Standard Form Question – Sec 3 G2 and G3 Explained

Introduction

This standard form question is a very useful lower secondary Maths example because students must convert a large number into scientific notation and then round it correctly to the required significant figures. Many students know how to move the decimal point, but they lose marks in a standard form question because they forget the power of ten or round the first number incorrectly.

The Question / Scenario Explanation

Source: Standard Form Sec 3 G2 and G3

Question (as shown): The diameter of the Sun is \(1\ 397\ 570\) km. Express \(1\ 397\ 570\) in standard form correct to \(2\) significant figures.

Step-by-Step Solution / Explanation

Step 1: Write the number in standard form

For this standard form question, we want a number between \(1\) and \(10\), multiplied by a power of \(10\).

\(1\ 397\ 570 = 1.39757 \times 10^6\)

This is because the decimal point has been moved \(6\) places to the left.

Step 2: Round to 2 significant figures

Now round \(1.39757\) to \(2\) significant figures.

The first two significant figures are \(1\) and \(3\).

The next digit is \(9\), so we round \(1.3\) up to \(1.4\).

So:

\(1.39757 \times 10^6 \approx 1.4 \times 10^6\)

✅ Final Answer: \(1.4 \times 10^6\text{ km}\)

Step 3: Quick check

\(1.4 \times 10^6 = 1\ 400\ 000\)

This is close to \(1\ 397\ 570\), so the rounded answer makes sense.

Key Concepts Students Must Know

• In a standard form question, the number must be written as \(a \times 10^n\), where \(1 \leq a < 10\).
• The power of \(10\) depends on how many places the decimal point moves.
• Significant figures begin from the first non-zero digit.
• Always round the number in front first, while keeping the power of \(10\) unchanged.

Exam Tips / Common Mistakes

Exam Tips

• Move the decimal point until the first number is between \(1\) and \(10\).
• For this standard form question, count the decimal shift carefully to get the correct power of \(10\).
• Round only the first number, not the power of \(10\).
• Check whether the question asks for standard form, significant figures, or both.

Common Mistakes

• Writing \(13.9757 \times 10^5\), which is not valid standard form because the first number is not between \(1\) and \(10\).
• Using the wrong power of \(10\) after moving the decimal point.
• Rounding \(1.39757\) to \(1.3\) instead of \(1.4\).
• Forgetting to include the unit km in the final answer.

Parent Insight

This standard form question looks simple, but it builds two important secondary Maths habits: place value understanding and accurate rounding. Many students can read large numbers, but still lose marks when they must convert them into standard form with the correct number of significant figures. With regular practice, these steps become much faster and more reliable.

Conclusion

To solve this standard form question, we first wrote \(1\ 397\ 570\) as \(1.39757 \times 10^6\). Then we rounded \(1.39757\) to \(2\) significant figures, giving \(1.4\). So the correct final answer is \(1.4 \times 10^6\text{ km}\).

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