Fixed-length integers and fractions are widely used for fast computation in computer hardware. These aren't the only ways to represent numbers. It is possible to have a program allocate extra memory as it is needed to represent very large integers, and perform arithmetic on them. The cost of this is extra storage and extra processing time. It is also possible to store and manipulate fractions as ratios --- 3/5, for example --- and carry out arithmetic on them (for example in the programming languages LISP or Scheme).
Other sorts of information can be stored using bit patterns. There were a variety of systems for representing the upper- and lower-case letters of the Latin alphabet (the one we use in English), plus numerals, punctuation, and significant non-printing symbols (end-of-line, for example). These became standardized in the American Standard Code for Information Interchange (ASCII) system where 7 bits are used to represent 128 different symbols. Computers often organize bits into groups of eight (called bytes), and the ASCII code is often extended by one bit, which doubles the number of symbols that can be represented (but there isn't agreement on which symbols to assign to the extra 128 bit patterns). [ASCII character encoding].
By using two bytes (16 bits) the number of characters that can be represented increases enormously: 65,536 different bit patterns are available. Unicode now allows the possibility that text written in many different writing systems can be represented in a standard way on computers. [Unicode Home Page].
Sound can be represented by sampling the amplitude (strength) of the sound wave at regular intervals, and storing the strengths as numbers. This technique is plausible if you think of sound being propagated to your brain by the amplitude and frequency at which your eardrum moves. Sampling 8000 times per second has been sufficient for telephone technology, but music recording requires a great deal more (44K for CDs, and formats with greatly increased frequency are now available).
Images can be represented as a grid of numbers, with each number representing the strength of a particular colour in one pixel (picture element) of the image. Since a detailed picture c'ontains a large number of pixels, a great deal of storage is needed, even for relatively small images. Different image formats make different choices about how many different colours to encode for each pixel. A common bit map format is to use one byte (8 bits) for each of three primary colours. The values of these three bytes specify the intensity of red, blue, and green light for that pixel, and the combination gives a large range of colours. [Different formats of image files]. If you're at a CDF terminal, try typing 'showrgb | less' (omit the quote marks).