When do zeros count?

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When do zeros count?

Postby Andrea_1H » Sun Oct 06, 2019 8:02 pm

I'm still unclear as to when zeros are counted in the number of sig figs and when they aren't. Why does 1.00 have 3, but 0.01 only have 1? Can someone explain the difference?

Lelija Kazlauskas 3J
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Re: When do zeros count?

Postby Lelija Kazlauskas 3J » Sun Oct 06, 2019 8:04 pm

1.00 has 3 sig figs because there is a decimal point. When there's that decimal point, it means that we are certain that the number 1.00 is within a hundredths place of the actual value.

0.01 only has 1 sig fig because it contains leading zeroes. If you had 0.0000000001, it would still have only 1 sig fig, but if you had 0.000000000101, it would have 3 sig figs.

Kendra Barreras 3E
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Re: When do zeros count?

Postby Kendra Barreras 3E » Sun Oct 06, 2019 8:06 pm

The zeroes before a non zero number never count (ie 0.0005 has 1 sigfig)
The zeroes after a non zero count because they are telling you that you are sure of that digit until that last zero (ie 12.2300 has 6sf) because a sig fig is all the digits that you are sure of plus the one you are unsure of, therefore for 12.2300 you are sure of the first 5 digits and the 6th you are unsure of.
Lastly, "sandwiched" zeroes always count (ie 3004 has 4 sig figs)

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Re: When do zeros count?

Postby gabbymaraziti » Sun Oct 06, 2019 9:05 pm

Why is it that 3000 only has one sig fig, but 3000. has four? What is the significance of the decimal when there are no figures following it?

Indy Bui 1l
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Re: When do zeros count?

Postby Indy Bui 1l » Sun Oct 06, 2019 9:34 pm

Leading zeroes don't count. For example, "0.001" or "002" each only have one significant figure. Any zeroes coming before a number do not count towards sig figs. Sandwiched zeroes do, however, count "1001" has four sig figs and "202" has three.

zeroes coming after a figure do not count, UNLESS there is a decimal.

For the example "3000" has 1 sig fig but when written "3000." it has four. The decimal is inserted to specify four sig figs in this example. Sig figs are usually specified when using certain scientific instruments that are set for millimeters, centimeters, etc. Sig figs are important in this regard because it shows exactly how and by how much an instrument measures by. 300.00 being five sig figs may look silly compared to just writing a single sig fig number like 300 , but it is important to note that the instrument measures to the 0.00 degree.

Anna Heckler 2C
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Re: When do zeros count?

Postby Anna Heckler 2C » Sun Oct 06, 2019 9:38 pm

The fact that 3000 has 1 sig fig but 3000. has 4 sig figs has to do with the accuracy of a measurement. If you reported a measurement as 3000 lbs, someone could infer that the scale you were using was accurate to the nearest thousand. However, if you reported a measurement as 3000. lbs, someone can infer that this scale was accurate to the lb. In summary, sig figs demonstrate the accuracy of a measuring device.

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