Chapter 1: Problem 32

Review Working It Out 1.1 . Convert the following numbers to standard notation: a. \(5.34 \times 10^{8}\) b. \(4.1 \times 10^{3}\) c. \(6.24 \times 10^{-5}\)

Short Answer

Expert verified

a. 534,000,000 b. 4,100 c. 0.0000624

Step by step solution

- Understand Scientific Notation

Scientific notation is a way to represent very large or very small numbers. It consists of a number between 1 and 10 multiplied by a power of 10.

- Convert a. 5.34 × 10^{8}

To convert to standard notation, move the decimal point 8 places to the right. Starting with 5.34: 5.34 → 534 → 53400 → 5340000 → 534000000. So, the number in standard notation is 534,000,000.

- Convert b. 4.1 × 10^{3}

Move the decimal point 3 places to the right. Starting with 4.1: 4.1 → 41 → 410 → 4100. So, the number in standard notation is 4,100.

- Convert c. 6.24 × 10^{-5}

Move the decimal point 5 places to the left adding zeros as needed. Starting with 6.24: 6.24 → 0.624 → 0.0624 → 0.00624 → 0.000624 → 0.0000624. So, the number in standard notation is 0.0000624.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

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

Standard Notation

Standard notation is a way of writing numbers without using exponents. Instead of expressing a number like 4.1 × 10^{3}, which can be confusing, we write it as 4100. This makes it easier to read and understand, especially for everyday use.
To convert from scientific notation to standard notation, follow these steps:

Identify the exponent on the 10.
Move the decimal point in the base number accordingly.
If the exponent is positive, move the decimal point to the right; if it's negative, move it to the left.

For example, with 5.34 × 10^{8}, move the decimal 8 places to the right to get 534,000,000. This is the standard notation.

Powers of 10

Understanding powers of 10 is crucial for mastering scientific notation. Powers of 10 tell us how many times to multiply or divide by 10.
For instance:

10^{3} means 10 × 10 × 10 = 1000.
10^{-2} means 1 / (10 × 10) = 0.01.

This system makes it easier to work with very large or very small numbers. For example, 4.1 × 10^{3} means moving the decimal point 3 places to the right, resulting in 4100. Conversely, 6.24 × 10^{-5} means moving the decimal 5 places to the left, leading to 0.0000624.

Decimal Point Movement

When converting between scientific notation and standard notation, the key is moving the decimal point. The direction and number of places to move the decimal are determined by the exponent on the 10.
Here are the steps:

For a positive exponent, move the decimal point to the right.
For a negative exponent, move the decimal point to the left.

Consider 5.34 × 10^{8}: The exponent 8 is positive, so move the decimal point 8 places to the right, resulting in 534,000,000.
Now, let's look at 6.24 × 10^{-5}: The exponent -5 is negative, so move the decimal point 5 places to the left. Don’t forget to add zeros as placeholders where necessary. This gives us 0.0000624.

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Review Working It Out 1.1 . Convert the following numbers to standard notation: a. \(5.34 \times 10^{8}\) b. \(4.1 \times 10^{3}\) c. \(6.24 \times 10^{-5}\)

Short Answer

Step by step solution

- Understand Scientific Notation

- Convert a. 5.34 × 10^{8}

- Convert b. 4.1 × 10^{3}

- Convert c. 6.24 × 10^{-5}

Key Concepts

Standard Notation

Powers of 10

Decimal Point Movement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physical Quantities And Units

Modern Physics

Radiation

Engineering Physics

Further Mechanics and Thermal Physics

Magnetism and Electromagnetic Induction

Study anywhere. Anytime. Across all devices.