Facebook
Google
GitHub
LinkedinMathematics for Electronics
Scientific Notation and Metric Prefixes
5 questions By Tony R. Kuphaldt
-
Question 1 of 5
Write the following exponential expressions in expanded form:
101 = 102 = 103 = 104 = 10−1 = 10−2 = 10−3 = 10−4 = Reveal answer101 = 10 102 = 100 103 = 1000 104 = 10000 10−1 = 1 1010−2 = 1 10010−3 = 1 100010−4 = 1 10000Notes:I have found that many students entering college (at least those entering a technical college in the United States) have a very limited understanding of exponents, especially negative exponents. You may find it necessary to review this concept, explaining what a negative exponent is and how it is defined.
-
Question 2 of 5
Evaluate the following arithmetic expressions, expressing the answers in expanded form:
3.6 ×102 = 1.53 ×10−4 = 8.2 ×101 = 6 ×10−3 = Comment on the effect multiplication by a power of ten has on how a number is written.
Reveal answer3.6 ×102 = 360 1.53 ×10−4 = 0.000153 8.2 ×101 = 82 6 ×10−3 = 0.006 The effect that multiplication by a power of ten has on a number’s written expression should be obvious: the decimal point gets shifted.
Notes:The fact that multiplication by powers of ten simply shifts the decimal point is not a coincidence. Rather, it is a logical consequence of using a base-10 numeration system. If we all used binary for our daily enumeration, we would be using “powers of two” for scientific notation!
-
Question 3 of 5
Express the following numbers in scientific notation:
0.00045 = 23,000,000 = 700,000,000,000 = 0.00000000000000000001 = 0.000098 = Reveal answer0.00045 = 4.5 ×10−4 23,000,000 = 2.3 ×107 700,000,000,000 = 7 ×1011 0.00000000000000000001 = 1 ×10−20 0.000098 = 9.8 ×10−5 Follow-up question: explain why scientific notation is used so frequently by scientists and engineers.
Notes:The convenience in which scientific notation allows us to express and manipulate extremely large and small quantities is perhaps the most important reason why it is used by scientists and engineers.
Your students will be pleased to discover that their calculators can be used to easily convert between “expanded” (sometimes called fixed-point) and scientific notations.
