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Ignacio Green

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What is scientific notation

Short answer:

Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing 0.0000000056, we write 5.6 x 10⁻⁹.

Scientific notation is the expression of a number based on the largest exponent of 10 for its value, where the form is a decimal number A x 10ⁿ where A is greater than or equal to 1 and less than 10, so that when the multiplication is carried out the original number results.

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Long answer:

Scientific Notation

Scientific notation is a way to "easily" or "conveniently" write very large or very small numbers. As these numbers are frequently encountered in the sciences, the term scientific notationwas introduced to name this method of expressing these quantities so that they might be more easily grasped and understood.

Scientific notation allows them to be presented in a form where their magnitude can be seen more easily. Also it can simplify calculations by allowing you to concentrate on the significant digits rather than the orders of magnitude which are very easily dealt with separately. This latter advantage has somewhat diminished with the widespread availability of calculators and computers. But previously, people used log tables and slide rules for multiplication and division. These calculating devices depended on thinking of numbers in their scientific notation and utilizing the significant digits.

The Form of Scientific Notation The idea behind scientific notation is to write numbers in terms of powers of ten - either positive (for very large numbers), or negative (for very small ones). As an example, consider the mass of an electron, which is approximately 0.0000000000000000000000000001 grams. An easier way to write it uses the significant digit 1 and an exponent based on a multiple of ten. The number becomes the easily represented 1 x 10⁻²⁸ g.

The simple rule is to take your "numbers" and move the decimal point to the left or right so that only one figure is to the left of the decimal. Then write the rest of the significant digits to the right of the decimal, and tack on the appropriate power of ten (again, either positive or negative) to restore the proper value to the figure.

Coefficient and Base in Scientific Notation Scientific Notation also avoids the headache and potential errors of counting lots of zeros.

The number 123000000 in scientific notation is written as:

1.23 x 10⁸

The first number 1.23 is called the coefficient. It is always a single digit followed by a decimal point and then the rest, but usually only two digits.

The second number is called the base and in scientific notation must always be 10. In the number 1.23 x 10⁸ the number 8 is the exponent or power of ten.

How to Write a Number in Scientific Notation For large numbers :

1) Put the decimal after the first digit and drop the zeroes. In the number 123,000,000 the coefficient will be 1.23

2) Then write the times "x" and the base 10.

3) To find the exponent count the number of places from the "new" decimal point to the end of the number. In 123000000 there are 8 places. Therefore the exponent is 8.

There are some minor variations that have evolved to fill different needs, usually because not all fonts or printers allow superscripts: 123000000 can be written as:

1.23 E+11 or 1.23 X 10^11 or 1.23 x 10¹¹

For small numbers :

For numbers less than one we use a similar approach. These numbers all have negative exponents. For example 0.00000123 second (1.23 microseconds) is written:

1.23 E-6 or 1.23 x 10^-6 or 1.23 x 10⁻⁶

Take the original number 0.00000123 and shift the decimal point to the right until you get the coefficient in proper form, as above. The number of digits shifted is then the negative exponent.

Notes:

a) Numbers less than one all use negative exponents, but what about negative numbers, such as -0.04? We can write this as

-4.0 x 10⁻²

b) Always make sure the E is capitalized in 1.23 E-6, otherwise it can be confused with "e" the base of the natural log system.

c) Some scientific and engineering fields have special rules, such as electronics where scientific notation is usually in powers divisible by three, such as -3, 3, 6, 9, 12, etc; this is called engineering notation. This is because electronic components are made using standard SI prefixes such as kilo, micro, nano, or pico.

d) Usually, Scientific Notation is ignored if you want to keep numbers in common formats, such as 315 microseconds, instead of 3.15 x 10⁻⁴ seconds, but this is a matter of preference.

Scientific notation is normally used for numbers that are either far to large or far to small to be written conveniently in decimal notation.A,B

For example the Earth's mass is approximately: 5,973,600,000,000,000,000,000,000.0 kg

In scientific notation this would be written as:

5.9736 x 1024 kg.

In normalised scientific notation numbers are written in the form:[A,B]

a x 10

Where:

a is a number between 1 and 10

n is a positive or negative whole number.

In engineering notation, the n value is commonly in the form of multiples of 3. In this way the number will always explicitly match the corresponding SI prefixes.[B]

For example a distance of 50,000 m would be written as:

Scientific Notation: 5 x 10⁴ m

Engineering notation: 50 x 10³ m

In this example 10³ corresponds to the SI prefix "kilo"[C] as such the engineering notation could be directly described verbally as "fifty kilometres" (50 km) whereas scientific notation yields the much more unwieldy "five times ten to the power four metres" which is much less intuitively easy to understand, even though it is exactly the same distance.

Guidance on converting to and from scientific notation is given in the related links. Specifically References A and B.

References:

A Scientific notation - Engineering Maths Help from the 'mathcentre' Academic Website.

B Scientific notation: Wikipedia Entry.

C List of SI prefixes: Wikipedia Entry.

Please see related links.

