# How come 84000 has 2 Significant Digits and 84000.0 has 6 Significant Digits?

Isn't there a decimal point after every whole number. So shouldn't 84000 also have 6 Significant Digits?

• More on significant figures. – Qmechanic Apr 12 '18 at 8:36
• Ty for your help. So basically you're trying to say that the extra zero was added to the quantity after the decimal point because it was measured to that extent and so it becomes a significant digit. – An Engineering aspirant Apr 12 '18 at 9:01

## 3 Answers

When the value is written as $84000$ it is not clear which of the zeroes is significant as the value could be $84000\pm 1000$ or $84000\pm 100$ or $84000\pm 10$ or $84000\pm 1$ and that is why it is best to write the number in standard form.

So $8.40 \times 10^{4}$ shows the zero to be significant and the value is given to three significant figures.

The last zero which is after the decimal point in $84000.0$ is significant and so the value is given to $6$ significant figures.

• Yes. Or if there is a unit, sometimes an SI prefix can help. Like if it was a voltage, writing $84000~\mathrm{V}$ does not clearly show the precision, while $84.0~\mathrm{kV}$ seems to indicate three significant digits. Of course, when crucial, write the uncertaincy explicitly with some convention, such as $\pm$. – Jeppe Stig Nielsen Apr 12 '18 at 9:00
• @JeppeStigNielsen The use of a prefix for the unit is really using the engineers version of standard form where the exponent changes in multiples of three. – Farcher Apr 12 '18 at 9:14

84000 has two significant digits because a numerical value for some measurable parameter is known to the nearest thousand. In the case of 84000. it has five significant figures because the value measured is known to the nearest unit, which is the last number before the decimal point in this case. I would read 84000.0 as having 6 significant digits since by including the last zero it is saying that it is significant.

As a general rule setting the last digits of a number to zero means we don't know what they are. So if I write $84000$ it would generally be taken to mean $84000 \pm 500$.

But it could be that I do know the number to five digit accuracy and it is just chance that the last three digits turn out to be zero. In that case I might write it as $84000.0$ to indicate to the reader that the error is around $\pm 0.5$. (Strictly speaking I should write $84000.$ but I've never seen that notation used.)

Footnote:

I've just seen Farcher's answer and I think he puts it nicely. When written as $84000$ the zeros are ambiguous - do they mean we don't know them or does the number really end in $000$. Writing it in scientific notation is a good way to remove the ambiguity and make it clear to the reader what the errors are.

## protected by Qmechanic♦Apr 12 '18 at 8:42

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