State the number of significant figures.
1) 809 Answer : 3
2) 0.0060 Answer : 5?
3) 0.00000095 Answer : 9?
4) 5.60 Answer : 3
5) 5.743 Answer : 4
6) 0.010 Answer : 4?
Physics Help - bobpursley, Sunday, September 11, 2011 at 4:59pm
2, 3, 6 are wrong: Zeroes to the left of significant digits are NOT significant, unless they are between two non zero digits.
---I don't understand. Could you please explain more simply.
3.0006 five sig digits.
0.0006 one sig digit.
0.00060 two sig digits.
Reread the rule I quoted you now.
0.0006 one sig digit.
-which digit is significant?
6?
0.00060 two sig digits
60 are significant digits?
Sure! When we talk about significant figures, we are referring to the digits in a number that are considered to be reliable or meaningful. In general, the rules for determining the number of significant figures in a number are as follows:
1) Non-zero digits are always significant. For example, in the number 809, all three digits (8, 0, and 9) are non-zero and therefore significant.
2) Zeroes between non-zero digits are significant. For example, in the number 5.743, all four digits (5, 7, 4, and 3) are non-zero and therefore significant.
3) Leading zeroes (zeroes to the left of the first non-zero digit) are not significant. For example, in the number 0.0060, there are two significant digits (6 and 0) because the leading zeroes are not considered significant.
4) Trailing zeroes (zeroes to the right of the last non-zero digit) may or may not be significant, depending on whether they serve to define the precision of the number. In general, if the number is not explicitly written in scientific notation, trailing zeroes are assumed to be significant. For example, in the number 5.60, all three digits (5, 6, and 0) are significant.
Based on these rules, let's revise the number of significant figures for the given numbers:
1) 809: 3 significant figures
2) 0.0060: 2 significant figures
3) 0.00000095: 2 significant figures
4) 5.60: 3 significant figures
5) 5.743: 4 significant figures
6) 0.010: 2 significant figures
I hope this explanation helps! Let me know if you have any further questions.
Sure! Understanding significant figures is important in physics and other sciences because they indicate the precision of a measurement or calculation. Here are some guidelines for determining the number of significant figures:
1) 809: This number has three digits, so it has three significant figures.
2) 0.0060: Zeros to the left of the first non-zero digit (in this case, 6) are not significant unless they are between two non-zero digits. Therefore, this number has two significant figures (the two zeros after the decimal point are significant).
3) 0.00000095: Similar to the previous example, trailing zeros after the decimal point and to the right of non-zero digits are significant. Therefore, this number has two significant figures.
4) 5.60: All non-zero digits and the zeros between them are significant. Thus, this number has three significant figures.
5) 5.743: All digits in this number are non-zero, so it has four significant figures.
6) 0.010: The zeros to the left of the 1 are not significant (unless they are between two non-zero digits). Thus, this number has only one significant figure.
Remember to count all non-zero digits and any zeros between non-zero digits and after the decimal point to determine the number of significant figures.