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1.6 The Units of Measurement -- Part 3

- Chemical problem solving involves calculation.
- Sometimes precise numerical calculation is not necessary.
- Sometimes we don't need a high degree of precision, but a rough estimate or a simplified "back of the envelope" calculation is enough.

- The easiest way to make estimates is to simplify the numbers.
- Thus, 4.36 becomes 105 and 2.7 becomes 10-3.

- If the number is more than 5, round it up to 10 and rewrite it as a power of 10.
- 6.1101 * 10-3 becomes 10 * 10-2

- We have powers of 10 when we make these approximations.
- We should not assume that the results of an order-of-magnitude calculation are accurate because our answer is only as reliable as the numbers used to get it.

- Assuming a counting rate of ten atoms per second, we can estimate the number of atoms that an immortal being could have counted in the 14 billion years that the universe has existed.

- A million trillion atoms may seem like a lot, but as we discuss in Chapter 2, a speck of matter made up of a million trillion atoms is nearly impossible to see with a microscope.

- The last step is to make sure the results seem reasonable.
- Order-of-magnitude estimates can help us catch the kinds of mistakes that can happen in a detailed calculation, such as entering an incorrect exponent or signing into a calculator.

- Problems involving equations and conversions can be solved the same way.
- We usually have to find one of the variables in the equation.

- This conceptual plan has an equation instead of a conversion factor.
- The equation doesn't need to be solved for the quantity on the right at this point.
- Guidance for developing a strategy to solve problems involving equations can be found in the procedure that follows and two examples.
- The three-column format is used again.
- If you want to apply the same general procedure to the second problem, you need to work through one problem from top to bottom.

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