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Chapter 5: Problem 18

Write each number in scientific notation. $$ 0.0000004 $$

Short Answer

Expert verified
4.0 脳 10^{-7}

Step by step solution

01

Identify the significant figure

First, identify the significant figure in the number. In 0.0000004, the significant figure is 4.
02

Place the decimal point after the significant figure

Rewrite 4 with the decimal point after it: 4.0.
03

Count the places the decimal has moved

Count how many places the decimal point moved from its original position to the new position. From 0.0000004, the decimal point moved 7 places to the right.
04

Express in scientific notation

Combine the significant figure with the exponent based on the number of places moved: 4.0 脳 10^{-7}.

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Key Concepts

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

significant figure
In scientific notation, identifying the significant figure is the first step.
The significant figure is the non-zero digit or combination of digits that carry meaningful contributions to a number's precision.
In the original exercise, **0.0000004**, the significant figure is 4 because it is the only non-zero digit.
By focusing on significant figures, you can simplify complex numbers into a more manageable form. You will need this number as a base for creating scientific notation.
decimal point
The decimal point plays a crucial role in both standard and scientific notation.
In scientific notation, you reposition the decimal point right after the significant figure.
For the number **0.0000004**, moving the decimal point after 4 gives us **4.0**.
This positioning is essential to express numbers in a consistent, easy-to-read format.
Changing the decimal position helps create a standard form and ensures the integrity and precision of the number.
exponentiation
Exponentiation in scientific notation involves counting how many places the decimal point has moved.
This count becomes the exponent of 10.
In the example of **0.0000004**, moving the decimal point 7 places to the right transforms the number into **4.0**.
Consequently, you multiply the significant figure by **10^{-7}** to represent the original number: \(\text{4.0} \times 10^{-7} \).
This method makes large or small numbers easier to work with in practical and scientific calculations.

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Most popular questions from this chapter

Write each number without exponents. $$ 8.56 \times 10^{0} $$

Use scientific notation to calculate the answer to each problem. In 2007 , the state of Minnesota had about \(7.9 \times 10^{4}\) farms with an average of \(3.5 \times 10^{2}\) acres per farm. What was the total number of acres devoted to farmland in Minnesota that year?

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