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Chapter 5: Problem 88

Convert to decimal notation. $$ 7.034 \times 10^{-2} $$

Short Answer

Expert verified
0.07034

Step by step solution

01

Understand the Scientific Notation

Scientific notation consists of two parts: a number (in this case, 7.034) and a power of 10 (in this case, 10^{-2}). The power indicates how many places to move the decimal point.
02

Identify the Direction for Decimal Movement

Since the power of 10 is negative (-2), the decimal point will be moved 2 places to the left.
03

Move the Decimal Point

Start with the number 7.034 and move the decimal point 2 places to the left. This will involve adding zeros as needed.
04

Write the Decimal Notation

After moving the decimal, 7.034 becomes 0.07034.

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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 a way of representing numbers using the base-10 number system, which includes positions for ones, tens, hundreds, and so forth. Each place value is ten times the place value to its immediate right. This makes it easy to write very large or very small numbers.
When converting from scientific notation to decimal notation, you'll move the decimal point to the right for positive exponents and to the left for negative exponents.
  • For example, converting \(7.034 \times 10^{-2}\) means you will move the decimal point two places to the left.
  • This makes the number smaller, resulting in 0.07034.
Power of 10
The power of 10 is a fundamental concept in scientific notation. It tells us how many times to multiply or divide the number by 10. In the context of scientific notation:
  • An exponent of 2, or \(10^2\), means multiplying by 100 (i.e., 10 multiplied by itself twice).
  • An exponent of -2, or \(10^{-2}\), means dividing by 100, or multiplying by 0.01.
This is why the decimal point is moved to the left when the exponent is negative, effectively making the number smaller. Understanding powers of 10 helps simplify complex calculations and conversions between scientific and decimal forms.
Negative Exponent
A negative exponent indicates that the number should be divided by 10 for each count of the exponent. For example, with an exponent of -2, you move the decimal point two places to the left.
Here鈥檚 how it works in detail:
  • If you start with 7.034 and have an exponent of -2, you move the decimal point two places left, changing \(7.034\) to \(0.07034\).
  • Each shift to the left divides the number by 10 once, so two shifts mean dividing by 100.
It's important to remember that whenever you see a negative exponent in scientific notation, you are essentially decreasing the magnitude of the original number by moving the decimal point to the left.

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Most popular questions from this chapter

Write the reciprocal of \(8.00 \times 10^{-23}\) in scientific notation.

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