Why are significant figure used in science?

Answer 1

Many numeric values in science cannot be expressed precisely. This may be because of variability. For example, the distance to the moon can be measured to an accuracy of around a millimetre, but the lunar orbit ranges from 356,400 km to 406,700 km so that a figure given accurate to 0.000 001 km is ludicrous!

Sometimes the values are not precise because of limitations in measurement: particularly when dealing with extremely large or small numbers. The Milky Way galaxy is thought to have a diameter of around 100,000 light years, but it could be as much as 180,000 ly.

Sometimes, even when the number is a constant, it may not be possible to express it exactly. As an example, the ratio of a circle's circumference to its diameter, pi, is an irrational number and so has infinitely many digits. It has been calculated to over 10 trillion digits. However, it has been estimated that just 40 digits is sufficient to describe the angle subtended by a hydrogen atom (the smallest atom) at the far end of the know universe. For school work, 3 significant figures (3.14) is usually sufficient and, you will rarely have to use more that 6 sig figs (3.14159).