significant figures and trailing zeros

[KiaraTenorio_14B]

In the week one HW there is a question on sig figs and on of the hints talks about the importance of the decimal and determining if the trailing and leading co-efficient are significant. I am just confused on as to why all zeros trailing are significant with a decimal but not the zeros that are leading.

[905783577]

Essentially, leading zeros are never significant, regardless of whether there is a decimal or not. This is because leading zeros do not determine how accurate your measurement is, whereas trailing zeros indicate to what accuracy you measured something. Take the number 0.090; there are two significant figures, and the trailing zero indicates that you used a tool to measure to the thousandths place. I hope this helps!

[Rachel Martinez 1A]

Yeah same here, but I do recall that it mentioned:

- All non-zero digits are significant.

- Zeros appearing anywhere between two non-zero digits are significant.

- Leading zeros are not significant.

- Trailing zeros in a number showing a decimal point are significant.

so I just went with that. when doing the homework

[Theo Teske 3B]

Another thing to keep in mind is that exact numbers (such as the conversion rate from meters to yards, for instance) and defined numbers (constants like the speed of light) have an infinite number of significant figures, but they're generally not reported. Not sure if this will come up in class but potentially good to know!

[AJackman]

Numbers with decimals imply that there is some significance in the tens place or beyond. The zeros beforehand are necessary to show what decimal place the numbers are in, but are irrelevant to the actual number. Think of 0.00046 as 000046. The numbers preceding it are insignificant in both situations, but neccessary to understand the actual value in the first.

[Aparna Pillai 1E]

Think of the leading zeros in a number with a decimal necessary, and the trailing zeros unnecessary. For instance, in the number 0.0040, you need the zeros in front of the 4, but you do not need the zero after it. Accordingly, the trailing zeros display the extent of the accuracy of your measurement. Measuring 0.004 and exactly 0.0040 are different, because the latter was measured to a greater accuracy.

[michaelcrisera]

The way that I deal with these sig fig problems is to first consider whether or not there is a decimal point in the number. If there is a decimal point, you start from the left side of the number and move right until you reach a nonzero number. All numbers including this one and the ones after are significant. If there is no decimal point, you start from the right and move left until you find the first nonzero number. Then all numbers including this one and the ones to the left are significant. I think of this distinction as decimal point Present (Pacific ocean = left), decimal point Absent (Atlantic ocean = right).

[Sophia Dominguez 3I]

The leading zeros are known as placeholder zeros and do not add to the precision of the measurement. Trailing zeros with a decimal are significant because they indicate the precision of measurement. Non-decimal trailing zeros are ambiguous and are not counted as significant figures. Non-zero digits and zeros in between are significant figures.

[Joseph Liao 3C]

The trailing zeros that come after a decimal place are essentially only there to mark the number of significant figures there are. The reason why leading zeros do not count as significant figures is because they need to be there in order to express some decimals, whereas trailing zeros will serve no purpose other than marking a number of sig figs.

[LaurenAkason2A]

Hi! I always just remember the sig fig rules. This link: https://ccnmtl.columbia.edu/projects/mm ... /6665.html is super helpful. Hope this helps!