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Chapter 5: Problem 151

Describe one advantage of expressing a number in scientific notation over decimal notation.

Short Answer

Expert verified
Scientific notation can concisely represent extremely large or small numbers, making them easier to understand, work with, and compare. It reduces the number of zeros needed, thus maintaining accuracy without loss of readability.

Step by step solution

01

Understanding Scientific Notation

Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It's represented by \[a 脳 10^n\] where \(1 \leq |a| < 10\) and 'n' is an integer.
02

Identify an Advantage

One significant advantage of scientific notation is its ability to succinctly represent very large or very small numbers. This makes it easier to understand, work with and compare such numbers.
03

Description of the Advantage

Specifically, scientific notation reduces the number of zeros needed to denote a very large or very small number, which maintains accuracy without loss of readability. For example, the number 400,000,000 can instead be expressed as \(4 脳 10^8\) in scientific notation, which is substantially simpler.

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Most popular questions from this chapter

Use a vertical format to find each product. $$\begin{aligned}&3 y^{3}+2 y^{2}+y+4\\\&y+3\end{aligned}$$

Perform the indicated computations. Express answers in scientific notation. $$\frac{\left(1.2 \times 10^{6}\right)\left(8.7 \times 10^{-2}\right)}{\left(2.9 \times 10^{6}\right)\left(3 \times 10^{-3}\right)}$$

Are the expressions $$ \frac{12 x^{2}+6 x}{3 x} \text { and } 4 x+2 $$ equal for every value of \(x ?\) Explain.

Exercises \(110-112\) will help you prepare for the material covered in the next section. In each exercise, perform the long division without using a calculator, and then state the quotient and the remainder. $$2 4 \longdiv { 2 9 5 8 }$$

Solve: \(8-6 x>4 x-12\)
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