Computers and calculators are the tools of modern mathematicians.
A graphical calculator
There are many makes and types of calculators.
The examples below use keys typical to most scientific calulators.
To enter negative integers into a calculator use the . On some calculators this button is used.
e.g. To calculate -3 + -7 press:
Some calculators have a fraction button .
e.g. To calculate 3⁄4 + 8⁄9 press:
1 23 36 which means 123⁄36
If your calculator does not have a fraction button press:
1.638888889 which is equivalent to 123⁄36
Calculators have special buttons for square roots and cube roots . To find any other roots use the button
e.g To find the fourth root of 16,i.e. press:
To enter a number in standard form into a calculator:
||Enter 2.3 × 104 into calculator||23000|
Calculations can be carried out using the button.
e.g. To calculate (3.65 × 104) × (2.67 × 105) press:
9745500000 = 9.7455 × 109
In earlier years you may have studied the following calculator operations:
Calculators know about the order that calculations are carried out. i.e. BEDMAS
e.g. Calculate 35 + 4 × 27 on a calculator. Press: 143
Some calculators do not round numbers. e.g. gives 0.666666666. This is called truncating.
Some calculators round numbers up or down e.g. gives 0.666666667. This is called rounding.
This number is rounded to 9 decimal places as there are 9 digits after the decimal point.
|If the digit to the right of the rounded digit is between 0 and 4.||The rounded digit stays the same.|
|If the digit to the right of the rounded digit is 5 or above.||The rounded digit has ONE added.|
To find the square root of a number use this key e.g. To find the square root of 36, press 6
Square roots are often not whole numbers e.g. 6.08276253
The two brackets keys and are useful for calculations involving fractions.
e.g. Calculate Press: 0.357894736
There is a button for an index of 2 (squared) e.g. To find 1262, press 15876
To calculate with an index greater than 2 use the button e.g. To find 234, press 279841
Computer programs such as Microsoft Office and Appleworks include a part called a spreadsheet.
Spreadsheets can perform calculations using numbers and formulae arranged in rows and columns of cells.
Words or numbers can be typed into the cells and calculations and other mathematical operations can be carried out.
The spreadsheet on the left shows only 32 cells. Some spreadsheets have thousands of cells.
The letters are at the top of the columns.
To move around a spreadsheet use the cursor or keys such as the TAB, pg up, pg down (the arrow keys)
Many features of a spreadsheet can be changed (formatted) using various menu commands:
- The columns can be made wider
- The rows can be made higher
- Numbers and text in a cell can be made bold, coloured or a different size and font
- Numbers and text in a cell can be put on the left hand side, the right hand side or in the centre.
Spreadsheets do calculations differently from normal maths equations and calculators. To do a calculation you have to type in the EQUALS sign first. To do multiplication use the * key and for division use the / key.
The values in cells can also be used in calculations.
Numbers and words in both rows and columns can be sorted into order.
To do the sort shown below BOTH columns must be selected and the spreadsheet told to sort on the B column.
Most spreadsheets will produce graphs, such as pie graphs, line graphs, bar graphs and scattergraphs.
See the units on Statisitcial Graphs for instructions and practice with these.