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Chapter 0: Problem 78

Write each number in scientific notation. $$64,000$$

Short Answer

Expert verified
The number 64,000 can be written in scientific notation as \(6.4 \times 10^4\).

Step by step solution

01

Identify the Coefficient

Looking at the number 64,000, the first non-zero digit from the left is '6'. This is the starting point of the coefficient. Following this, we consider all numbers until the first zero to the right, which gives us '64'. Thus, the coefficient in this case is '6.4'.
02

Identify the Exponent

The exponent is determined by counting how many places you would move the decimal point to the right to get from the coefficient to the original number. Here, starting from '6.4' and moving to '64,000', the decimal point needs to be moved 4 places to the right. Thus the exponent is 4.
03

Combine Coefficient and Exponent into Scientific Notation

Now combine the coefficient '6.4' and the exponent '4' into the format for scientific notation, which is \(a \times 10^n\), where 'a' is the coefficient and 'n' is the exponent. The scientific notation for 64,000 is then expressed as \(6.4 \times 10^4\).

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although I can solve \(3 x+\frac{1}{5}=\frac{1}{4}\) by first subtracting \(\frac{1}{5}\) from both sides, I find it easier to begin by multiplying both sides by \(20,\) the least common denominator.

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Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. On two examinations, you have grades of 86 and \(88 .\) There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90 . a. What must you get on the final to earn an A in the course? b. By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than \(80,\) you will lose your \(\mathrm{B}\) in the course. Describe the grades on the final that will cause this to happen.

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