How do you know which numbers are significant?

Answer 1

The basic idea is to count the digits, except for leading zeroes. Take this number as an example: 0.003080. The leading zeroes are only there to fill in, to give the number its proper magnitude - so they are not significant. (In scientific notation, the number would be 3.080 x 10-4 - the leading zeroes can be omitted in this case.) The other zeroes are significant: the final zero has only been added to indicate that this digit is known precisely; the zero in between just happens to be zero. So, the number in this example has 4 significant digits.

Another example: 25,000. Unfortunately, we don't know whether the zeroes just happen to be zero, or whether the number has been rounded to two significant digits. If you don't know more information, assume it has 2 significant digits. However, to avoid ambiguities, if the number does have more significant digits, this should somehow be stated. One option is to use scientific notation: 2.5 x 104 has 2 significant digits, while 2.500 x 104 has 4.

The basic idea is to count the digits, except for leading zeroes. Take this number as an example: 0.003080. The leading zeroes are only there to fill in, to give the number its proper magnitude - so they are not significant. (In scientific notation, the number would be 3.080 x 10-4 - the leading zeroes can be omitted in this case.) The other zeroes are significant: the final zero has only been added to indicate that this digit is known precisely; the zero in between just happens to be zero. So, the number in this example has 4 significant digits.

Another example: 25,000. Unfortunately, we don't know whether the zeroes just happen to be zero, or whether the number has been rounded to two significant digits. If you don't know more information, assume it has 2 significant digits. However, to avoid ambiguities, if the number does have more significant digits, this should somehow be stated. One option is to use scientific notation: 2.5 x 104 has 2 significant digits, while 2.500 x 104 has 4.

The basic idea is to count the digits, except for leading zeroes. Take this number as an example: 0.003080. The leading zeroes are only there to fill in, to give the number its proper magnitude - so they are not significant. (In scientific notation, the number would be 3.080 x 10-4 - the leading zeroes can be omitted in this case.) The other zeroes are significant: the final zero has only been added to indicate that this digit is known precisely; the zero in between just happens to be zero. So, the number in this example has 4 significant digits.

Another example: 25,000. Unfortunately, we don't know whether the zeroes just happen to be zero, or whether the number has been rounded to two significant digits. If you don't know more information, assume it has 2 significant digits. However, to avoid ambiguities, if the number does have more significant digits, this should somehow be stated. One option is to use scientific notation: 2.5 x 104 has 2 significant digits, while 2.500 x 104 has 4.

The basic idea is to count the digits, except for leading zeroes. Take this number as an example: 0.003080. The leading zeroes are only there to fill in, to give the number its proper magnitude - so they are not significant. (In scientific notation, the number would be 3.080 x 10-4 - the leading zeroes can be omitted in this case.) The other zeroes are significant: the final zero has only been added to indicate that this digit is known precisely; the zero in between just happens to be zero. So, the number in this example has 4 significant digits.

Another example: 25,000. Unfortunately, we don't know whether the zeroes just happen to be zero, or whether the number has been rounded to two significant digits. If you don't know more information, assume it has 2 significant digits. However, to avoid ambiguities, if the number does have more significant digits, this should somehow be stated. One option is to use scientific notation: 2.5 x 104 has 2 significant digits, while 2.500 x 104 has 4.

Answer 2

The basic idea is to count the digits, except for leading zeroes. Take this number as an example: 0.003080. The leading zeroes are only there to fill in, to give the number its proper magnitude - so they are not significant. (In scientific notation, the number would be 3.080 x 10-4 - the leading zeroes can be omitted in this case.) The other zeroes are significant: the final zero has only been added to indicate that this digit is known precisely; the zero in between just happens to be zero. So, the number in this example has 4 significant digits.

Another example: 25,000. Unfortunately, we don't know whether the zeroes just happen to be zero, or whether the number has been rounded to two significant digits. If you don't know more information, assume it has 2 significant digits. However, to avoid ambiguities, if the number does have more significant digits, this should somehow be stated. One option is to use scientific notation: 2.5 x 104 has 2 significant digits, while 2.500 x 104 has 4.