Scientific notation is used to turn small or large inconvenient numbers into manageable ones.

**Concept:** Understanding Scientific Notation

Now, majority of you may remember scientific notation in algebra or from of course you recently take it. Now, scientific notation is a way of changing very large or very small numbers into more manageable ones, scientific notation is really a simple type of idea, but it's going to form the basis of all our chemical calculations from this point on. Now, in order to understand scientific notation you just have to remember the three components that make it up. So, let's take a look at this number, we have 6.88 times 10 to the negative 12, we're going to say the first number 6.88 is called the coefficient and the thing about the coefficient is, the coefficient must be greater than or equal to 1 but less than 10. So, that's the range that we're dealing with, we're going to say that the second number, which is the 10, is known as the base and when it comes to scientific notation the base is always 10, that's not ever going to change, finally we're going to say in 6.88 times 10 to the negative 12, the negative 12 number is known as our exponent. So, those are the three portions that make up any scientific notation number that you're given. So, just remember the guidelines for some of them and you'll be fine.

A scientific notation value is comprised of 3 parts: the **coefficient**, **base** and **exponent**.

**Example:** Convert the following numbers into scientific notation.

Express the following number in scientific notation 0.000275 _____________________

How many significant figures in your answer _______________

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Perform the following mathematical operations and express the result to the correct number of significant figures.

d. (3.8 x 10^{-12} + 4.0 x 10^{-13}) / (4 x 10^{12} + 6.3 x 10^{13})

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Perform the following mathematical operations and express the result to the correct number of significant figures.

c. 6.071 x 10^{-5} - 8.2 x 10^{-6} - 0.521 x 10^{-4}

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Use scientific notation to express each quantity with only the base units (no prefix multipliers).

d. 35 µm

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Use scientific notation to express each quantity with only the base units (no prefix multipliers).

c. 128 pm

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Use scientific notation to express each quantity with only the base units (no prefix multipliers).

b. 18 fs

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Use scientific notation to express each quantity with only the base units (no prefix multipliers).

a. 4.5 ns

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Write the following number in scientific notation and round off to three significant figures: 31152 x 10^{-15} .

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Write the following number in scientific notation and round off to five significant figures: 0.00392708 x 10 ^{81} .

a) 3.9271 x 10 ^{84}

b) 3.9270 x 10 ^{78}

c) 0.39271 x 10 ^{78}

d) 3.9270 x 10 ^{80}

e) 3.9271 x 10 ^{78}

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