Working With Fdp

边玩边学

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课程笔记

Converting Fractions, Decimals & Percentages

Percentage to decimal: Divide by 100 (move digits two places right). E.g., 6% = 0.06, 350% = 3.5.
Decimal to percentage: Multiply by 100 (move digits two places left, add %). E.g., 0.35 = 35%, 0.004 = 0.4%.
Decimal to fraction: Write digits over 10ⁿ (n = decimal places). E.g., 0.3 = 3/10, 0.07 = 7/100, 0.513 = 513/1000.
Percentage to fraction: Write over 100. E.g., 37% = 37/100.
Fraction to decimal: Convert to fraction over power of 10. E.g., 3/5 = 6/10 = 0.6; 7/20 = 35/100 = 0.35.
Fraction to percentage: Convert to decimal then multiply by 100. E.g., 4/5 = 0.8 = 80%.
Learn simple recurring decimals: 0.333… = 1/3, 0.666… = 2/3.

Recurring Decimals

Recurring decimal: A decimal with a repeating pattern; e.g., 0.323232… = 0.3̇2̇.
Notation: Dot over single repeating digit; dots over first and last of repeating block (e.g., 0.1̇2̇ for 0.121212…).
Converting to fraction: Set x = decimal, multiply by 10ⁿ until two lines have same repeating part, subtract, solve for x.
Worked example: 0.3̇07̇ → x = 0.307307…, 1000x = 307.307…, subtract: 999x = 307, so x = 307/999.
Always simplify fraction to lowest terms.

Ordering Fractions, Decimals & Percentages

Ordering fractions only: Write all with a common denominator, then compare numerators.
Example: 3/5, 1/2, 13/20, 7/12 → common denominator 60 → 36/60, 30/60, 39/60, 35/60 → order: 1/2, 7/12, 3/5, 13/20.
Ordering mixed FDP: Convert everything to decimals (or percentages) for easy comparison.
Example: 7/8, 5/6, 0.8, 78% → decimals: 0.875, 0.833…, 0.8, 0.78 → order: 78% < 0.8 < 5/6 < 7/8.
Use symbols: < (less than), > (greater than), ≤, ≥, =, ≠.

Ordering FDP: the 5-step method

Common Conversions & Tips

Memorise: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10%.
Calculator tip: Use calculator to check conversions even in non-calculator questions (for verification).
Non-calculator tip: For fractions, use short division or halving (e.g., 7/8 = half of 7/4, etc.).

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练习题

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1.Which of the following is the decimal equivalent of 3/5?
Easy
- A0.35
- B0.6
- C1.67
2.Write 0.45 as a percentage.
Easy
- A4.5%
- B45%
- C0.45%
- D450%
3.Convert 72% to a fraction in its simplest form.
Easy
- A72/100
- B18/25
- C36/50
- D7.2/10
4.Which number has the largest value?
Medium
- A0.3030
- B1/3
- C0.0330
- D3/10
- E33%
5.Mr Mason asks 240 Year 11 students what they want to do next year. 15% want to go to college, 3/4 want to stay at school, and the rest do not know. How many students do not know?
Medium
- A24
- B36
- C60
- D12
6.Karen got 32 out of 80 in a maths test and 38% in an English test. Did she get a higher percentage in maths or English?
Medium
- AMaths
- BEnglish
- CSame
- DCannot tell
7.Prove algebraically that the recurring decimal 0.25̇ (0.25555...) equals which fraction?
Hard
- A23/90
- B25/99
- C23/99
- D25/90
8.Show that the recurring decimal 0.17̇ (0.17777...) equals which fraction?
Hard
- A8/45
- B17/99
- C16/90
- D8/90

复习笔记

## Working with FDP – Revision Notes ### Converting Fractions, Decimals & Percentages - **Percentage to decimal**: Divide by 100 (move digits two places right). - 6% = 0.06, 40% = 0.4, 350% = 3.5, 0.2% = 0.002 - **Decimal to percentage**: Multiply by 100 (move digits two places left, add %). - 0.35 = 35%, 1.32 = 132%, 0.004 = 0.4% - **Decimal to fraction**: Write digits over 10^n (n = decimal places). - 0.3 = 3/10, 0.07 = 7/100, 0.513 = 513/1000 - **Percentage to fraction**: Write over 100. - 37% = 37/100 - **Fraction to decimal**: Convert to denominator 10, 100, 1000… - 3/5 = 6/10 = 0.6, 7/20 = 35/100 = 0.35 - **Fraction to percentage**: Convert to decimal then multiply by 100. - 4/5 = 0.8 → 80% ### Recurring Decimals - **Definition**: A decimal with a repeating pattern (e.g., 0.333… = 0.3̇). - **Converting to fraction**: 1. Let x = recurring decimal (e.g., x = 0.353535…) 2. Multiply by 10 repeatedly until two lines have same repeating part. 3. Subtract those lines: 100x – x = 35.3535… – 0.3535… → 99x = 35 4. Solve: x = 35/99 (simplify if needed). - **Common ones**: 0.3̇ = 1/3, 0.6̇ = 2/3. ### Ordering FDP - **All fractions**: Write over common denominator, compare numerators. - **Mixed FDP**: Convert everything to decimals, then order. - **Symbols**: < (less than), > (greater than), ≤, ≥, =, ≠. ### Key Tips - Use a calculator to check conversions (if allowed). - For ordering, write decimals to same number of places.

Recurring decimal: A decimal with a repeating pattern of digits, e.g., 0.333… = 0.3̇. It is rational and can be written as a fraction.
Terminating decimal: A decimal that ends, e.g., 0.25.
Lowest common denominator: The smallest number that is a multiple of all denominators in a set of fractions, used to compare or add them.

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