When doing complicated computations with very large or very small numbers, people often write the numbers in scientific notation so that they can more easily estimate the magnitude of the number. In scientific notation, every number is written as a decimal number greater than or equal to 1 but less than 10, multiplied by a power of 10. Thus, the decimal always has exactly one non-zero digit to the left of the decimal point. For example, 6,253 would be written 6.253 • 10³, and .06253 would be written 6.253 • 10^-2. The best way to remember how to find the correct power of 10 is to write the number with one digit to the left of the decimal point and then think about what to do to that decimal to make it equal to the original number.

Problem B6

Write the following numbers using scientific notation:

Scientific notation can help us quickly perform operations on large numbers. Calculating 2,300,000 • 3,000,000,000 is much easier to think of as the following:

(2.3 • 10⁶) • (3.0 • 10⁹) = 6.9 • 10¹⁵

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