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Course: Arithmetic (all content)>Unit 6

Lesson 14: Significant figures

Rules of significant figures

This video teaches significant figures rules, crucial for measurements and calculations. It covers identifying significant digits, including non-zero digits, zeros in between, leading zeros, and trailing zeros. Additionally, it introduces scientific notation for clearer representation of significant figures. Created by Sal Khan.

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• What would you use significant figures for?
• In engineering significant figures has to do with how accurately you are able to measure something. According to Google, Mt. Everest is 29,029 feet tall. Well, I suspect it is not EXACTLY 29,029 feet tall... to the inch? the thousandth of an inch? how accurately is it measured?

If the height were given as 29,000 feet, that would still be a pretty good measurement, but it implies the number is really only 'good' to the thousands place (plus or minus 500 feet). 20,029 implies that measurement is 'good' to the individual foot (plus or minus 6 inches)... a very different impression of accuracy.

The intent (as I understand it) is to avoid giving the impression of accuracy where it does not exist.
• What is the difference between 5.60, 5.600, and 5.60000? We all know that the zero is a placeholder for a non-existing value when placed after a decimal and after a non-zero digit. I understand that that would show that the measurer took the time and had an appropriate measuring device to arrive at a more and more accurate measurement, and that it is essentially superfluous to write additional zeros after the first trailing zero. What is a little ambiguous to me, is the difference between 5.0, 5.00 and 5.000... (All trailing zeros that reflect additional accuracy). I guess my real question is, what are the circumstances for counting additional trailing zeros as significant?? ...is it simply the amount of significant figures that the measuring device reads that decides this scenario?
• Mathematically there is no difference between the exact, precise numbers 5.0 and 5.00 and 5.000.

However for measurements in the real world (for science, engineering etc.) there is always a limit to the precision of a measure. Someone wanting to make use of a measurement needs to know how precise it is because they need to know how precise accurate their final result is.

A measurement of 5.0 (2 SF) could be anywhere between 5.04 or 4.95
A measurement of 5.00 (3 SF) could be in reality anywhere between 5.004 and 4.995
A measurement of 5.000 (4 SF) could be in reality anywhere between 5.0004 and 4.9995.

Measuring the carpet to cover a floor as 5.0 Meters (2SF) by 6.0 Meters (2SF) means the area could be as little as 4.95x5.95, 29.4525M^2. However, at that precision the area could be 5.04x6.04, 30.4416M^2. That is a difference of 1 M^2

When measuring accurately to 4 SF means a difference of 2 thousandths of a meter squared.

Knowing accuracy and knowing possible error for future calculations is the difference between 5.60, 5.600 and 5.6000.

It is the precision of the measuring device that decides the significant figures.
• Why are the zeroes significant when there is a unit?
• Whether or not a value has a unit does not affect whether a zero is significant or not.
• How do we remember trailing 0s, leading, whatever? It's really confusing.
• Remember it like a group of three people walking on the road. The one in the front is leading the others. the one in the back is trailing them. So, the leading zeroes are the ones in front (like 0.052; the first two zeroes are leading) and the ones in the back are trailing (like in 56.00, the last two are trailing). Hope this helps!
• So if I had o choose in between having to count the zeros as shown in the last example on , I should count only the non-zero digits, but if there is a decimal point, it automatically means I should count the zeros as significant digits as well?
• The 0,00700 is considered 3 significant figure for the 700 part, however, the decimal is quite further off, and we are ignoring the 0.00. Thats' conflicting. Can anyone explain?
• The first three zeros are just placeholders, not significant.
• I have several conflicting sources regarding leading zeros. I have always been told that if the number is less than one, then a single zero before the decimal is considered significant. The reason for this is because it shows a purposeful inclusion of the place in the accuracy of the measurement, rather than just leaving the place blank, and therefore ambiguous. An example would be 0.345. Can you verify this? I DO understand that leading zeros, such as the zeros in the famous ( or infamous, depending on your opinion) 007, would not be considered significant. In the Rules of significant figures video, at Sal simply states that all leading zeros are not significant. Are there exceptions to this? Thank you.
• how many significant figures do percentages have? Do they have one? (5%) or 3? (.005)
• then it would just be 1 sig fig because of 0.005
(1 vote)
• How many significant figures are in 870.050
• 870.050 has 6 significant figures.

If it were 870.05, it would have 5. However, the trailing zero above is included, so there are six.