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Number - Using a Calculator

Grade 9IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Follow the correct order of operations, known as BIDMASBIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction). Most scientific calculators handle this automatically if the expression is entered correctly.

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Use the fraction button □□\frac{\Box}{\Box} to enter complex divisions. This ensures the calculator treats the entire numerator and the entire denominator as grouped terms.

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The S↔DS \leftrightarrow D key (Standard to Decimal) is essential for converting results between fractions, surds, and decimals.

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For numbers in standard form, use the scientific notation key (often labeled EXPEXP or ×10x\times 10^x). Standard form is written as a×10na \times 10^n, where 1≤a<101 \leq a < 10.

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Use the AnsAns key to retrieve the exact result of the last calculation. This prevents rounding errors that occur when intermediate results are truncated.

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Ensure the calculator is in the correct mode (usually 'Degree' mode for IGCSE geometry and trigonometry) unless 'Radians' are specifically required.

📐Formulae

a×10na \times 10^n

xn\sqrt[n]{x}

x−n=1xnx^{-n} = \frac{1}{x^n}

Percentage=PartWhole×100\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100

💡Examples

Problem 1:

Calculate the value of 25.6+4.121.2×3\frac{\sqrt{25.6 + 4.1^2}}{1.2 \times 3} and give your answer correct to 3 significant figures.

Solution:

Numerator: 25.6+16.81=42.41≈6.51229...\text{Numerator: } \sqrt{25.6 + 16.81} = \sqrt{42.41} \approx 6.51229... Denominator: 1.2×3=3.6\text{Denominator: } 1.2 \times 3 = 3.6 6.51229...3.6=1.80897...\frac{6.51229...}{3.6} = 1.80897... Answer: 1.811.81

Explanation:

Evaluate the terms inside the square root first, then the denominator. Finally, divide the two results and round to the specified significant figures.

Problem 2:

Work out (4.5×106)×(2.0×10−3)(4.5 \times 10^6) \times (2.0 \times 10^{-3}) and give the result in standard form.

Solution:

4.5×2.0=9.04.5 \times 2.0 = 9.0 106×10−3=106−3=10310^6 \times 10^{-3} = 10^{6-3} = 10^3 Answer: 9.0×1039.0 \times 10^3

Explanation:

You can enter this directly into the calculator using the ×10x\times 10^x button. The calculator will often provide the answer in standard form or as 90009000.

Problem 3:

A bank account starts with Rs 80000000. After a large withdrawal of Rs 34567892, calculate the remaining balance and verify using vertical subtraction.

Solution:

80000000−3456789245432108\begin{array}{r} 80000000 \\ -34567892 \\ \hline 45432108 \end{array} Remaining balance: Rs 45432108

Explanation:

Calculators are used to handle large integers quickly. Verification through vertical subtraction ensures no digits were skipped during entry.