Note that the inputs are standard notation numbers. The answers are formatted in scientific notation and E notation. In scientific notation a large number is converted to an equivalent decimal number between 1 and 10, multiplied by 10 raised to some power. Very small numbers are converted to an equivalent decimal number between 1 and 10, multiplied by 10 raised to some negative power.
In this example scientific notation calculation we're solving 1. E notation is also known as exponential notation.
E notation is the same as scientific notation where a decimal number between 1 and 10 is multiplied by 10 raised to some power. In E notation the "times 10 raised to a power" is replaced with the letter e in either uppercase or lowercase.
The number after the "e" indicates how many powers of In this example calculation we're adding 1. There are some cases where you would not want to auto-calculate significant figures.
If your calculation involves a constant or an exact value as you might find in a formula, do not check the "auto-calculate" box. If you measure a radius of 2. The order of magnitude when written in standard form, is the nth power of For example, 3.
See the Scientific Notation Calculator to add, subtract, multiply and divide numbers in scientific notation or E notation. To round significant figures use the Significant Figures Calculator. To see how standard form is similar to scientific notation visit Standard Form Calculator.
If you need a scientific calculator see our resources on scientific calculators. Note that if you attempt to use for subtraction, for example , you will generate a Syntax Error.
Calculate each of the following using your calculator. In each case, give your answer as a decimal not as a fraction. Remember to press to obtain a decimal answer. You may have been surprised that the correct answer to part 5 is negative. If we wanted to calculate the square of , we write this mathematically as and would need to use the brackets when evaluating it on a calculator. When your calculator is in Math mode, as recommended, fractions are entered using the button in the left-hand column of the function key area of the calculator keypad.
When the button is first pressed, the cursor is located in the top box ready for you to enter the numerator. To move to the bottom box to enter the denominator, use the cursor down key.
If there are further parts of a calculation to be entered when the template has been completed, the right cursor key can be used to move out of the denominator in preparation for the input of the rest of the calculation.
Mixed numbers such as can be entered similarly using the mixed number template obtained using the key sequence. This template provides three boxes to fill, one for the whole number part, and one each for the numerator and denominator of the fractional part.
The decimal answer can be obtained by using. Remember to use the cursor right key to move the cursor out of the denominator of the fraction before entering the multiplication sign.
If you obtained the answer , you calculated by mistake. You may have noticed that the results of both these exercises were displayed on the calculator as top-heavy fractions.
This is the default behaviour of the calculator in Math mode. You can toggle between a top-heavy fraction and its mixed number equivalent using the key sequence.
Here, the key is used to access part of the on-screen menu that is not initially visible. Remember to use to toggle between the top-heavy fraction and mixed number answers. Remember to use the template obtained using and to use the cursor arrow keys to move between the boxes when inputting the mixed number. The volume of wood in cubic metres contained in a log of length metres with a distance around its middle of metres is given by the formula. In this section we consider several different approaches that can be used to evaluate this and other more complex expressions using different functions on your calculator.
While the first method — considered in Activity 9 — is probably the most straightforward for this relatively simple expression, it is useful to see how you might use other calculator functions when you are faced with more complicated expressions to evaluate. The expression for the volume of wood requires the value of.
You could enter an approximate value for by hand, but this is time-consuming and may be prone to error. The calculator has an approximation for built into it, which is obtained using the key sequence. The key is located on the bottom row of the keypad. The most obvious way of calculating is to enter it as a fraction on your calculator.
The key sequence used was. Note that it is not strictly necessary to include the multiplication between the 4 and the in the denominator since if the sign is omitted, it will be assumed by the calculator.
Another way to carry out the calculation in Activity 9 is to use the key. Can you explain why? Then type this new expression into the calculator and check that you obtain the same answer as in the activity above.
Typing into the calculator and pressing will not give the correct answer because the calculator will follow the BIDMAS rules and divide by 4 and then multiply by , instead of dividing by. To obtain the correct result, you have to type. Alternatively, you can type. Note that on some later models of the calculator, the correct answer is obtained without adding the brackets to the denominator; however it is good practice to add the brackets to ensure the correct calculation is carried out.
An alternative approach to our calculation is to calculate the denominator of the fraction first, and then divide the numerator by this.
You could write down the answer to the first part of the calculation on paper, and enter it into the calculator again. However, it is possible that you may make an error either in writing down the number or in typing it into the calculator. A better method is to use the fact that the calculator retains the last calculated answer, which can then be inserted in the subsequent calculation using the key located at the bottom of the keypad.
Note that the key only remembers the result of your last calculation. Use your calculator to calculate the value of the denominator of , then complete the calculation by finding the value of to 3 significant figures. A variation on the above method is to break the calculation into two parts, and use the memory functions of the calculator to store the result of the first part.
