ChemistryChapter 16: Empirical Data Collection and Analysis
Scientific Notation
Scientific notation writes a number as A x 10^n, where A is the mantissa and 1 <= A < 10.
Learning objectives
- State the main idea of scientific notation in clear words.
- Explain why scientific notation is useful in chemistry.
- Apply the correct method, observation, equation, or comparison.
- Avoid the common mistakes and write a complete exam answer.
Definition
Scientific notation writes a number as A x 10^n, where A is the mantissa and 1 <= A < 10. n is an integer. 1.7 x 10^0 is allowed, because A still sits in that range and 10^0 = 1.
Formula
m = 6.4 x 106 m. Count how many places the
Important terms
- A x 10^n
- Scientific notation writes a number as A x 10^n, where A is the mantissa and 1 <= A < 10.
- mantissa
- Scientific notation writes a number as A x 10^n, where A is the mantissa and 1 <= A < 10.
- 1 <= A < 10
- Scientific notation writes a number as A x 10^n, where A is the mantissa and 1 <= A < 10.
- 1.7 x 10^0
- Scientific notation writes a number as A x 10^n, where A is the mantissa and 1 <= A < 10.
Relationship
- 1 <= A < 10
Overview
Move the decimal point until A is legal:
Numbers Greater Than 10
If the number is greater than 10, move the point left. Each left step adds 1 to the exponent. 650000000 = 6.5 x 108. 6000 = 6 x 103. 14 x 105 is NOT standard, because 14 is not less than 10; rewrite as 1.4 x 10^6.
Examples 650000000 = 6.5 x 10^8 · 6000 = 6 x 10^3 · Earth 12700000 m = 1.27 x 10^7 m
Numbers Less Than 1
If the number is less than 1, move the point right. Each right step makes the exponent more negative. 0.006 = 6 x 10-3. 0.00000046 = 4.6 x 10-7.
Examples 0.006 = 6 x 10^-3 · Mosquito 0.01 m = 1 x 10^-2 m · RBC 0.0000075 m = 7.5 x 10^-6 m
WHAT — Core idea
Scientific notation writes a number as A x 10^n, where A is the mantissa and 1 <= A < 10. n is an integer. 1.7 x 10^0 is allowed, because A still sits in that range and 10^0 = 1.
WHY — Why it matters
Great Wall length 6400000 m = 6.4 x 10^6 m. Count how many places the point moved: that count is n. Left move: n is positive. Right move: n is negative.
HOW — Method, evidence, or comparison
1. 1. NUMBERS GREATER THAN 10: If the number is greater than 10, move the point left. Each left step adds 1 to the exponent. 650000000 = 6.5 x 108. 6000 = 6 x 103. 14 x 105 is NOT standard, because 14 is not less than 10; rewrite as 1.4 x 10^6. 2. 2. NUMBERS LESS THAN 1: If the number is less than 1, move the point right. Each right step makes the exponent more negative. 0.006 = 6 x 10-3. 0.00000046 = 4.6 x 10-7.
HOW — Answer in an exam
A must satisfy 1 <= A < 10. If A is 14, 0.65, or 10, the form is not finished. Shift the point one more place and adjust n.
Explanation
Great Wall length 6400000 m = 6.4 x 10^6 m. Count how many places the point moved: that count is n. Left move: n is positive. Right move: n is negative.
In simple words
A must satisfy 1 <= A < 10. If A is 14, 0.65, or 10, the form is not finished. Shift the point one more place and adjust n.
Key points
- A x 10^n
- mantissa
- 1 <= A < 10
- 1.7 x 10^0
- move the point left
- 650000000 = 6.5 x 108
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Scientific Notation
Sticky Notes · Quick Revision
WHAT
- Scientific notation writes a number as A x 10^n, where A is the mantissa and 1 <= A < 10.
Key Points
- A x 10^n
- mantissa
- 1 <= A < 10
- 1.7 x 10^0
HOW
- If the number is greater than 10, move the point left.
- If the number is less than 1, move the point right.
Example
- 650000000 = 6.5 x 108
- 6000 = 6 x 103
- Earth 12700000 m = 1.27 x 107 m
Common Mistake
- In standard scientific notation, the first number must be at least 1 but less than 10.
Exam Tip
- A must satisfy 1 <= A < 10.
- If A is 14, 0.65, or 10, the form is not finished.
60-second revision
- Scientific notation writes a number as A x 10^n, where A is the mantissa and 1 <= A < 10.
- n is an integer.
- If the number is greater than 10, move the point left.
- If the number is less than 1, move the point right.
- A must satisfy 1 <= A < 10.
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