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Chapter 7: Problem 5

Convert each number into scientific notation. $$0.00007$$

Short Answer

Expert verified
7.0 x 10^{-5}

Step by step solution

01

Identify the significant figures

The significant figures are the non-zero digits or zeros between them. In the number 0.00007, the significant figure is 7.
02

Place the decimal point

Place the decimal point immediately after the first significant figure. This gives us 7.0.
03

Count the decimal places moved

Count how many places the decimal point was moved to get from the original number (0.00007) to the position after the first significant figure (7.0). It was moved 5 places to the right.
04

Write in scientific notation

Combine the significant figure with the decimal point and the appropriate power of 10. Since the decimal moved 5 places to the right, the exponent will be negative 5. This gives us 7.0 x 10^{-5}.

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Key Concepts

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

significant figures
When working with scientific notation, it's important to understand significant figures. Significant figures are the digits in a number that carry meaningful information about its precision. They include all non-zero digits, any zeros between them, and trailing zeros in a decimal part. For example, in the number 0.00007, the only significant figure is 7. This means that 7 is the digit that carries the information about the precision of the number.
decimal place
The position of the decimal point is a key factor in scientific notation. In our example, we need to determine how many decimal places the decimal point must move. A decimal place is the position of a digit to the right of the decimal point. In the number 0.00007, the decimal point must move 5 places to the right to position it immediately after the significant figure 7. This results in the value 7.0. This placement is essential for standardizing the number for scientific notation.
power of 10
The power of 10 component in scientific notation allows us to express very large or very small numbers concisely. It adjusts the decimal place back to its original position. In our example, we moved the decimal point 5 places to the right, which is represented as a negative exponent. Therefore, we write the number as 7.0 x 10^{-5}. Here, -5 denotes that the decimal point must be moved 5 places to the left to retrieve the original number. This way, scientific notation efficiently displays and communicates the scale of the number.

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Most popular questions from this chapter

Convert each number into standard notation. $$3.52 \times 10^{-3}$$

Multiply out each of the following. As you work out the problems, identify those exercises that are either a perfect square or the difference of two squares. $$(x+6)(x-2)$$

Simplify each of the following expressions as completely as possible. Final answers should be expressed with positive exponents only. (Assume that all variables represent positive quantities.) $$(x y)^{4}$$

Convert each number into scientific notation. $$0.00000003$$

Do your computation using scientific notation. $$(0.004)(250)$$
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