Chapter 5.4, Problem 12P

Suppose you multiply a 6-digit number by an 8-digit number. How many digits will the product have? The following problem will help you answer this question:

1. When you write a 6-digit number and an 8-digit number in scientific notation, what will the exponents on the 10s be?
2. Write $(1.3\times {10}^5)\times (2.5\times {10}^7)$ and $(7.9\times {10}^5)\times (8.3\times {10}^7)$ In scientific notation.
3. Suppose you write a 6-digit number and an 8-digit number in scientific notation. If you multiply these numbers and write the product in scientific notation, what will the exponent on the 10 be when the product is expressed in scientific notation? Explain why your answer is in an “either. . .or …” form. (Hint: See part (b).)
4. Use your answer to part (c) to answer the following question: When you multiply a 6-digit number by an 8-