Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityEasy
An environmental scientist is measuring the concentration of a pollutant in a water sample. The initial concentration is 0.0000000045 grams per liter. How is this concentration expressed in scientific notation?
- A0.45 x 10^-8 g/L
- B45 x 10^-10 g/L
- C4.5 x 10^-8 g/L
- D4.5 x 10^-9 g/L
Show answer & explanationAnswer & explanation
Correct answer: D. 4.5 x 10^-9 g/L
To convert 0.0000000045 to scientific notation, move the decimal point to the right until there is only one non-zero digit to its left. The decimal point moves 9 places to the right, so the exponent is -9. The number becomes 4.5 x 10^-9.
Why the other options are wrong
- A. This is incorrect because the mantissa (0.45) is not between 1 and 10.
- B. This is incorrect because the mantissa (45) is not between 1 and 10.
- C. This implies moving the decimal 8 places, which is incorrect.
Converting Small Decimals to Scientific Notation
To convert a small decimal (less than 1) to scientific notation, move the decimal point to the right until there is exactly one non-zero digit to its left. The number of places moved is the negative exponent of 10.
- Move decimal right for negative exponent
- Count places moved to determine exponent value
- Mantissa (coefficient) must be between 1 and 10 (inclusive of 1)
Memory trick: Scientific: Single digit, then power of ten, for big and small.