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By awareness the role of megapixels in a digital camera, you will be able to buy the most excellent option at the cheapest cost. Even beginners will be able to decide a better camera.

Higher the megapixel count, better is photo-quality?

This is one of the most misunderstood concept about rating of digital camera and their photo quality. Consider a mosaic of tiles, each megapixel is like a tile and a mosaic of these tiles make a picture clearer. That is all right, but it doesn't mean that picture taken by a 10 or 12 or 50 megapixel camera will be more sharp than a 3 megapixel camera, because for most practicable purposes, 3 megapixel quality is fine enough. At the most you may require 6 - 8 megapixel for photo-quality as appears in megazines. Anything ahead of that isn't of much use to a non-professional photographer.
One megapixel is like one tile. When a picture is taken, the CCD or CMOS sensor in the camera receives an array of such tiles to create an image. It then converts it to electrical signals which are processed to make a picture. An array of 2048*1536 generates a pixel count of 31,45,728 pixel which is total to 3.1 megapixels.

What affects the quality of pictures then?

The quality of the lens, the algorithms used to make the photo from raw data composed by the sensor and the focusing mechanism are some of the other factors that affect the final result.
It should also be well thought-out, how large is the sensor in the camera. Consumer digital cameras have tiny image sensors. They are measured in microns. A micron is a millionth of a meter. Most sensors in consumer cameras are less than 10 microns. It is kept so so as to trim down the size of the camera so you can carry it in your pocket.

DSLR cameras have larger sensors. The main disadvantages of a smaller sensor is that it produce images with more noise than a large sensor. If you have to focus on a small area, it is difficult to do with a small sensor. Further, any shaking in handling the camera is exaggerated in a small sensor.

That means in right hand, with a appropriate sized sensor, a 6 MP camera is also good enough. In few scenarios a larger megapixel count may be useful, but for general purposes, it is not required.

In what scenario is a higher megapixel beneficial?

If you have to take the photograph of an aeroplane or a bird flying at a distance and you starting zooming with a digital camera, use digital zoom to reach it, the picture becomes granular. This is a typical defect of the digital zoom. In such a case, if you have a higher megapixel count, you won't need the digital zoom.

Buy wisely choosing the appropriate megapixel rating you will be able to get a cheapest yet a better digital camera.