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Radioisotope dating involves calculations involving the half-life of specific radioactive isotopes. If these calculations are not correct (which sometimes happens), the age of the sample will be incorrect.
For example: (this questions was posted on eNotes previously)
I am a famous paleontologist and an expert in radioactive-dating techniques. I examine a dinosaur fossil footprint and discover that the fresh mud the dinosaur stepped in had just been covered with a thin layer of volcanic ash. I study the amount of potassium-40 and argon-40 in the ash. The ratio shows that 1/10 of one potassium-40 half-life has passed since the footprint was made. I know that the half-life of potassium-40 is 1.3 billion years.
If you do the calculations correctly, you will find an age of 130 million years for the fossil. If you don't get the correct decimal placement, you will find another number (13 million, 1.3 million, etc.).