This is one of those things that is so hard to teach and explain, but once you see it, it is actually pretty simple. Scientific notation is simply a different way to state a number besides the number itself. A number is written in scientific notation if it is in the form of 1≤N<10, N is the number. That form basically states that the number being multiplied (just hang on, I will explain that next) is between 1 (inclusive) and 10 (exclusive), including decimals. Say you are given the number 4100. It is easier to put it into product form first. The product form of 4100 would be 41×100 (41 times 100), because the number being multiplied has to be between 1 and 100. Now it is time to put it into scientific notation. It is going to be very similar to the product form. Since the number that is being multiplied FIRST is a number with some...what's the word... consistency? The first number is not 1 or 10 in this case, it would be 4.1 . You divide the first set of numbers by 10. So, 41/10 is 4.1. And now for the "hard" part. To get back to the 4100, you would have to multiply 4.1 by 1000 to get there. But you have to put the 1000 into a "power of 10" if you will. This is figured out by finding out how many times you would have to multiply 10 by itself. You would have to do 10 × 10 × 10 to get to 1000. You use 10 three times, so you would have 10³. And now the easiest part, putting it together. You have that 4.1, which will go first. And then, you multiply it by the 10³. Remember that the 10³ is equivalent to 1000, and you have to multiply 4.1 by 1000 to get the original number of 4100. So all together, 4100 in scientific notation is 4.1×10³.

Lets try it with another number, maybe seeing more numbers will make sense.

Here's a number- 7243.

The number between 1 and 10- 7.243 (times 1000 gets you back to the original number)

Remember, 1000= 10³

7.243 × 10³ is your final answer. Scientific notation is a way of writing numbers that are too big or too small to be conveniently written in decimal form.

In normalized scientific notation all numbers are written in the form a x 10^b (a times ten raised to the power of b) where a is a nonzero single-digit integer and b is an integer.
scientific notation is a way to simplify a number with a lot of zeros. :)

* * * * *

Scientific notation is a way to deal with very large or very small numbers.

Numbers are split into two parts and expressed as a*10b

where 1 ≤ a < 10 and b is an integer.

For example,

12345 = 1.2345*104

123.45 = 1.2345*102

0.0012345 = 1.2345*10-3


when you break down a number for example 753,000 in scientififc notation is 7.53x10 to the fifth power

Which of these elements has the smallest atomic radius

The answer choices for this question wasn't provided. Oxygen has the smallest atomic radius. The higher the electronegativity in an element makes the atomic radius smaller.

What is the activity series of metals

We arrange metals into an ordered list with the best reducing agent at the top and the worst reducing agent at the bottom. This is an Activity Series for metals. Metals near the top of the list give up electrons most easily. Those metals near the bottom of the list give up electrons with difficulty. Hydrogen, even though it is not a metal, can be placed in the list. Metals above hydrogen in the Activity Series will react with 1.0 Molar hydrochloric acid at room temperature. The Activity Series for metals is developed by experiment.


A list of metals arranged in order of reactivity~APEX

What is the molar mass of a compound

The mass in grams of 1 mole of the compound (apex)

What is 0.000098 in scientific notation

This number in scientific notation is 9.8x10-5.

What is the correct formula for Ca2 reacting with NO21

Ca(NO2)2

What are state symbols in a chemical equation

They are representations of what condition the reactant or product is at in a chemical reaction.

What is the mass of 1 mole of MgSO4

120.4

How does one determine a percent composition from an empirical formula

divide the total mass of the element by the mass of the compound and multiply by 100%

What is made when salt is dissolved in water

A solution

What are unit conversions used for

Unit conversions express an amount in a different unit

Which best describes a mole as used in chemistry

A very large number of objects

In what order do electrons fill orbitals

Electrons fill orbitals in order of increasing orbital energy.

The exact order of these energy levels is shown at the related link below.

What is the percent composition of sulfur in SO2

32.1g

__________________

X100%

(32.1g + 16.0g + 16.0g)

How does one determine a molecular formula from the empirical formula

molar mass over grams of element

The above answer is somewhat correct. In order to find the molecular formula when given the empirical formula, you must first find the molar mass of the empirical formula.

MOLAR MASS

# atoms element A x atomic mass element A (periodic table) = mass A

# atoms element B x atomic mass element B (periodic table) = mass B

... etc.

Add up all of the mass values found above and you have the molar mass.

Then, after you have found the empirical formula's molar mass, you divide the molar mass of the molecular formula by the empirical formula's molar mass (solving for n).

MOLECULAR FORMULA EQUATION: N (Empirical formula) (read as N times empirical formula) where:

N = Molar mass substance

---- Molar Mass emp. form.

What reaction shows a compound breaking apart into separate substances

Decomposition reaction

What is the molecular formula of the compound CH2 with molar mass 168

C12h24

What would be useful for converting g mol to g L

Molarity

What is the best definition of a physical change

Answer this question… Which of the following is the best definition of a physical change?

What happens in a double replacement reaction

In this reaction a change of bonds of the reactants occur: the general form is:
AB + CD = AD + BC

Which of the following reactions shows a physical change in chemistry

Burning coal is a chemical reaction, a chemical change; but the solid reactant is transformed in gaseous products (H2O and CO2) - this is a physical change.

Which of the following describes a single-replacement reaction

One element takes the place of another in a compound.

Hown many atoms does 32 g of sulfur contain

32g of Sulfur is a Mole of Sulfur and therefore contains Avogadro's number of atoms of Sulfur.

Avogadro's number is 6.023 × 10 to the 23.

so3 is an empirical formula for which of the following A. so4B.s2o6C.s4o2D.s2o3

B. s2o6

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