that calcula- tion is displayed. Multi-statements A multi-statement is an expression that is made up of two or more smaller expressions, which are joined using a colon (:). Example: Multiply

and then use the result as exponent of

3 3 ( ) 2 The following screen illustrates this example: Next, you should press , and the screen changes to: Note that this shows the first statement, and the annunciator appears in the screen to indicate that this is just an intermediate result. Pressing we can view the second statement and the final result:13

In order to perform basic calculations press the key, and then press to set the calculator into the COMP mode: COMP ....................................................MODE 1 Arithmetic Calculations Precedence Order of the Operations The following order of precedence applies to all calculations:

1. Coordinate transformation: from polar to

rectangular or vice versa ( or ).

2. Type A functions. These are all functions in

which the user first enters a value, and then the function key is pressed. E.g.: , , , , , etc. Angle unit conversions

5. Abbreviated multiplication format in front of

6. Type B functions. With these functions, the

user first enters a function key and then the value is entered. E.g.: , , , , , , , , , , , , , , , , , , .

7. Abbreviated multiplication format in front of

8. Permutations and combinations: ,

All operations are performed from left to right. However, if you concatenate operations of the same precedence, they will be carried out from right to left. E.g.:

When to use parentheses? Any operations enclosed in parentheses are performed first. Example:

All operations before can be neglected, since the calculator understands that the user aimed to close all pending parentheses before computing the result.15

Negative numbers within a calculation must be enclosed within parentheses. The negative sign is treated as a Type B function, so when the calculation includes a high-priority Type A func- tion (or power or root operations), parentheses are required to ensure a correct result. Example:

Remember: Any negative numbers within an expression should be enclosed within paren- theses. However, it is not necessary to enclose negative exponents within parentheses. E.g.:

Percentage Operations Percentage means “parts per hundred”. It can also be expressed as a fraction with a denominator of

100. Thus, a 10 percent solution may be ex-

pressed as 10%, 10/100, 0.10, or 10 parts per 100 parts. Example 1: To calculate 10% or 1200 1200 10 (%) Result: 12016

Example 2: To increase 1200 by 10% 1200 10 (%) Result: 1320 Example 3: To find out what percentage of 1200 is 120 120 1200 (%) Result: 10% Example 4: To reduce 1200 by 20% 1200 20 (%) Result: 960 Fraction Calculations Decimal / Fraction Conversion This calculator can work directly with fractions. Fractions can be classified according to 3 groups:

• Proper Fractions: The numerator is smaller than the denominator E.g.

• Improper Fractions: The numerator is greater than (or equal to) the denominator E.g.

• Mixed Fractions: A combination of an integer number and a proper fraction to express the decimal part. This calculator allows using any of these 3 types of fractions. To input an improper or proper fraction, you should key in the numerator, then press , and next enter the denominator. The symbol is displayed in the screen to separate one number from another (e.g. numerator from denominator). As stated above, mixed fractions are formed by an integer number and a fraction combined into one “mixed” number. Again, to enter a mixed fraction you should first key in the integer number, then press , enter the numerator, press again, and next enter the denominator. Operating with Fractions Example 1: calculations with proper fractions

Result: 11 15 This fraction can be converted into a decimal number by pressing . Example 2: conversions decimal / fraction

Result: 0.75 Result: 3 4 Example 3: calculations with mixed fractions

Result: 3 5 6 Example 4: simplifying a fraction

Result: 1 2 Operations involving fractions and decimal values result always in a decimal number. Example 5:

Result: 2.25 It should be noted that when the total number of digits of a fractional value (i.e. integer + numera- tor + denominator + separator marks) exceeds 10 characters, the values are automatically displayed in decimal format. Improper Fraction / Mixed Fraction Conversion The same amount can be represented either with an improper fraction or a mixed fraction. This19

conversion can be carried out simply pressing and . Example 1:

Some of the settings of the calculator can be changed at any time, depending on the user preferences. Thus, you can adjust the number of decimal positions, the number of significant digits, or the exponential display format. These settings are adjusted by pressing the key a number of times until you reach the following setup screen:

In order to perform basic calculations press the key, and then press to set the calculator into the COMP mode: COMP ....................................................MODE 1 Answer Memory Every time the calculator computes the result of an expression, the result is automatically stored in the Answer Memory. Therefore, the Answer Memory is updated when- ever the user presses any of the following keys: Function Keys Carry out current operation Add to memory Subtract from memory

(i.e. ) Store in memory followed by a variable name (A through F, X, Y or

You can recall Answer Memory contents by pressing . The contents of Answer Memory do not change if the operation performed by any of the above key operations results in an error. Answer Memory can store up to 12 digits for the mantissa and 2 digits for the exponent. Independent Memory Variable M is used as independent memory. Thus, you can input a value directly into memory with ( ), add it to memory pressing , or subtract it from memory with ( ). Independent memory is convenient for calculating cumulative totals. To clear independent memory M, press ( ) (M). Example:

