What is significant figures or numbers?

Answer 1

"Numbers is just what you think.

any combination of 0-9.

for example: 0, 5, 312312033331984912841, pi, sqrt(2), sin(3), ... all of those are numbers.

Now, when you talk about significant figures you are USUALLY talking about measurements.

For example: How far did you walk today? If you answered 1 mile. I am willing to bet you did not walk EXACTLY 1 mile. But somewhere between 1/2 mile to 1 1/2 miles. Now, if someone said they walked 1.1 miles. They probably used a measuring device and it is accurate to say 1.05 to 1.15 miles. Similarly if they say that they walked 1.1134 miles, then it is actually between 1.11335 and 1.11345 miles that they actually walked, because the instrument they used was only accurate to the ten-thousand's of a mile.

So, to count significant figures you do the following

1) Count all non-zero digits.

2) Count all 0's BETWEEN 2 non-zero digits

3) count all 0's AFTER a decimal if it is ALSO after a non-zero digit (eg. 0.003 only has 1, but 0.0030 has 2)."

The number of significant digits is the number of digits in a measurement that are statistically justified. This number is solely defined by the degree of uncertainty on the measurement. If your measurement is 5.70 +/- 0.01 you have three significant digits. If your measurement is 56.798 +/- 0.002 the number of significant digits is 5.

Note that leading zeros do not count (0.00000078 = 7.8 E-7)

Answer 2

Significant figures are the digits of a number which convey useful meaning. If I say that there are about 7 billion people in the world, the full number is 7,000,000,000 however, the nine zeroes do not really tell me anything other than how large the number is, since the world does not actually have exactly seven billion people. This number has only one significant digit, which is the 7. If I were able to determine (hypothetically) that there are precisely, 7,004,867,591 people in the world at this very moment (and of course, people are being born, and people are dying, all the time) then I would have ten significant digits.