Maths – Standard Notation (WASSCE)

1. What is Standard Notation?

Standard notation (also called standard form) is a way of writing very large or very small numbers using powers of 10.

It is written as:

a \times 10^n

Where:

1 \le a < 10

n is an integer (positive or negative)

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2. Why Do We Use Standard Notation?

A. To make large numbers shorter
B. To make small numbers easier to read
C. To simplify calculations in science and mathematics

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3. Writing Large Numbers in Standard Notation

Steps:

1. Move the decimal point so the number is between 1 and 10
2. Count how many places you moved the decimal
3. Write that number as a power of 10

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Example 1:

45,000

Move decimal 4 places left:

4.5 \times 10^4

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Example 2:

3,200,000

Move decimal 6 places left:

3.2 \times 10^6

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4. Writing Small Numbers in Standard Notation

Steps:

1. Move the decimal point to make the number between 1 and 10
2. Count how many places you moved
3. Use a negative power of 10

Example 1:

0.006

Move decimal 3 places right:

6 \times 10^{-3}

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Example 2:

0.00045

Move decimal 4 places right:

4.5 \times 10^{-4}

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5. Converting from Standard Notation to Ordinary Numbers

Example 1:

2.3 \times 10^3

Move decimal 3 places right:

2,300

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Example 2:

7.5 \times 10^{-2}

Move decimal 2 places left:

0.075

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6. Key Rules to Remember

Positive index → move decimal right
Negative index → move decimal left

The number in front must be between 1 and 10.

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7. Worked Example

Write 0.000092 in standard notation.

Move decimal 5 places right:

9.2 \times 10^{-5}

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8. Common Mistakes to Avoid

A. Writing a number less than 1  or  greater than 10 in front
B. Forgetting the negative sign for small numbers.
C. Counting decimal places incorrectly.

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9. Quick Practice

Try these:

1. Write  6,700  in standard notation
2. Write  0.0048  in standard notation
3. Convert 5.6 \times 10^2 to ordinary number

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