Registers The calculator has nine general purpose registers that can be accessed as program variables (A through F, M, X and Y). These registers can be used to store data, constants, results, etc. Data stored in a particular register (e.g. A) can be deleted by pressing ( )

All the registers can be cleared at once by keying in ( ) (Mcl) . Example:

In order to perform scientific function calcula- tions press the key, and then press to set the calculator into the COMP mode: COMP ....................................................MODE 1 When using scientific functions, certain types of calculations may require some time to be com- pleted. Before starting the next calculation, wait for the result of the previous formula to appear on the display. The following constants will be used below:

Trigonometric / Inverse Trigonometric Functions This calculator can operate with trigonometric functions using either degrees, radians or grads. 90radians100 grads

You can set the default angle unit (degrees, ra- dians or grads), by pressing the key twice until you reach the following angle unit setup screen: Press the number key ( , , ) that corresponds to the angle units you want to use. Example 1: cos(23º 35' 2") = 0.916475268

Hyperbolic / Inverse Hyperbolic Functions The hyperbolic functions are analogs of the ordi- nary trigonometric functions: Just as the points (cos, sin)

Logarithms This calculator allows dealing with logarithms in an easy way. The base-10 logarithm of a given number is the power or exponent to which the27

base must be raised in order to produce the given number. Example 1: log 10003

Another widely used base for logarithms (beyond

10) is the mathematical constant

e » . This type of logarithm is known as natural logarithm (ln) , and can be easily used as illustrated below in the example. Example 2: ln 1

Roots and Exponents The keyboard arrangement of this calculator disposes roots and exponents in a single row for their easy localization. Using them is quite intui- tive: Example 1:

Permutations and Combinations Example 1: Determine how many different 4-digit values can be produced using the numbers 1 through 5, taking into account that numbers cannot be duplicated within the same 4-digit value (i.e. 1234 is allowed, but 1123 is not). 5 ( ) 4 Result:

Example 2: Determine how many different 3- member groups can be organized in a group of 8 individuals . 8 ( ) 3 Result:

Random Numbers Example: Generate a random number between

Result (this result differs each time):

Pressing the number key , or converts the displayed value to the corresponding angle unit. Example 1: Convert 2.25 radians to degrees. First of all, we should set the calculator in Deg. mode (which corresponds to the final units we want to obtain): (Deg. mode) Next, we introduce the value (2.25) followed by the specification of the units in which the number is expressed (radians).

Example 2: Convert 45 degrees to radians. (to set Rad. mode)30

And if you want to convert this into a

radians to degrees. (to set Deg. mode) 2 ( ) Result:

Conversion Polar / Rectangular coordinates Coordinates can be expressed in many different spaces. This calculator allows mutual conversion between Rectangular (also known as Cartesian) and Polar coordinates. Calculation results are automatically assigned to registers E and F. These registers are accessible by pressing ( ) and ( ), respectively. Example 1: Convert polar coordinates

= into rectangular coordinates

This result corresponds to the

coordinate, and has been stored in register E. To recall the value of coordinate

, press: ( ) Result:

If you want to see again the

coordinate, you must recall register E by pressing Example 2: Convert rectangular coordinates (2,2) into polar coordinates

Engineering Notation When we have to express very big or very small numbers, it is useful to use scientific notation, that is, instead of typing all the zeros, the number is expressed as a coefficient multiplied by a power of ten:

Normally, the coefficient can be any real number (2.3 in the previous example), and the exponent is an integer (8). The only difference between engineering notation and scientific notation is that in engineering32

notation the exponent is restricted to multiples of

3. Therefore, the previous number would be

Using only the exponents that are multiples of 3 allows to memorize a number of prefixes asso- ciated to every exponent: Magnitude prefixe Metric Symbol Power of Ten tera T

Example 1: Convert 0.00238 meters into millime- ters.

To go back to the magnitude in meters:33

Example 2: Convert 12320 meters into kilometers.

Data Input Considerations

• In the two statistical modes (SD and REG), the key operates as data input ( ).

• Make sure you clear statistical memory by means of ( ) before starting any data input.

• Multiple entries of the same data can also be introduced by means of ( ). Statistical Calculations34

• The existing data can be viewed by means of the cursor keys:

• To delete a data value, you should look for it using the cursor keys and then key in ( ). Deleting a data value causes all following values to be shifted up.

• When scrolling through data, the calculator shows both the data item and a separate screen for the data frequency (Freq) in the case you introduced multiple entries of the same data using ( ) to specify the number items of the same data values. It is possible to replace a data value while scrol- ling through data by entering the new value, and then pressing the key to replace the old value with the new one. This also means that if you want to carry out some other opera- tion (e.g. execute a statistical calculation, etc.), you should always press the key first to exit data display.

