Base 10 Alice
All the questions in this assignment refer to base 10 cake and
beverage.
1. For each of the quantities shown below, find Alice’s height after
eating that amount of cake. In each case, assume that she starts at
a height of 5 feet.
a. 4 ounces
b. 8 ounces
c. 15 ounces
2. If Alice eats a whole number of ounces of cake and starts from a
height of 5 feet, what do you know about the possible heights she
can grow to?
3. Suppose Alice is 5 feet tall and wants to know how many ounces
of cake she needs to eat to become 50,000,000,000 feet tall.
(That’s 50 billion feet, which is roughly 10 million miles.) What
shortcut can you use in answering her question?
4. Pick three different whole numbers of ounces of beverage for
Alice to drink and find her height after consuming each amount.
Assume in each case that she starts out 5 feet tall.
5. Find a simple rule for writing Alice’s final height for situations
like those you made up in Question 4. Your rule should deal
specifically with the case of whole-number ounces of beverage.
Warming Up to Scientific Notation
Scientific notation of a number is expressing it in the form
A * 10B
Math 577, based on IMP2
where A is a real number and B is an integer. Most commonly, A is
chosen to be a finite decimal whose whole number part is between
1 and 9 inclusive.
Scientific notation may be a new way for you to express numbers.
It often takes some practice to get used to working with scientific
notation, but it’s worth the effort because many ideas in
mathematics and science are expressed using this special way of
writing numbers.
This homework assignment gives you several ways to get
accustomed to scientific notation.
1 . Write each of these numbers in scientific notation.
a. 34,200
b. 0.0034
2. Write each of these numbers in ordinary notation.
a. 4.2 * 105
b. 7.503 * 10-2
3. Each of the next series of problems gives a product or quotient
of two numbers written in scientific notation. Find the numerical
value of each result without using a calculator and write your final
answers in scientific notation.
a. (5 * 104) * (2 * 107)
d. (9 * 103) ÷ (5 * 10-4)
b. (5 * 105) * (7 * 10-2)
e. (6 * 10-3) ÷ (2 * 10-8)
c. (7 * 108) ÷ (2 * 105)
f. (2 * 105) ÷ (4 * 103)
4. Based on the examples in Question 3, develop some general
principles for multiplying and dividing numbers written in
scientific notation. Make up more examples as needed, and
illustrate your rules.
Math 577, based on IMP2
5. Figure out and describe how to enter numbers in scientific
notation on your own scientific calculator. Describe how your
scientific calculator displays numbers in scientific notation.
Math 577, based on IMP2