# Significant figures in practical investigation report

• winkyinky146
In summary, the student is unsure how to make their significant figures consistent and also need to keep the decimal places consistent.
winkyinky146

## Homework Statement

I am writing a prac report regarding Hooke's Law, and am uncertain how many significant figures I should write my results in in my results table. I have heard that in my prac report, I must keep my significant figures consistent, that is, all data measured by the same device should have the same number of significant figures.
My masses were pre-measured and inscribed on the weights themselves. The spring extension was measured with a centimeter ruler, and 1mm was the smallest increment.

## Homework Equations

I have data similar to this:
Mass (g)__Ave. Extension (cm) ___Uncertainty (cm)
50________2.1_________________0.05
100_______6.8_________________0.2
150 _____ 11.8________________ etc.
200 ______16.7_________________

## The Attempt at a Solution

As shown above, the significant figures are inconsistent, but I'm not sure how to make them consistent. For the masses for example, I can't just add a ".0" to the end of "50" for example, to make "50.0" in order to make the number of significant figures 3, in line with the rest of the masses, as that would increase the accuracy of the measurement. Like wise with the extension, the smallest increment was 1mm, so I can't just add a "0" to "2.1" to make "2.10" for the number of significant figures to fit with "11.8" and "16.7". As for the uncertainty, I have no idea what to do with it. I was taught that uncertainty for analogue devices was plus or minus half the smallest increment. So for the ruler it would be 0.05cm. This only has one significant figure however, do I need to change this at all?
Thanks! Any help would really be appreciated!

In Physics experiments, it is usual to give readings taken to decimal places. If you want to give Extension ( in cm ??)
to 2 decimal places - I would suggest truncating/ rounding down to 1 dec. place - you have to have read extension to 3
decimal places, which you haven't
Mass / Kg _ Average extension/m _Uncertainty/m
0.0500 _________0.0205 ___________+/- 0.0005

winkyinky146
Janosh89 said:
In Physics experiments, it is usual to give readings taken to decimal places. If you want to give Extension ( in cm ??)
to 2 decimal places - I would suggest truncating/ rounding down to 1 dec. place - you have to have read extension to 3
decimal places, which you haven't
Mass / Kg _ Average extension/m _Uncertainty/m
0.0500 _________0.0205 ___________+/- 0.0005
So basically I don't need to keep the significant figures consistent, but I should keep the decimal places consistent? And also I should use SI units?

winkyinky146 said:
I must keep my significant figures consistent, that is, all data measured by the same device should have the same number of significant figures.
That would be wrong. Your ruler can't measure 5 mm with more than one significant figure, but it certainly can do so for 50 mm. The absolute uncertainty is the same, the relative uncertainty is not.
winkyinky146 said:
I was taught that uncertainty for analogue devices was plus or minus half the smallest increment. So for the ruler it would be 0.05cm.
That is usually a reasonable estimate.
winkyinky146 said:
This only has one significant figure however
It is the uncertainty. More than one significant figure for an uncertainty rarely makes sense.

Don't focus on significant figures here. Look at the absolute uncertainties, that is much more useful.

winkyinky146
I auto-corrected the extension - of course, the extension could have been 2.15cm!

## What are significant figures in practical investigation report?

Significant figures are numbers that represent the precision or accuracy of a measured quantity. They are the digits that carry meaning in a measurement or calculation.

## Why are significant figures important in a practical investigation report?

Significant figures are important in a practical investigation report because they help convey the level of accuracy and precision in the data being presented. They also ensure that the reported results are not misleading or falsely precise.

## How do you determine the number of significant figures in a measurement?

The number of significant figures in a measurement is determined by the precision of the measuring tool. All non-zero digits are significant, while leading and trailing zeros may or may not be significant depending on the context.

## What is the rule for rounding off numbers with significant figures?

The general rule for rounding off numbers with significant figures is to round to the same number of decimal places as the measurement with the fewest significant figures. If the digit following the last significant figure is 5 or greater, round up. If the digit is less than 5, round down.

## Why is it important to be consistent with significant figures in calculations?

It is important to be consistent with significant figures in calculations because it ensures that the final result is not more precise than the least precise measurement used in the calculation. This helps avoid the appearance of falsely precise results.

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