• After changing a value on the display, if you press ( ) instead of the key, the value you input is registered as a new data item, and the old value is leaved as it was.35

Memory Limit All data values are stored in the calculator memory. If there is no memory left for data storage, the calculator will show the screen: If this happens, you will not be able to input any more data. In this case, press the key, to display the following screen: Press if you want to register the value you just input, without saving it in memory. If you do this, however, you will not be able to display or edit any of the data you have input. On the con- trary, press to exit data input without storing the value you just input. Standard Deviation mode To perform statistical calculations using standard deviation press the key, and then press to set the calculator into the SD mode: SD ....................................................36

The MILAN M-240 calculator allows you to per- form statistical calculations on raw data. Once data is stored in memory, several operations can be carried out in SD mode. These operations are reached through two menus ( and ):

- mean - population standard deviation - sample standard deviation Once you reach any of these two menus, you should press the number key ( , ,

that corresponds to the function you want to compute, followed by the key .

key operation formula sum of squares of values

number of samples n37

key operation formula mean

sample standard deviation

Example: Consider the following data that corresponds to the readings of different temperature sensors covering an area to be monitored: 15, 14, 11, 15, 13, 13, 14, 12. Calculate

You should first set the SD Mode pressing , and then clear statistical memory by means of ( ) . Then, data can be already input following the key sequence: 15 ( ) 14 ( ) 11 ( ) 15 ( ) 13 ( ) ( ) 14 ( ) 12 ( )38

Population standard deviation:

Sample standard deviation:

Sum of squared of values:

Different types of regression can be selected in the menus that appear after entering the REG mode: key operation

Log Logarithmic regression

<x-data_n> <y-data_n> ( ) Be careful! If you press , this will input the same data twice. Use the following key operations to carry out the desired regression calculation: Key operation Calculation

Regression coefficient B For statistical regressions other than quadratic regression: Key operation Calculation

Correlation coefficient r

In the case of quadratic regression, use the key operations of the table below:41

Key operation Calculation

Linear Regression The regression formula for linear regression is: yABx

Example: Consider the following table with the annual average temperature and latitude of some European capitals. City Temperature

Determine the equation of the regression line of the average temperature

, and the correlation coefficient for both variables. Next, use the regression formula to estimate the expected average temperature for a city located at latitude 44 North. First of all, we should enter the data: 13 54 ( ) 24 37 ( ) 13 52 ( ) 14 52 ( ) 11 54 ( ) 13 53 ( ) 19 39 ( ) 14 53 ( ) 14 50 ( ) 19 40 ( ) 15 49 ( ) 22 42 ( ) Now, we can already compute the Regression Coefficient A (as described in the table above):

Correlation coefficient r:

Expected average temperature for a city at lati- tude 44 North: 44 ( ) Result:

Logarithmic, Exponential, Power, Inverse and Quadratic Regression The table below shows the regression formulas for each type of regression. Logarithmic Regression

All the types of regression described in the previous table can be recalled using the same key operations as those of linear regression.44

After introducing statistical data in the calculator’s memory under the SD or REG modes, it is not allowed to display or edit individual data items any longer. Therefore, to display individual data items, you should either (1) change to another mode; or (2) change the regression type (Lin, Log, Exp, Pwr, Inv, Quad).

When you have a problem... If calculation results are incorrect or if an error occurs, carry out the following steps:

• Press ( ) (Mode) , to initialize all modes and settings.

• Check the formula you are working with to confirm it is correct.

• Check if you have entered the correct mode and try performing the calculation again. If the above steps do not correct the problem, press the key , which makes the calculator perform a self-check operation and delete all data stored in memory if any abnormality is detected. Handling Errors45

Error Messages The calculator is locked up while an error message is on the display. Press to clear the error, or press or to display the calculation and correct the problem. Math ERROR Causes:

• The result of a formula is outside the allowable calculation range.

• Attempt to perform a function calculation using a value that exceeds the allowable input range.

• Attempt to perform an illogical operation (e.g. division by zero, etc.) Action:

• Check your input values and make sure they are all within the allowable ranges. Pay special attention to values stored in the registers A through F, X, Y or M. Stack ERROR Cause:

• The capacity of any of the two memory stacks has been exceeded. Action:

• Simplify the calculation. The numeric stack has 10 levels and the operator stack has 24 levels.

• Divide your calculation into two or more separate parts.46

• Attempt to perform an illegal mathematical operation. Action:

• Press or to display the calculation with the cursor located at the location of the error and make the required corrections. Arg ERROR Cause:

• Improper use of an argument. Action: