1.4.6. Controlling the appearance of floating point number

MATLAB by default displays only 4 decimals in the result of the calculations, for example 163.6667, as shown in above examples. However, MATLAB does numerical calculations in double precision, which is 15 digits.

When you perform calculations in MATLAB, the results are shown with four decimal places by default. For example, if you calculate a number like -163.6667, that's how it will appear in the output. However, MATLAB actually performs these calculations using a method that allows for much greater precision, up to 15 decimal places. This difference is important when you need highly accurate results, but often you don't need to see all 15 digits in everyday calculations.

Think of it like a high-quality camera. The camera can capture many more details (15 digits of precision), but the pictures you usually see are cropped down to a more manageable level (4 decimal places) to make them easier to view and use. If you needed a super detailed image, you would get the original high-res file, much like getting the full floating point representation from MATLAB.

The command format controls how the results of computations are displayed. Here are some examples of the different formats together with the resulting outputs.

format short x=-163.6667 If we want to see all 15 digits, we use the command format long format long x= -1.636666666666667e+002 To return to the standard format, enter format short, or simply format.

MATLAB provides a command called 'format' that lets you control how numbers are displayed after calculations. You can set it to 'short' for displaying a few decimals or 'long' to see all available digits (15). For example, when you type 'format short', it will display numbers like -163.6667. If you change it to 'format long', it will show you a more precise version like -1.636666666666667e+002, which gives different detailed information about the number. You can always switch back to the default behavior using 'format short'.

Imagine switching between two types of digital watch faces. One shows the time simply in hours and minutes (like format short), while the other shows the seconds and fractions of seconds (like format long). Depending on what you need, you can choose the more detailed display or go back to a simpler time view.

Note - Up to now, we have let MATLAB repeat everything that we enter at the prompt (>>). Sometimes this is not quite useful, in particular when the output is pages en length. To prevent MATLAB from echoing what we type, simply enter a semicolon (;) at the end of the command. For example,

x=-163.6667; and then ask about the value of x by typing, x x = -163.6667

In MATLAB, when you enter a command, it typically displays the command you wrote along with the result. Sometimes, this can lead to a lot of output being cluttered on the screen, especially if the results are lengthy. To avoid this echoing of commands, you can put a semicolon (;) at the end of any command. This tells MATLAB to perform the operation without showing it on the screen. You can still check the result later by typing the variable name, like you would do with 'x'.

Think of it like chatting with a friend. If every time you spoke, your friend repeated back everything you said before giving a response, conversations would feel repetitive and slow. But if your friend only answered back with what's important and relevant (the result) without repeating your full statements (the command), the conversation would flow much smoother.

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