The calculator memory is particularly useful when you want to calculate the values of several expressions that have a common part. This common part need be entered only once and its value reused several times subsequently. For example, rewriting the formula for the volume of wood contained in a log as. If we wished to calculate the volume of wood contained in several different logs, it might be efficient to calculate the value of once, store it in memory and reuse this value in the subsequent calculations.
The calculator has several different memories. Before using the calculator memory, it is good practice to always clear any previous data stored in the calculator using the key sequence CLR Memory Yes.
To store the result of an expression just calculated i. After selecting the store function, we need to tell the calculator which memory the value is to be stored in.
Once or STO has been pressed, the display indicator RCL or STO is shown on the display to indicate that the calculator is waiting to know which memory to recall store the value from in.
The value of which equals 0. This value can then be used to find the final result using M , which gives 0. Expressions can also be stored in, added to or subtracted from the memory at the same time as they are evaluated by replacing the at the end of a calculation with one of the memory access sequences. For example, to calculate and store the result straight into the memory, use the key sequence STO M. Each memory name is printed in red above the key used to access it.
If the result of a calculation is a number greater than or equal to i. For example, calculating gives the answer. Small numbers are also automatically displayed using scientific notation. However, how small the number needs to be for this to happen depends on the mode the calculator is working in:. In Activity 1 you will have already set your calculator to use Norm 2 mode, and we suggest that for the moment you continue to use this.
You can also set the calculator to always display results using scientific notation with a set number of significant figures using the key sequence SETUP Sci followed by the number of significant figures required, for example. When your calculator is set in this fashion, the display indicator SCI is displayed at the top of the screen.
Numbers expressed in scientific notation can be input directly to the calculator by using the key on the bottom row of keys. For example, can be entered using the key sequence. Use the scientific notation functions of your calculator to calculate each of the following, giving your answer in both scientific and ordinary forms. In Activity 4 you saw how to use the key to input powers on the calculator.
The key can be used with other functions, such as the fraction template , to calculate fractional and negative powers. Calculate each of the following using your calculator, giving your answer correct to 3 significant figures. Just as there are keys on your calculator for entering powers, roots can also be entered directly.
Square roots can be calculated using the key. For example, can be entered using. Cube roots are entered using the second function of this key. For higher roots, such as fourth or fifth roots you need to use the more general template, which is the second function of the key. This template is filled in by using the number and arrow keys and in a way similar to that used when the fraction template is completed. You will notice from the result of Activity 15, part 4 that the calculator sometimes presents answers using surds.
To find the decimal equivalent of an answer like this, you can use the or keys that you used earlier to find the decimal forms of fractional answers. Sometimes when entering into your calculator an expression involving roots, you may accidentally forget to press the appropriate function key. However, moving the cursor to the correct point and pressing the missing key, as in section 1, will not work as this simply inserts an empty template.
If you wish to edit an expression to insert a missing root, first move the cursor to the correct place — that is, to the left of the number. There are various different units in which an angle can be measured, degrees being one of the possibilities. Before using your calculator to find the values of the trigonometric ratios of angles measured in degrees, you need to ensure that it is set to use the correct units.
Always check that your calculator is using the correct system of angle measurement before using trigonometric ratios. Your calculator is set to use degrees if the display indicator is shown at the top of the screen. If you see the indicator or , then your calculator is set to use different units for measuring angles. To calculate the sine, cosine or tangent of an angle, press the , or key and then type in the size of the angle. Note that the , and keys automatically open a bracket for you.
If you are simply calculating the sine, cosine or tangent of an angle, just press after entering the angle — there is no need to close the bracket.
If you are using these ratios as part of a larger calculation, then you will need to remember to close the bracket yourself by pressing before entering the remainder of the calculation. Some older models of calculator require the angle to be input first, followed by the , or button.
Calculate the value of each of the following using your calculator, giving your answers correct to 3 significant figures. If you obtained the answer 0. Note that when entering this expression in your calculator, it is possible to omit explicitly entering the multiplication between the 2 and since the calculator will assume it.
Note that means first find the sine of , then square the answer. The key sequence to enter into the calculator is thus. The first is necessary to close the bracket automatically opened when pressing , and the second closes the bracket opened at the start of the sequence.
Since the calculator evaluates the sine as soon as it encounters the first closing bracket, it is possible to enter this expression using the alternative sequence , but this is not recommended as the former is more clear. It is a property of trigonometric ratios that for any angle ,.
You will notice from the answer to part 3 that the calculator displays the ratios of some angles as fractions, involving surds where needed, and not in decimal form.
The decimal form can be found using or.
0コメント