You can make sense of these often confusing and sometimes contradictory numbers with just two tools: (1) an understanding of the meaning of large numbers and (2) an ability to make rough, common-sense, estimates starting from just a few basic facts. (LocationĀ 108)

Only if the answer is just right will you need to put more work into solving the problem and refining the answer. (LocationĀ 149)

It is often easier to establish lower and upper bounds for a quantity than to estimate it directly. (LocationĀ 155)

This is not the best choice because it is a factor of 50 greater than our lower bound and only a factor of two lower than our upper bound. (LocationĀ 157)

If the sum of the exponents is odd, it is a little more complicated. Then you should decrease the exponent sum by one so it is even, and multiply the final answer by three. Therefore, (LocationĀ 164)

Any number can be written as the product of a number between 1 and 10 and a number that is a power of ten. (LocationĀ 249)

When we multiply numbers, we multiply coefficients and add exponents. (LocationĀ 260)

we divide coefficients and subtract exponents. For example, (LocationĀ 262)

When we add or subtract numbers using scientific notation, the exponents of both numbers must be the same. (LocationĀ 267)

The most important part of any number is the exponent. After that, the next most important number is the first digit of the coefficient (the number that multiplies the (LocationĀ 276)

power of ten). The second and subsequent digits of the coefficient are just small corrections to the first digit. (LocationĀ 277)

Similarly, the silliness of having too many digits is illustrated by the following anecdote. Suppose that you ask a museum guard how old a dinosaur skeleton is. He responds that it is 75 million and 3 (75,000,003) years old. When you look puzzled, he explains that when he started the job three years ago, the skeleton was already 75 million years old. (LocationĀ 285)