ACT Preparation / Unit 7 ACT 0609 worked example, 60 to 90 seconds
Computing in Scientific Notation
The idea
To multiply or divide numbers in scientific notation, work in three steps. First, multiply or divide the leading numbers. Second, combine the powers of ten with the exponent rules: add exponents when multiplying, subtract when dividing. Third, if the leading number has left the range from 1 to less than 10, shift the decimal and adjust the exponent to restore the form.
In practice
Worked example: (6 × 10⁵)(4 × 10³). Step one: 6 × 4 = 24. Step two: 10⁵ × 10³ = 10⁸, so 24 × 10⁸. Step three: 24 = 2.4 × 10, so the product is 2.4 × 10⁹. Second: (3 × 10⁴) ÷ (6 × 10⁻²). Step one: 3 ÷ 6 = 0.5. Step two: 10⁴ ÷ 10⁻² = 10⁶. Step three: 0.5 = 5 × 10⁻¹, so the quotient is 5 × 10⁵.
Where people slip
Adjusting the leading number moves the exponent the opposite way: making 24 ten times smaller makes the power of ten one larger.
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