When is 0 a significant figure/digit?

Question

I have my maths gcse tomorow and I'm still not clear on this. When is a zero a significant figure? Or, when is it NOT a significant figure?

Thanks

Answer 1

Zero is significant when (a) it is placed to the right of a non-zero digit in a whole number and (b) it is placed to the right of a decimal point.



Zero is insignificant when (a) there are no non-zero digits to its left in whole numbers and (b) it is placed to the left of decimal point without other digits behind it.

Answer 2

Leading zeros are never significant digits.



Trailing zeros are significant digits if there is a decimal point in the number.



The word 'significant digit' means a digit that carries information related to the *precision* of the number.



For example, 72.000 carries more implied precision than 72.0 or just 72 ... so the three 0's after the decimal point are significant. In other words, it says that the value is known to be *exactly* 72 to at least to three decimal places (so 72.000 has a total of five significant digits).



This is why it's important never to add zeros to a measurement to make it look more precise than it is. For example, if I take a tape measure and measure the width of a piece of carpet as about 72 inches (6 feet) ... reporting this as 72.000 inches *implies* precision that I don't really have in the measurement.



It's also important not to *drop* a trailing zero, if that is part of the measurement. If I measure something as *exactly* 72.0 inches, then dropping the trailing zero to report this as 72 inches loses some precision. That's why the zero is 'significant' (meaningful).





Leading zeros are never significant digits. For example, 74 has two significant digits. So does 0.000000074. That still has only two significant digits.



74.0 has three significant digits. So does 0.00000740.





What about trailing digits with no decimal point? This is trickier.



For example, if I say that the population of Chicago is 2,900,000, those zeros are not significant digits. I.e. it is the same as saying "2.9 million."



But if I say that the population is 2,895,380, then that last zero probably *is* significant (i.e. it is not there because of rounding, but because we have an exact count right down to the person ... i.e. it's one more than 2,895,379).

Answer 3

For the best answers, search on this site https://shorturl.im/HHKzG



Here are some general rules for determining significant figures: 1. Trailing zeros to the right of a decimal place are always significant. Ex: 1.5000 2. Leading zeros to the right of a decimal place are not significant unless there is a non-zero integer to the left of the decimal. Ex: 0.000345 --- Zeros are not significant -50.005 - All digits are significant (integer is -50) 50.500 - All digits are significant (integer is 50 AND Rule 1 applies to trailing zeros) 3. Trailing zeros to the left of the decimal point are not significant UNLESS there is either a marked decimal point and/or there are digits to the right of the decimal point. Ex: 500 has only one significant figure (no decimal) 500. (There is a decimal point after the last zero) -- all digits are significant 500.0 All digits are significant (Rules 1 and 3 apply) 500.004 All digits are significant (Rules 1 and 2 apply) 500.050 All digits are significant (Rules 1, 2, and 3) 4. Counting numbers (anything that is not measured and therefore has no possibility of error) has an infinite number of significant figures. The relationship to certainty to significant figures can be shown in this example: If you said the distance between New York City and Los Angeles, CA is 3000 miles, than you can only say for certain that the actual distance is somewhere between 2500 and 3500 miles.(1 significant figure) If you said this distance were 3200 miles (2 sig figs) then you know for certain that the actual distance is between 3150 and 3250 miles. If you said this distance were 3220 miles, (3 sig figs) then you know for certain that the actual distance is between 3215 and 3225 miles. Special note: If this were written as 3200 miles with a bar above the next-to-last zero (this may be older notation, I'm not sure what they might be using), that would specify that the next-to-last zero IS significant, and you would be certain the distance is between 3195 and 3210 miles). So, an otherwise insignificant zero may be considered significant IF specified. If you said the distance were 3224 miles (4 significant digits), then you know for certain that the actual distance is somewhere between 3223.5 and 3224.5 miles. If you said the distance were 3224.000234 miles (10 significant digits), than you know for certain that the distance is between 3224.0002335 and 3224.0002345 miles. So the number of significant digits that you can use in calculations and answers is based on the precision of your measurements. The more precise your measurements can be made, the more significant digits that can be used. You couldn't use 10 significant figures in the last example, unless you are able to make measurements to the nearest 0.0000005 inches. This also explains why counting numbers have an infinite number of significant digits because they are not measured quantities and therefore not subject to any possibility of error. Accuracy relates more to the generally accepted value and does not necessarily have any relationship to precision. In answer your last two questions why your calculations are limited by the quantity with the least number of significant figures; this is because the possible error introduced by the measurement with the least number of significant digits is greater than the precision of your final answer and thus overriding the answer itself. This would be like saying the distance from Los Angeles to New York City wan be calculated to 3224.000234 miles- but can you really make measurements with that kind of precision? So, you can say that if you can make your measurements more precise, you can use more significant figures; just not necessarily the other way around. In answer to your last question, the reason 800.1 has 4 significant digits:See Rule 3 (with decimal) above. Hope this helps.

Answer 4

This Site Might Help You.



RE:

When is 0 a significant figure/digit?

I have my maths gcse tomorow and I'm still not clear on this. When is a zero a significant figure? Or, when is it NOT a significant figure?



Thanks