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Chapter 1: Problem 31

Convert to decimal notation. $$7.001 \times 10^{-5}$$

Short Answer

Expert verified
0.00007001

Step by step solution

01

Understand Scientific Notation

Recognize that scientific notation is a way of writing numbers that are too large or too small to be conveniently written in decimal form. The format is typically written as the product of a number between 1 and 10 and a power of 10.
02

Identify the Components

Identify the components of the scientific notation. In this case, the number is 7.001 and the exponent is -5. This indicates that the decimal point needs to move 5 places to the left to convert the number from scientific notation to decimal notation.
03

Move the Decimal Point

Move the decimal point in 7.001 five places to the left. To do this, you need to add leading zeros. 7.001 becomes 0.00007001.

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Key Concepts

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

decimal notation
Understanding decimal notation is essential for mastering scientific notation conversion. Decimal notation refers to the standard system of writing numbers which we use every day. This system is based on powers of ten and employs a decimal point to separate the whole number part from the fractional part.

For example, the number 123.45 in decimal notation means:
  • 123 (the whole number part, left side of the decimal point)
  • 0.45 (the fractional part, right side of the decimal point)
In decimal notation, the position of each digit conveys its value due to its place. Each position represents a power of ten, making it easier to understand large and small numbers when written correctly.
powers of ten
Powers of ten are fundamental in converting between scientific and decimal notation. A power of ten is expressed as 10 raised to an exponent, which indicates how many times to use 10 in a multiplication. For instance, 103 means 10 * 10 * 10, which equals 1000.

When the exponent is negative, like in 10-3, it indicates division rather than multiplication. So, 10-3 equals 1/1000 or 0.001.

In scientific notation, the exponent tells us how many places to move the decimal point. For example, in 7.001 脳 10-5, the decimal point will move five places to the left due to the negative exponent.
leading zeros
When converting from scientific notation to decimal notation, adding leading zeros is a common step. Leading zeros are zeros that appear in front of all the non-zero digits of a number. They help maintain the correct value when shifting the decimal point.

For instance, in the example 7.001 脳 10-5, moving the decimal point five places to the left requires adding leading zeros:
  • Start with 7.001
  • Move the decimal five places to the left, filling in each empty space with zeros.
  • Result is 0.00007001

Leading zeros ensure we aptly represent the size of the number in decimal notation. Therefore, 0.00007001 accurately corresponds to 7.001 脳 10-5.

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