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Chapter 6: Problem 565

Convert each number to decimal form. $$1.93 \times 10^{-5}$$

Short Answer

Expert verified
0.0000193

Step by step solution

01

Identify the Given Scientific Notation

The given number is written as $$1.93 \times 10^{-5}$$.
02

Understand the Exponent

The exponent in the scientific notation is -5. This means the decimal point in the number 1.93 has to be moved 5 places to the left.
03

Move the Decimal Point

Take the number 1.93. Moving the decimal point 5 places to the left gives:$$00001.93.$$
04

Fill in Leading Zeros

Move the decimal point 5 places to the left to get:$$0.0000193.$$

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Key Concepts

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

Decimal Form
When dealing with scientific notation, converting it to decimal form can make the number easier to understand for many people. Scientific notation is a way to express very large or very small numbers. However, working with actual numbers in decimal form can sometimes provide better clarity.

To convert from scientific notation to decimal form:
  • Identify the number provided in scientific notation.
  • Look at the exponent of the 10 鈥� it tells you how many places to move the decimal point.
  • Move the decimal point accordingly and fill in with leading zeros if necessary.
In this case, the number given is $$1.93 \times 10^{-5}$$. Let's break down the process a bit more with this example.
Exponents
Understanding exponents is crucial when working with scientific notation. Exponents indicate how many times a number is multiplied by 10.

Key Points about Exponents:
  • A positive exponent means you move the decimal point to the right.
  • A negative exponent means you move the decimal point to the left.
For example, in the problem $$1.93 \times 10^{-5}$$, the exponent is -5, meaning we move the decimal point 5 places to the left.

Visualizing the step:
Take the number 1.93. Notice we start with one digit before the decimal. Moving it 5 places to the left will take us past the decimal point, requiring us to add leading zeros. The resulting number is: $$0.0000193$$.
Leading Zeros
Leading zeros are zeros that appear in front of real numbers, particularly when dealing with decimal form after moving the decimal point. They are crucial when the number becomes much smaller.

Steps with Leading Zeros:
  • Identify how many places you need to move the decimal point.
  • If moving left, count the number of moves until you place the decimal.
  • Any empty spaces are filled with zeros.
In our example of $$1.93 \times 10^{-5}$$:

  • We move the decimal 5 places to the left.
  • We end up filling four positions with zeros since we already have one digit to the left of the decimal in 1.93.
The result is the number 0.0000193 in decimal form. This shows how leading zeros help us accurately represent very small numbers.

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Most popular questions from this chapter

Simplify. (a) \((-5)^{-2}\) (b) \(-5^{-2}\) (c) \(\left(-\frac{1}{5}\right)^{-2}\) (d) \(-\left(\frac{1}{5}\right)^{-2}\)

Maurice simplifies the quotient \(\frac{d^{7}}{d}\) by writing \(\frac{d^{7}}{d}=7 .\) What is wrong with his reasoning?

Divide each polynomial by the monomial. $$\frac{20 b^{2}-12 b}{-4}$$

Divide each polynomial by the binomial. $$\left(p^{2}+11 p+16\right) \div(p+8)$$

Divide each polynomial by the monomial. $$\left(9 n^{4}+6 n^{3}\right) \div 3 n$$
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