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Scientific Notation
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.
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Scientific Notation
What is it?
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.
In simple words
- 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.
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.
What you should learn
- 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.
Examples
- 650000000 = 6.5 x 108
- 6000 = 6 x 103
- Earth 12700000 m = 1.27 x 107 m
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 10^8. 6000 = 6 x 10^3. 14 x 10^5 is NOT standard, because 14 is not less than 10; rewrite as 1.4 x 10^6.
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.
Recommended for Class 9
Full school-level explanation
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.
Move the decimal point until A is legal:
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 10^8. 6000 = 6 x 10^3. 14 x 10^5 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.
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 10^8. 6000 = 6 x 10^3. 14 x 10^5 is NOT standard, because 14 is not less than 10; rewrite as 1.4 x 10^6.
Remember
- move the point left
- 650000000 = 6.5 x 108
- NOT standard
- 1.4 x 10^6
Examples
- 650000000 = 6.5 x 108
- 6000 = 6 x 103
- Earth 12700000 m = 1.27 x 107 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.
Remember
- move the point right
- 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
Remember
- A x 10^n
- mantissa
- 1 <= A < 10
- 1.7 x 10^0
- 6.4 x 10^6
- 1 <= A < 10
- move the point left
- 650000000 = 6.5 x 108
How the ideas connect
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.
Deeper understanding
Go beyond memorising Scientific Notation. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
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.
Common mistakes
Exam focus
WHAT
Key Points
HOW
Example
Exam focus
Quick revision
- A x 10^n
- mantissa
- 1 <= A < 10
- 1.7 x 10^0
- 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.
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.
For long answers on Scientific Notation: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- A x 10^n
- mantissa
- 1 <= A < 10
- 1.7 x 10^0
Important formulas
- A x 10^n
- mantissa
- 1 <= A < 10
Common exam traps
- In standard scientific notation, the first number must be at least 1 but less than 10.
- Moving the decimal right gives a negative power for a small number.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
In standard scientific notation, the first number must be at least 1 but less than 10.
- Mistake
Moving the decimal right gives a negative power for a small number.
- Mistake
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.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
A x 10^n
mantissa
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. n is an integer. 1.7 x 10^0 is allowed, because A still sits in that r
1 <= A < 10
- 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 r
- Formula
- 1 <= A < 10
- Example
- 650000000 = 6.5 x 108
- Critical warning
- In standard scientific notation, the first number must be at least 1 but less than 10.
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Exam Practice
Define
Q1. Define Scientific Notation.
Explain
Q2. Explain: NUMBERS GREATER THAN 10.
Example
Q3. Give one clear example of Scientific Notation and say why it fits.
Mistake
Q4. State one common mistake students make about Scientific Notation.
Exam note
Q5. Write a short exam note on Scientific Notation: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.