Number and Quantity
Number and Quantity
The Number and Quantity domain on OST Algebra I tests whether you can reason with quantities, units, precision, exponents, radicals, and scientific notation. Items often embed these skills inside multi-step word problems rather than asking isolated arithmetic.
Core rules
- Treat units as algebra: multiply and divide them, cancel them, and choose conversion factors so unwanted units disappear.
- When adding or subtracting in scientific notation, rewrite to the same power of ten first; when multiplying, multiply coefficients and add exponents; when dividing, divide coefficients and subtract exponents.
- For integer exponents, a^m a^n = a^(m+n), (a^m)^n = a^(mn), a^(-n) = 1/a^n, and a^0 = 1 for a not equal to 0.
- √(ab) = √a√b and √(a^2) = |a|. Perfect squares through 15^2 = 225 and cubes through 5^3 = 125 are worth memorizing.
- Precision is limited by the least precise measurement; do not report more decimal places than the given data justify.
Worked example
Compute (3.2 × 10^5)(4.0 × 10^-2). Multiply coefficients: 3.2 × 4.0 = 12.8. Add exponents: 5 + (-2) = 3. Result: 12.8 × 10^3. Since 12.8 is not between 1 and 10, rewrite: 1.28 × 10^4.
Traps
Adding exponents while multiplying coefficients without adjusting the decimal; writing 25 × 10^2 and calling it scientific notation; dropping absolute value when simplifying √(x^2); and claiming a converted answer is more precise than the original measurement.