 # Significant Figures : Errors In Measurements ## What are Significant Figures?

“The significant figures of numbers are digits convey the meaning that contributes to its measurement resolution”. The number 13.2 is comprised of three significant digits. Non-zero digits are always significant. 3.14159 has 6 significant digits (all the numbers give you useful information). Thus, 67 has 2 significant digits, and 67.3 has three significant digits.

1000 has 1 significant digit (only the one is interesting; you don’t know anything for sure about the units, tens and hundreds of places; the zeroes may just be place holders; Similarly for decimals, 0.00069 has 2 significant digits (only the 6 and 9 tell us something; the other zeroes are placeholders, only providing information about relative size). But this rule has an exception, as in the case of 0.000690 has 3 significant digits (that last zero tells us that the measurement was made accurate to that last digit, which just happened to have a value of zero). one thousand six (1006) has 4 significant digits (the one and six are significant, and we have to count the zeroes because they’re between 2 the significant digits).

### Application of Significant Figures

These examples can be incorporated into a list of rules for Significant Figures;

• All nonzero digits are significant: 4.321g has four significant figures.
• Zeroes between nonzero digits are significant: 1002kg has 4 figures.
• Leading zeros to the left of the first nonzero digits are not significant;
• Trailing zeroes that are also to the right of a decimal point in a number are significant:0.0260 mL has three significant figures.
• When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant: 140 kilometres may be 2 or 3 significant figures.

To resolve this confusion presented by the last rule, we can use the standard exponential representation of the numbers. For example,

3.69 × 104 calories (3 significant figures)

3.069 × 104 calories (4 significant figures)

### Exact Number

Some numbers are known with certainty like there are 12 inches in a foot or there are 50 students in a class. Such measurements do have scope for uncertainty. Exact numbers are often found as conversion factors or as counts of objects.

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