Fractions Decimals And Percentages

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Lesson notes

Converting Fractions, Decimals & Percentages

To convert a percentage to a decimal, divide by 100 (move digits two places right). E.g., 6% = 0.06.
To convert a decimal to a percentage, multiply by 100 (move digits two places left and add %). E.g., 0.35 = 35%.
To convert a decimal to a fraction: for 1 decimal place, write over 10; for 2 decimal places, over 100; for n decimal places, over 10ⁿ. Simplify if needed.
To convert a percentage to a fraction, write the percentage over 100 and simplify. E.g., 37% = 37/100.
To convert a fraction to a decimal, rewrite with denominator 10, 100, 1000, etc., or use division. E.g., 3/5 = 6/10 = 0.6.
To convert a fraction to a percentage, first convert to decimal then multiply by 100. E.g., 4/5 = 0.8 = 80%.
Common recurring decimals: 0.333... = 1/3, 0.666... = 2/3.

Ordering Fractions, Decimals & Percentages

To order only fractions, write them with a common denominator (lowest common denominator) and compare numerators.
To order a mixture of fractions, decimals, and percentages, convert everything to decimals first.
Use symbols: < (less than), > (greater than), ≤ (less than or equal), ≥ (greater than or equal), = (equal), ≠ (not equal).
When ordering, write all numbers with the same number of decimal places to compare easily.
Example: 78% < 0.8 < 5/6 < 7/8 (after converting all to decimals).

Ordering FDP: the 5-step method

Common Conversions to Memorise

1/2 = 0.5 = 50%
1/4 = 0.25 = 25%
3/4 = 0.75 = 75%
1/5 = 0.2 = 20%
2/5 = 0.4 = 40%
1/10 = 0.1 = 10%
1/3 ≈ 0.333 = 33.3%

Common FDP Equivalents

Tips for Exam Questions

A calculator can be used to check conversions between fractions and decimals (even if the question says 'without a calculator').
For ordering, convert all values to decimals (using calculator if allowed) then compare.
When shading a grid for a percentage, count total squares and shade the given percentage of them.
Always simplify fractions to lowest terms (e.g., 36/124 = 9/31).
To find a fraction of a quantity, multiply the quantity by the fraction (e.g., 5/8 of 128 = 80).

Worked Example: Ordering Fractions Only

Order 1/3, 2/5, 9/25, 4/15 from smallest to largest.
Find LCM of denominators: LCM of 3,5,25,15 is 75.
Rewrite: 1/3 = 25/75, 2/5 = 30/75, 9/25 = 27/75, 4/15 = 20/75.
Order by numerators: 20/75, 25/75, 27/75, 30/75.
Original order: 4/15, 1/3, 9/25, 2/5.

Comparing 1/3, 2/5, 9/25, 4/15

Worked Example: Ordering Mixed FDP

Order 7/8, 5/6, 0.8, 78% from smallest to largest.
Convert all to decimals: 7/8 = 0.875, 5/6 ≈ 0.8333, 0.8 = 0.800, 78% = 0.78.
Compare: 0.78, 0.800, 0.8333, 0.875.
Original order: 78% < 0.8 < 5/6 < 7/8.

Comparing 7/8, 5/6, 0.8, 78%

Slides

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Practice questions

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1.Write 2/5 as a decimal.
Easy
- A0.4
- B0.25
- C0.5
- D0.2
2.Write 15% as a decimal.
Easy
- A0.15
- B1.5
- C0.015
- D15
3.Write 3/4 as a percentage.
Easy
- A75%
- B34%
- C0.75%
- D7.5%
4.Write 0.45 as a fraction in its simplest form.
Easy
- A9/20
- B45/100
- C9/10
- D4/5
5.Write 3/10 as a percentage.
Easy
- A30%
- B3%
- C0.3%
- D13%
6.Write 26% as a decimal.
Easy
- A0.26
- B2.6
- C0.026
- D26
7.Write 0.48 as a fraction in its simplest form.
Easy
- A12/25
- B48/100
- C12/50
- D24/25
8.Write these numbers in order, starting with the smallest: 3/4, 72%, 0.78, 8/10.
Medium
- A72%, 0.78, 3/4, 8/10
- B72%, 3/4, 0.78, 8/10
- C0.78, 72%, 3/4, 8/10
- D3/4, 72%, 0.78, 8/10

