Scientific Notation, Rounding & Significant Figures

Estimation, rounding, and scientific notation help you judge whether an answer is sensible. They are not just presentation skills; they help you catch arithmetic mistakes before they cost marks.

CSEC Paper 01 often tests these ideas directly, while Paper 02 expects you to use them inside longer calculations. Keep full accuracy while working, then round only when the question asks or when giving the final answer. If a value is very large or very small, scientific notation makes it easier to read and compare.

Scientific notation is a way to write extremely large or extremely small numbers in a compact form.

What Is Scientific Notation?¶

Any number in scientific notation is written as:

$a × 10^n$

Where:

• a is a number between 1 and 10 (like 1.5, 2.34, 9.999)
• $10^n$ means 10 multiplied by itself n times

Why Do We Use Scientific Notation?¶

Instead of writing: 43,500,000,000,000 (hard to count the zeros)

We write: $4.35 × 10^{12}$ (much cleaner!)

Converting to Scientific Notation¶

Conversion is about moving the decimal point until the first number is between 1 and 10. The exponent records how many places the decimal moved and in which direction.

For large numbers: Move the decimal point to the LEFT until there's one digit before the decimal. Count how many places you moved—that's your exponent.

For small numbers: Move the decimal point to the RIGHT until there's one digit before the decimal. Count how many places you moved—that's your negative exponent.

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Rounding and Significant Figures¶

Rounding is used to report an answer at a sensible level of accuracy. In exam working, keep extra digits until the final answer so rounding errors do not build up.

Rounding to Decimal Places¶

Decimal places count digits after the decimal point. This is useful for money, measurements, and calculator answers where a fixed number of decimal places is requested.

When you round to a certain number of decimal places, look at the next digit:

• If it's 5 or more, round up
• If it's less than 5, round down

Significant Figures¶

Significant figures count meaningful digits from the first non-zero digit. They are useful when numbers are very large, very small, or measured rather than exact.

Significant figures are the digits that carry meaning in a number.

Rules:

1. All non-zero digits are significant: 123 has 3 sig figs
2. Zeros between non-zero digits are significant: 1023 has 4 sig figs
3. Leading zeros are NOT significant: 0.00425 has 3 sig figs (only 4, 2, 5)
4. Trailing zeros after a decimal are significant: 5.280 has 4 sig figs

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Unit Conversion¶

Common Conversions You Must Know¶

Length:

• 1 km = 1,000 m
• 1 m = 100 cm
• 1 cm = 10 mm

Time:

• 1 hour = 60 minutes
• 1 minute = 60 seconds
• 1 hour = 3,600 seconds

Currency: Always use the given exchange rate in the question.

How to Convert¶

A conversion factor is a multiplier equal to 1, such as $\frac{100 \text{ cm}}{1 \text{ m}}$. Multiplying by it changes the unit without changing the actual size of the measurement.

Multiply by the conversion factor.

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Arithmetic Mean (Average)¶

The arithmetic mean balances a set of values as if the total were shared equally. In CSEC, it may appear in Computation as a direct calculation and in Statistics as part of data interpretation.

The arithmetic mean is the average of a set of numbers.

$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$

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Key Takeaways¶

✓ Know your number types: natural, whole, integers, rational, irrational

✓ Master the four operations with positive and negative numbers

✓ Always follow BODMAS when calculating

✓ Fractions, decimals, and percentages are the same thing — just learn to convert between them

✓ Ratios compare quantities — you must understand how to divide amounts in a ratio

✓ Scientific notation makes large and small numbers manageable

✓ Show all your working in exams — partial credit is better than none