Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:06 minutes

Problem 78

Textbook Question

In Exercises 77–86, write each number in scientific notation. 64,000

Verified step by step guidance

Step 1: Understand the concept of scientific notation. Scientific notation is a way to express very large or very small numbers as a product of a number between 1 and 10 and a power of 10. The general form is:

a × 10

^b, where

1 ≤ a < 10

and

b

is an integer.

Step 2: Identify the given number, which is 64,000. To convert this number into scientific notation, we need to rewrite it as a product of a number between 1 and 10 and a power of 10.

Step 3: Move the decimal point in 64,000 to create a number between 1 and 10. The decimal point in 64,000 is initially at the end of the number (64,000.0). Move the decimal point 4 places to the left, resulting in 6.4.

Step 4: Count the number of places the decimal point was moved. Since the decimal point was moved 4 places to the left, the exponent of 10 will be 4.

Step 5: Combine the number and the power of 10 to write the number in scientific notation. The result is

6.4 × 10

⁴.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a compact form. It is written as the product of a number between 1 and 10 and a power of ten. For example, the number 64,000 can be expressed as 6.4 x 10^4 in scientific notation.

Powers of Ten

Powers of ten are used in scientific notation to indicate how many times a number should be multiplied or divided by ten. Each power corresponds to a place value in the decimal system. For instance, 10^4 means 10 multiplied by itself four times, which equals 10,000.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. In scientific notation, only the digits in the coefficient (the number between 1 and 10) are considered significant. For example, in 6.4 x 10^4, the '6' and '4' are significant figures, indicating the precision of the measurement.