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Chapter 7: Problem 20

Convert each number into scientific notation. $$0.07$$

Short Answer

Expert verified
7 \times 10^{-2}

Step by step solution

01

Identify the Decimal Point

Locate the decimal point in the number. For the number 0.07, the decimal point is between the 0 and 7.
02

Move the Decimal Point

Move the decimal point to create a number between 1 and 10. For 0.07, the decimal point moves two places to the right, resulting in the number 7.
03

Count the Number of Moves

Count how many places you moved the decimal point. Here, the decimal point moved 2 places.
04

Apply the Scientific Notation Form

Express the number in scientific notation by combining the new number with a power of 10. Since 0.07 became 7 and we moved the decimal 2 places, the notation is: \(0.07 = 7 \times 10^{-2}\).

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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 crucial when working with scientific notation. A decimal point separates the whole number part of a number from its fractional part. For example, in the number 0.07, the decimal point is between the 0 and the 7.
In scientific notation, we often need to move the decimal point to create a number between 1 and 10. In the case of 0.07, moving the decimal point two places to the right changes the number to 7.
This helps in simplifying the number, making it easier to work with using powers of ten.
Powers of Ten
Powers of ten are a foundational concept in scientific notation. A power of ten is written as 10 raised to an exponent. This exponent indicates how many times 10 is multiplied by itself. For example, 10^3 means 10 脳 10 脳 10.
When you move the decimal point to convert a number to scientific notation, you express how many places you moved the decimal as a power of ten. For example, in 0.07, the decimal moved two places to the right, which corresponds to 10^-2.
This means \(0.07 = 7 \times 10^{-2}\).
Notation Form
Scientific notation is a way of expressing very large or very small numbers in a compact form. It uses a number between 1 and 10 (called the coefficient) and a power of ten.
The steps to convert a number to scientific notation are: locate the decimal point, move the decimal point so you have a number between 1 and 10, then count how many places you moved the point and express that as a power of ten.
For example, converting 0.07: first, locate the decimal point, move it two places right to get 7, and write it as \(7 \times 10^{-2}\).
This makes working with such numbers much simpler and more manageable, especially in scientific and engineering fields.

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