Table of contents

1. Matter and Measurements4h 31m
2. Atoms and the Periodic Table5h 23m
3. Ionic Compounds2h 18m
4. Molecular Compounds2h 18m
5. Classification & Balancing of Chemical Reactions3h 17m
6. Chemical Reactions & Quantities2h 27m
7. Energy, Rate and Equilibrium3h 46m
8. Gases, Liquids and Solids3h 25m
9. Solutions4h 10m
10. Acids and Bases3h 29m
11. Nuclear Chemistry56m
BONUS: Lab Techniques and Procedures1h 38m
BONUS: Mathematical Operations and Functions47m
12. Introduction to Organic Chemistry1h 34m
13. Alkenes, Alkynes, and Aromatic Compounds2h 12m
14. Compounds with Oxygen or Sulfur1h 6m
15. Aldehydes and Ketones1h 1m
16. Carboxylic Acids and Their Derivatives1h 11m
17. Amines39m
18. Amino Acids and Proteins1h 51m
19. Enzymes1h 37m
20. Carbohydrates1h 41m
21. The Generation of Biochemical Energy2h 8m
22. Carbohydrate Metabolism2h 22m
23. Lipids2h 26m
24. Lipid Metabolism1h 45m
25. Protein and Amino Acid Metabolism1h 37m
26. Nucleic Acids and Protein Synthesis2h 54m

1. Matter and Measurements

Scientific Notation

GOB Chemistry

1. Matter and Measurements

Scientific Notation

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1:51 minutes

Problem 28a

Textbook Question

Which number in each of the following pairs is smaller?
a. 4.9 × 10^-3 or 5.5 × 10^-9

Verified step by step guidance

Step 1: Understand the problem. You are comparing two numbers written in scientific notation: 4.9 × 10⁻³ and 5.5 × 10⁻⁹. The goal is to determine which number is smaller.

Step 2: Recall how scientific notation works. A number in scientific notation is expressed as \( a \times 10^n \), where \( a \) is the coefficient (a number between 1 and 10) and \( n \) is the exponent (which indicates the power of 10).

Step 3: Compare the exponents first. The exponent \( n \) determines the order of magnitude of the number. A smaller exponent (more negative) indicates a smaller number. In this case, \( 10^{-3} \) is larger than \( 10^{-9} \), so the number with \( 10^{-9} \) will be smaller.

Step 4: If the exponents were the same, you would compare the coefficients (\( a \)). However, since the exponents are different here, you do not need to compare the coefficients because the exponent already determines which number is smaller.

Step 5: Conclude that the number with the smaller exponent, 5.5 × 10⁻⁹, is the smaller number in this pair.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is typically formatted as 'a x 10^n', where 'a' is a number greater than or equal to 1 and less than 10, and 'n' is an integer. This notation simplifies calculations and comparisons of very large or very small numbers.

Comparing Exponents

When comparing numbers in scientific notation, the first step is to compare the exponents of 10. The number with the larger exponent is the larger number. If the exponents are the same, then the coefficients (the 'a' values) are compared to determine which number is smaller or larger.

Decimal Conversion

To compare numbers in scientific notation directly, converting them to decimal form can be helpful. For example, 4.9 x 10⁻³ equals 0.0049, and 5.5 x 10⁻⁹ equals 0.0000000055. This conversion allows for straightforward comparison of the two values by examining their decimal representations.

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Which number in each of the following pairs is smaller? a. 4.9 × 10-3 or 5.5 × 10-9

Key Concepts

Scientific Notation

Comparing Exponents

Decimal Conversion

Watch next

Which number in each of the following pairs is smaller?
a. 4.9 × 10^-3 or 5.5 × 10^-9