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Chapter 5: Problem 17

Write each number in scientific notation. $$ 0.000007 $$

Short Answer

Expert verified
7 脳 10^{-6}

Step by step solution

01

Identify the Decimal Point Position

Locate the current position of the decimal point in the number. For 0.000007, the decimal point is just before the 7.
02

Move the Decimal Point

Move the decimal point to the right until there is exactly one non-zero digit to the left of the decimal point. In this case, moving it 6 places to the right positions it after the 7, forming 7.
03

Count the Number of Moves

Count how many places you moved the decimal point. Here, it was moved 6 places to the right.
04

Write as a Power of 10

Express the number of places moved as a negative exponent of 10. Since the decimal was moved 6 places, the exponent is -6.
05

Combine the Results

Compose the number using scientific notation, which combines the new decimal form with the exponent of 10. For 0.000007, this results in: 7 脳 10^{-6}

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Key Concepts

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

Decimal Point
Understanding the decimal point is essential in scientific notation.
It's the dot separating whole numbers from fractional parts in a decimal number.
For example, in 0.000007, the decimal point is before the 7.
In scientific notation, we move this decimal point to have a single non-zero digit to its left.
Exponent
The exponent in scientific notation tells you how many times to move the decimal point.
For 0.000007, moving the decimal point 6 places to the right becomes 7 脳 10^{-6}.
Here, -6 is the exponent, indicating the decimal moves 6 places to the left to revert to the original number.
Powers of 10
Powers of 10 are crucial in scientific notation.
They simplify large and small numbers using exponents.
For example, 10^{2} equals 100, while 10^{-2} equals 0.01.
In 7 脳 10^{-6}, 10^{-6} shows the decimal place relationship to the original number.
Notation
Scientific notation is a method to express very large or small numbers.
It's written as a product of a number (between 1 and 10) and a power of 10.
For instance, 0.000007 written as 7 脳 10^{-6} makes it easier to handle and understand.
It combines the significant digits with exponential notation for clarity.

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Most popular questions from this chapter

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Evaluate. $$ 38 \div 10 $$
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