Year 9: Scientific Notation

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1. What is scientific notation?

Scientific notation is a way of writing very large or very small numbers using powers of ten. It helps make numbers easier to work with in science and mathematics.

It has the form: a × 10ⁿ, where:

• a is a number greater than or equal to 1 and less than 10
• n is an integer (can be positive or negative)

2. Examples

• 5,000 = 5 × 10³
• 0.006 = 6 × 10^-3
• 98,000,000 = 9.8 × 10⁷
• 0.00042 = 4.2 × 10^-4

3. Converting to scientific notation

1. Move the decimal point so that there is only one non-zero digit to its left.
2. Count the number of places the decimal point moved. This becomes the exponent of 10.
3. If the original number was greater than 1, the exponent is positive.
4. If the original number was less than 1, the exponent is negative.

Example: 47,200 = 4.72 × 10⁴

Example: 0.00081 = 8.1 × 10^-4

4. Converting from scientific notation

To convert back to standard form:

1. Move the decimal point according to the exponent on 10.
2. Move it right if the exponent is positive.
3. Move it left if the exponent is negative.

Example: 3.6 × 10⁵ = 360,000

Example: 7.2 × 10^-3 = 0.0072

5. Calculations with scientific notation

Multiplying: Multiply the a-values and add the exponents.

Example: (2 × 10³) × (3 × 10⁴) = 6 × 10⁷

Dividing: Divide the a-values and subtract the exponents.

Example: (8 × 10⁶) ÷ (2 × 10²) = 4 × 10⁴

6. Practice questions

1. Write 6,500,000 in scientific notation.
2. Convert 4.3 × 10^-2 to standard form.
3. Multiply (3 × 10⁵) × (2 × 10³).
4. Divide (7.5 × 10⁶) ÷ (1.5 × 10²).

7. Solutions

1. 6.5 × 10⁶
2. 0.043
3. 6 × 10⁸
4. 5 × 10⁴