Decimals · 11+ GL Assessment

Complete concept guide + 150+ interactive practice questions. Click any question to reveal its solution & detailed explanation.

1. Understanding Place Value

The key to decimals is understanding that each digit to the right of the decimal point represents a fraction with a denominator of 10, 100, 1000, etc.

Tenths (0.1) first digit after decimal · 1/10

Hundredths (0.01) second digit · 1/100

Thousandths (0.001) third digit · 1/1000

Example: 45.367

4 is 4 tens (40) · 5 is 5 units (5) · 3 is 3 tenths (3/10 or 0.3) · 6 is 6 hundredths (6/100 or 0.06) · 7 is 7 thousandths (7/1000 or 0.007)

So, 45.367 = 40 + 5 + 0.3 + 0.06 + 0.007

2. Adding & Subtracting Decimals

Golden Rule: Line up the decimal points! You can add zeroes to the right to help keep everything aligned.

Example (Addition): 12.45 + 3.8 12.45 + 3.80 -------- 16.25

Example (Subtraction): 7.5 - 2.34 7.50 - 2.34 -------- 5.16

3. Multiplying Decimals

1. Multiply the numbers as if they were whole numbers (ignore decimal points).
2. Count the total number of decimal places in both original numbers.
3. Place the decimal point in your answer so it has the same total number of decimal places.

Example: 1.3 × 0.25

1. 13 × 25 = 325
2. 1.3 has 1 decimal place, 0.25 has 2. Total = 3 decimal places.
3. Answer: 0.325

4. Dividing Decimals

The easiest way is to make the divisor a whole number.

Example: 6.84 ÷ 0.4

1. Multiply both numbers by 10 (to make the divisor, 0.4, a whole number): 68.4 ÷ 4
2. Now do the division: 4 goes into 6 one time (1), remainder 2. Bring down 8, making 28. 4 goes into 28 seven times (7). Bring down 4. 4 goes into 4 one time (1).
3. The answer is 17.1

5. Converting between Decimals, Fractions & Percentages

Decimal → Fraction Write decimal as numerator, use 1 followed by zeros (10, 100, 1000) as denominator based on place value. Then simplify.
0.7 = 7/10 · 0.35 = 35/100 = 7/20 · 0.125 = 125/1000 = 1/8

Fraction → Decimal Divide the numerator by the denominator.
3/4 = 3 ÷ 4 = 0.75 · 1/8 = 1 ÷ 8 = 0.125

Decimal → Percentage Multiply by 100 and add % sign.
0.89 = 0.89 × 100 = 89% · 0.04 = 4%

Percentage → Decimal Divide by 100 (move decimal point two places left).
75% = 75 ÷ 100 = 0.75 · 5% = 0.05

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Part 2: 10 Practice Questions (Mixed Sub-topics)

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Part 3: 50+ Additional Practice Questions

Place Value & Ordering

Addition & Subtraction

Multiplication

Division

Conversions & Mixed Applications

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Part 4: 10 Previous Year GL Assessment Style Questions

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Additional Practice: Sections A – H

Section A: Place Value & Ordering

Section B: Addition & Subtraction

Section C: Multiplying & Dividing

Section D: Conversions & Mixed Applications

Section E: Mixed Problem Solving

Section F: Mixed Word Problems & Multi-step

Section G: Fictional "Previous Year Paper" (50 Questions)

Section H: 50 More GL Assessment Styles

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Money, Length & Weight Problems (with Solutions)

Money Problems

Length Problems

Weight Problems

Key Tips for Decimal Problems

1. Line up decimal points when adding or subtracting.

2. Check units — convert all measurements to the same unit before calculating.

3. Money calculations — always include two decimal places for pounds.

4. Division — if dividing by a decimal, multiply both numbers to make the divisor a whole number.

5. Real-life context — consider whether the answer needs to be a whole number (e.g., pieces of wood).