Topic 1.2.23 min read
1.2.2 Conversions from one Number system to the other
To convert from any base to decimal, we expand the number using positional weights (powers of the base) and add the results. To convert from decimal to any other base, we divide the integer part repeatedly by the new base and record remainders, and we multiply the fractional part repeatedly
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1.2.2 Conversions from one Number system to the other
What is it?
To convert from any base to decimal, we expand the number using positional weights (powers of the base) and add the results. To convert from decimal to any other base, we divide the integer part repeatedly by the new base and record remainders, and we multiply the fractional part repeatedly
In simple words
1.2.2 Conversions from one Number system to the other is a core idea in this chapter. Learn the meaning first, then the main parts, then one clear example.
Recommended for Class 10
Full school-level explanation
To convert from any base to decimal, we expand the number using positional weights (powers of the base) and add the results. To convert from decimal to any other base, we divide the integer part repeatedly by the new base and record remainders, and we multiply the fractional part repeatedly
Why it matters
Understanding 1.2.2 Conversions from one Number system to the other helps you answer definition, explanation, and application questions in this chapter.
Deeper understanding
Go deeper on 1.2.2 Conversions from one Number system to the other: connect the definition to reasons, relationships, exceptions, and exam wording.
Exam focus
Key Point 1
Key Point 2
Key Point 3
Key Point 4
Exam focus
Quick revision
- To convert from any base to decimal, we expand the number using positional weights (powers of the base) and add the
For long answers on 1.2.2 Conversions from one Number system to the other: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- To convert from any base to decimal, we expand the number using positional weights (powers of the base) and add the
Common exam traps
- Do not write about 1.2.2 Conversions from one Number system to the other without a clear definition.
- Do not mix this idea with a neighbouring chapter concept.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not write about 1.2.2 Conversions from one Number system to the other without a clear definition.
- Mistake
Do not mix this idea with a neighbouring chapter concept.
- Mistake
Do not list facts without showing how they connect.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
To convert from any base to decimal, we expand the number using positional weights (powers of the base) and add the
To convert from any base to decimal, we expand the number using positional weights (powers of the base) and add the results. To convert **from decimal to an
- Definition
- To convert from any base to decimal, we expand the number using positional weights (powers of the base) and add the results. To convert **from decimal to an
- Critical warning
- Do not write about 1.2.2 Conversions from one Number system to the other without a clear definition.
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Exam Practice
Define
Q1. Define 1.2.2 Conversions from one Number system to the other.
Explain
Q2. Explain the main ideas in 1.2.2 Conversions from one Number system to the other.
Example
Q3. Give one clear example of 1.2.2 Conversions from one Number system to the other and say why it fits.
Mistake
Q4. State one common mistake students make about 1.2.2 Conversions from one Number system to the other.
Exam note
Q5. Write a short exam note on 1.2.2 Conversions from one Number system to the other: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.