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Whenever you make a measurement properly, all the digits in the result are significant. But what if you were analyzing a reported value and trying to determine what is significant and what is not? Well, for starters, all nonzero digits are significant, and it is only zeros that require some thought. We will use the terms “leading,” “trailing,” and “captive” for the zeros and will consider how to deal with them.

The left diagram uses the example of 3090. The zero in the hundreds place is labeled “captive” and the zero in the ones place is labeled trailing. The right diagram uses the example 0.008020. The three zeros in the ones, tenths, and hundredths places are labeled “leading.” The zero in the ten-thousandths place is labeled “captive” and the zero in the millionths place is labeled “trailing.”

Starting with the first nonzero digit on the left, count this digit and all remaining digits to the right. This is the number of significant figures in the measurement unless the last digit is a trailing zero lying to the left of the decimal point.

The left diagram uses the example of 1267 meters. The number 1 is the first nonzero figure on the left. 1267 has 4 significant figures in total. The right diagram uses the example of 55.0 grams. The number 5 in the tens place is the first nonzero figure on the left. 55.0 has 3 significant figures. Note that the 0 is to the right of the decimal point and therefore is a significant figure.

Captive zeros result from measurement and are therefore always significant. Leading zeros, however, are never significant—they merely tell us where the decimal point is located.

The left diagram uses the example of 70.607 milliliters. The number 7 is the first nonzero figure on the left. 70.607 has 5 significant figures in total, as all figures are measured including the 2 zeros. The right diagram uses the example of 0.00832407 M L. The number 8 is the first nonzero figure on the left. 0.00832407 has 6 significant figures.

The leading zeros in this example are not significant. We could use exponential notation (as described in Appendix B) and express the number as 8.32407 × 10 −3 ; then the number 8.32407 contains all of the significant figures, and 10 −3 locates the decimal point.

The number of significant figures is uncertain in a number that ends with a zero to the left of the decimal point location. The zeros in the measurement 1,300 grams could be significant or they could simply indicate where the decimal point is located. The ambiguity can be resolved with the use of exponential notation: 1.3 × 10 3 (two significant figures), 1.30 × 10 3 (three significant figures, if the tens place was measured), or 1.300 × 10 3 (four significant figures, if the ones place was also measured). In cases where only the decimal-formatted number is available, it is prudent to assume that all trailing zeros are not significant.

This figure uses the example of 1300 grams. The one and the 3 are significant figures as they are clearly the result of measurement. The 2 zeros could be significant if they were measured or they could be placeholders.

When determining significant figures, be sure to pay attention to reported values and think about the measurement and significant figures in terms of what is reasonable or likely when evaluating whether the value makes sense. For example, the official January 2014 census reported the resident population of the US as 317,297,725. Do you think the US population was correctly determined to the reported nine significant figures, that is, to the exact number of people? People are constantly being born, dying, or moving into or out of the country, and assumptions are made to account for the large number of people who are not actually counted. Because of these uncertainties, it might be more reasonable to expect that we know the population to within perhaps a million or so, in which case the population should be reported as 3.17 × 10 8 people.

Significant figures in calculations

A second important principle of uncertainty is that results calculated from a measurement are at least as uncertain as the measurement itself. We must take the uncertainty in our measurements into account to avoid misrepresenting the uncertainty in calculated results. One way to do this is to report the result of a calculation with the correct number of significant figures, which is determined by the following three rules for rounding    numbers:

Questions & Answers

what is the formular for methane
Tamaranimiweremi Reply
CH4 , it is the simplest alkane
Abdelkarim
what is zero gravity
Blessing Reply
every object is that zero gravity
Rabiu
Probably when an object is in space and there are no nearby masses that pull her, and exert gravity
Abdelkarim
Alright. .good job
Rabiu
And all majesty to God, (وَهُوَ ٱلَّذِی خَلَقَ ٱلَّیۡلَ وَٱلنَّهَارَ وَٱلشَّمۡسَ وَٱلۡقَمَرَۖ كُلࣱّ فِی فَلَكࣲ یَسۡبَحُونَ) [سورة الأنبياء 33 And it is He who created the night and the day and the sun and the moon; all [heavenly bodies] in an orbit are swimming. General theory of relativity in Qur
Abdelkarim
what is lattice energy
Getrude Reply
why is CO a neutral oxide and CO2 an acidic oxide
Emmanuel Reply
Because when CO2 dissolves in water forming a weak acid. CO does not dissolve in water as it has strong triple bond.
Abdelkarim
What is acid
Progress Reply
which donate H+ or accept lone pair of electron
Kajal
kinetic theory of matter and gas law
Victoria Reply
hi
Victoria
pls explain
Victoria
what is clay
Thankgod Reply
material containing clay minerals. Clays develop plasticity when wet, due to a molecular film of water surrounding the clay particles, but become hard, brittle and non–plastic upon drying or firing. Most pure clay minerals are white or light-coloured, but natural clays show a variety of colours
Abdelkarim
due iron oxide. The four types of clay are Earthenware clay, Stoneware clay, Ball clay, and Porcelain. All of them can be used to make pottery, but the end result would differ a lot thanks to their different textures, colors, and flexibilities.
Abdelkarim
And do you know that god has created human from clay (وَلَقَدۡ خَلَقۡنَا ٱلۡإِنسَـٰنَ مِن صَلۡصَـٰلࣲ مِّنۡ حَمَإࣲ مَّسۡنُونࣲ) [سورة الحجر 26] And We did certainly create man out of clay from an altered black mud. You can install Quran from paly store for free with translations.
Abdelkarim
darw a periodic table
Hazard Reply
draw a periodic table
Hazard
You will arrange the elements into row and coloumns according to increasing proton number. You may want to use symbols or their names. Hydrogen, Helium, etc. God has created all these elements from nothing, in Islam we know God is the creator.
Abdelkarim
why are you drawing a periodic table? why not just print one from the internet and use as a reference
Jakhari
Great thought
Bright
how are you?
Abel Reply
alright , how about you
Marina
am fine
Agbo
your name is Agbo?
Marina
my name is amel
Farid
l use the email of my husband
Farid
Define organic chemistry
Edward Reply
It is the chemistry concerning molecules that have Carbon skeletons and hydrogen atoms. We find organic molecules like in plants, living derivatives, etc.
Abdelkarim
what's matter
Joshua Reply
Anything that can be to cutting from all dimensions to halve. So you end up with 4 cubes of 5 cm side. Repeat with one of the cubes. 10, 5, 2.5, .., 0 1st 2nd 3rd Nth Un= a(r) ^ n-1
Abdelkarim
Anything that has mass and can reflect or absorb waves. GOD created everything from nothing only he can destroy it as prooved.
Abdelkarim
Suppose you have a cube of side 10 cm. Then you start cutting from all dimensions to halve. So you end up with 4 cubes of 5 cm side. Repeat with one of the cubes. 10, 5, 2.5, .., 0 1st 2nd 3rd Nth Un= a(r) ^ n-1 0= 10 (1/2)^n-1 0= (1/2) ^ n-1 Log0= (n-1) Log(1/2) - infinity =( n-1)
Abdelkarim
matter is anything that has mass,volume and can occupy space
Getrude
what is electrolysis
Rabi Reply
good equation
Aliyu
differenciate between fat and oil
Mustapha Reply
what is the meaning of coordinate bond
Asmaa Reply
It is the alternative for dative which is a covalent bond but both electrons of the pair are from shared from the same (one) atom.
Abdelkarim
can someone please tell me what does an Entropy means
Afiwape Reply
What is the generic name for the compound
Orisanmi Reply
Practice Key Terms 6

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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