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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1:39 minutes

Problem 27a

Textbook Question

Which number in each of the following pairs is larger?
a. 7.2 × 10³ or 8.2 × 10²

Verified step by step guidance

Step 1: Understand the problem. You are comparing two numbers written in scientific notation: 7.2 × 10³ and 8.2 × 10². The goal is to determine which number is larger.

Step 2: Recall the structure of scientific notation. A number in scientific notation is written as \( a \times 10^n \), where \( a \) is the coefficient (a number between 1 and 10) and \( n \) is the exponent (an integer). The exponent determines the scale or magnitude of the number.

Step 3: Compare the exponents first. In this case, the exponents are 3 for \( 7.2 \times 10^3 \) and 2 for \( 8.2 \times 10^2 \). Since 10³ (1000) is larger than 10² (100), the number with the larger exponent will generally be larger.

Step 4: If the exponents were equal, you would compare the coefficients (7.2 and 8.2). However, since the exponents are different, the number with the larger exponent (7.2 × 10³) is automatically larger.

Step 5: Conclude that \( 7.2 \times 10^3 \) is larger than \( 8.2 \times 10^2 \) based on the comparison of their exponents.

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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 between very large or very small numbers.

Exponents

Exponents indicate how many times a number, known as the base, is multiplied by itself. In scientific notation, the exponent represents the power of ten that scales the number. Understanding exponents is crucial for comparing numbers in scientific notation, as a higher exponent indicates a larger value when the base is the same.

Comparing Numbers

To compare numbers in scientific notation, one must first ensure they are expressed with the same exponent. If the exponents differ, the number with the larger exponent is greater. If the exponents are the same, the coefficients (the numbers before the 'x') can be directly compared to determine which is larger.

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Which number in each of the following pairs is larger? a. 7.2 × 103 or 8.2 × 102

Key Concepts

Scientific Notation

Exponents

Comparing Numbers

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Which number in each of the following pairs is larger?
a. 7.2 × 10³ or 8.2 × 10²