Revision notes

## Fractions, Decimals & Percentages ### Converting - **Percentage → Decimal:** ÷ 100 (move digits 2 places right). e.g., 6% = 0.06, 40% = 0.4, 350% = 3.5, 0.2% = 0.002 - **Decimal → Percentage:** × 100 (move digits 2 places left, add %). e.g., 0.35 = 35%, 1.32 = 132%, 0.004 = 0.4% - **Decimal → Fraction:** Write digits over 10^n (n = decimal places). e.g., 0.3 = 3/10, 0.07 = 7/100, 0.513 = 513/1000 - **Percentage → Fraction:** Write over 100. e.g., 37% = 37/100 - **Fraction → Decimal:** Convert to fraction over power of 10. e.g., 3/5 = 6/10 = 0.6, 7/20 = 35/100 = 0.35 - **Fraction → Percentage:** Convert to decimal then × 100. e.g., 4/5 = 0.8 = 80% ### Ordering - **All fractions:** Write with lowest common denominator, compare numerators. e.g., 3/5, 1/2, 13/20, 7/12 → LCD 60 → 36/60, 30/60, 39/60, 35/60 → order: 1/2, 7/12, 3/5, 13/20 - **Mixed FDP:** Convert everything to decimals, then compare. e.g., 7/8 = 0.875, 5/6 ≈ 0.8333, 0.8, 78% = 0.78 → order: 78% < 0.8 < 5/6 < 7/8 ### Key Symbols - < less than, > greater than, ≤ less than or equal, ≥ greater than or equal, ≠ not equal ### Tips - Use a calculator to check conversions (even if question says without). - For ordering, convert all to decimals (calculator can help).

Fraction: A number expressed as a quotient a/b, where a is the numerator and b is the denominator.
Decimal: A number expressed in base 10 using a decimal point; e.g., 0.75.
Percentage: A fraction or ratio expressed as a number out of 100, denoted by the % sign.
Equivalent fraction: Fractions that represent the same value, e.g., 5/9 and 10/18.
Simplest form: A fraction where numerator and denominator have no common factors other than 1.
Lowest common denominator (LCD): The smallest multiple shared by the denominators of two or more fractions.

Flashcards

How do you convert a percentage to a decimal?

Divide by 100 (move digits two places to the right). For example, 6% = 0.06.

How do you convert a decimal to a percentage?

Multiply by 100 (move digits two places to the left and add a % sign). For example, 0.35 = 35%.

Convert 0.3 to a fraction.

0.3 = 3/10 (one decimal place, write over 10).

Convert 0.07 to a fraction.

0.07 = 7/100 (two decimal places, write over 100).

Convert 0.513 to a fraction.

0.513 = 513/1000 (three decimal places, write over 1000).

What is 0.33333... as a fraction?

0.33333... = 1/3.

What is 0.66666... as a fraction?

0.66666... = 2/3.

How do you convert a percentage to a fraction?

Write the percentage over 100. For example, 37% = 37/100.

Convert 3/5 to a decimal.

3/5 = 6/10 = 0.6.

Convert 7/20 to a decimal.

7/20 = 35/100 = 0.35.

Convert 4/5 to a percentage.

4/5 = 0.8 = 0.8 × 100 = 80%.

Write 2/5 as a decimal.

2/5 = 0.4.

Write 15% as a decimal.

15% = 0.15.

Write 3/4 as a decimal.

3/4 = 0.75.

Write 0.45 as a fraction in its simplest form.

0.45 = 45/100 = 9/20.

Write 2/5 as a percentage.

2/5 = 0.4 = 40%.

Write 3/10 as a percentage.

3/10 = 0.3 = 30%.

Write 45% as a fraction in its simplest form.

45% = 45/100 = 9/20.

How do you order a mixture of fractions, decimals, and percentages?

Convert everything to decimals, then compare. For example, 7/8 = 0.875, 5/6 ≈ 0.833, 0.8, 78% = 0.78; order: 78% < 0.8 < 5/6 < 7/8.

Order these numbers from smallest to largest: 3/4, 72%, 0.78, 8/10.

Convert: 3/4 = 0.75, 72% = 0.72, 0.78, 8/10 = 0.8. Order: 72%, 3/4, 0.78, 8/10.

Order from smallest to largest: 0.51, 1/2, 0.501, 48%, 2/5.

Convert: 1/2 = 0.5, 48% = 0.48, 2/5 = 0.4. Order: 2/5, 48%, 1/2, 0.501, 0.51.

Order from smallest to largest: 27%, 5/17, 0.268, 7/29.

Convert: 27% = 0.27, 5/17 ≈ 0.2941, 0.268, 7/29 ≈ 0.2414. Order: 7/29, 0.268, 27%, 5/17.

Order from smallest to largest: 11/27, 41%, 0.4, 16/39.

Convert: 11/27 ≈ 0.4074, 41% = 0.41, 0.4, 16/39 ≈ 0.4103. Order: 0.4, 11/27, 41%, 16/39.

Which is largest: 0.3030, 1/3, 0.0330, 3/10, 33%?

Convert: 1/3 ≈ 0.3333, 3/10 = 0.3, 33% = 0.33. Largest is 1/3.

Order from smallest to largest: 9/19, 3/7, 37%, 0.43.

Convert: 9/19 ≈ 0.4737, 3/7 ≈ 0.4286, 37% = 0.37, 0.43. Order: 37%, 3/7, 0.43, 9/19.

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