MathematicsChapter 5: Linear Equations and Inequalities
Decimals
Count the largest number of digits after the decimal point and multiply through by 10 to that power.
Learning objectives
- Define and explain decimals.
- Apply decimals to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
Count the largest number of digits after the decimal point and multiply through by 10 to that power. For 0.2x+0.5=1.3 multiply by 10 to get 2x+5=13, then 2x=8 and x=4. Mixed decimals such as 0.05x=0.2 need 100. The decimals disappear and you return to integers.
Formula
x=4. Mixed decimals such as 0.05x
Where / symbols
- Decimals
- Count the largest number of digits after the decimal point and multiply through by 10 to that power. For 0.2x+0.5=1.3 multiply by 10 to get 2x+5=13, then 2x=8 and x=4. Mixed decimals such as 0.05x=0.2 need 100. The decimals disappear and you return to integers.
Relationship
- x=4
Overview
Learn the idea, then use it:
Core Understanding
Count the largest number of digits after the decimal point and multiply through by 10 to that power. For 0.2x+0.5=1.3 multiply by 10 to get 2x+5=13, then 2x=8 and x=4. Mixed decimals such as 0.05x=0.2 need 100. The decimals disappear and you return to integers.
Examples multiply through by 10 · x=4 · integers · DECIMALS: Count the largest number of digits after the decimal point and multiply through by 10 to that power. For 0.2x+0.5=1.3 mu
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — DECIMALS
Count the largest number of digits after the decimal point and multiply through by 10 to that power. For 0.2x+0.5=1.3 multiply by 10 to get 2x+5=13, then 2x=8 and x=4. Mixed decimals such as 0.05x=0.2 need 100. The decimals disappear and you return to integers.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge decimals with a neighbouring idea that uses a different definition, rule, or method.
Key points
- multiply through by 10
- x=4
- integers
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Decimals
Sticky Notes · Quick Revision
Core Idea
- Count the largest number of digits after the decimal point and multiply through by 10 to that power.
Key Points
- multiply through by 10
- x=4
- integers
Simple Check
- Explain decimals in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge decimals with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- Count the largest number of digits after the decimal point and multiply through by 10 to that power.
- multiply through by 10
- x=4
- integers
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