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Chapter 1: Problem 32

Convert to decimal notation. $$2.049 \times 10^{-3}$$

Short Answer

Expert verified
0.002049

Step by step solution

01

Identify the components

Note that the number is in scientific notation, which consists of a decimal number and a power of ten. Here, the decimal number is 2.049 and the exponent is -3.
02

Understand the exponent

The exponent -3 indicates that the decimal point must be moved 3 places to the left. This is because negative exponents on 10 mean the number is very small.
03

Move the decimal point

Starting from 2.049, move the decimal point 3 places to the left. When you move the decimal point, if there are no more digits left to move past, you will need to add zeros.
04

Perform the conversion

Move the decimal point three places to the left: 2.049 becomes 0.002049.

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Key Concepts

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

Decimal Notation
Decimal notation is the standard system for denoting numbers. In this system, each number is represented using digits 0-9, and it can include a decimal point to represent numbers smaller than one. For instance, the number 12.34 is in decimal notation. This system is very familiar in daily life. When converting scientific notation (e.g., 1.23 脳 10^3) to decimal notation, we eliminate the exponent and express the number in its full decimal form.
Negative Exponent
An exponent is a number that indicates how many times a base number is multiplied by itself. A negative exponent indicates a reciprocal or division. For example, 10^{-3} is the same as 1/(10^3) or 0.001. When we see a negative exponent in scientific notation, it tells us to move the decimal point to the left. This shows a very small number.

Key points to remember:
  • An exponent tells how many times to multiply the base number.
  • A negative exponent indicates moving the decimal to the left.
  • A small number reaches closer to zero as the exponent becomes more negative.
Moving Decimal Points
Moving decimal points is an essential part of converting scientific notation to decimal notation. To convert 2.049 脳 10^{-3} to decimal notation, you need to move the decimal point based on the exponent value. The negative exponent, -3, means moving the decimal point three places to the left.

Steps to move the decimal point:
  • Start with the number given in scientific notation (e.g., 2.049).
  • Identify the exponent, which in this case is -3.
  • Move the decimal point to the left by the number of spaces indicated by the exponent.
  • Fill in any gaps with zeros.
Following these steps, 2.049 脳 10^{-3} becomes 0.002049.

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