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Chapter 1: Problem 16

Convert to scientific notation. 0.00000006

Short Answer

Expert verified
6.0 \times 10^{-8}

Step by step solution

01

Understand the Number

Identify the number that needs to be converted to scientific notation. In this case, the number is 0.00000006.
02

Move the Decimal Point

Move the decimal point to the right until there is only one non-zero digit to its left. For 0.00000006, moving the decimal point 8 places to the right gives 6.0.
03

Count the Decimal Movements

Count how many places you moved the decimal point. In this case, the decimal point was moved 8 places to the right.
04

Write in Scientific Notation

Combine the significant figure with a power of 10. Since the decimal point was moved 8 places to the right, the exponent will be negative. Thus, 0.00000006 is written as \[6.0 \times 10^{-8}\].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Decimal Point
The decimal point is a crucial part of writing numbers, especially in scientific notation. It separates the whole number part from the fractional part of a number. For example, in the number 0.00000006, the decimal point separates the zero whole number from the fractional part consisting of 0.00000006. When we convert to scientific notation, we shift this decimal point to create a number between 1 and 10. This helps to simplify large or small numbers and makes them more manageable to work with.
Exponents
Exponents are used in scientific notation to indicate how many times the decimal point has been moved. They are written as powers of 10. For instance, if we move the decimal point 8 places to the right for the number 0.00000006, the exponent will be -8. This translates the number into scientific notation as \[6.0 \times 10^{-8}\]. The negative exponent signifies that the original number is very small.
Significant Figures
Significant figures are the digits in a number that are meaningful in terms of accuracy and precision. They include all non-zero digits, zeros between significant digits, and trailing zeros in a decimal number. When converting to scientific notation, we only keep significant figures. For example, in 0.00000006, the significant figure is 6. Therefore, in scientific notation, it is written as \[6.0 \times 10^{-8}\] to maintain precision.

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Most popular questions from this chapter

To the student and the instructor: Throughout this text selected exercises are marked with the icon Ahal. Students who pause to inspect an Ahal exercise should find the answer more readily than those who proceed mechanically. This may involve looking at an earlier exercise or example, or performing calculations in a more efficient manner. Some Ahal exercises are left unmarked to encourage students to always pause before working a problem. Evaluate each expression using the values provided. \([5(r+s)]^{2},\) for \(r=1\) and \(s=2\)

Chess Ratings. The formula $$R=r+\frac{400(W-L)}{N}$$ is used to establish a chess player's rating \(R,\) after he or she has played \(N\) games, where \(W\) is the number of wins, \(L\) is the number of losses, and \(r\) is the average rating of the opponents. Ulana's rating is 1305 after winning 5 games and losing 3 games in tournament play. What was the average rating of her opponents? (Assume that there were no draws.)

Which numbers in the list provided are (a) whole numbers? (b) integers? (c) rational numbers? (d) irrational numbers? (e) real numbers?. $$ -17,-0.01,0, \frac{5}{4}, 8, \sqrt{77} $$

Write an equivalent expression without negative exponents and, if possible, simplify. $$ 9 x^{-4} $$

Subtract. $$ 0-9.09 $$
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