SAT-50: Unit Conversions and Dimensional Analysis

SAT-50: Unit Conversions and Dimensional Analysis

Description: Dimensional analysis converts units by multiplying by fractions that equal 1 (conversion factors), arranged so the units you don't want cancel. It's the safest way to handle SAT unit problems.

The idea

A conversion factor like (12 inches / 1 foot) equals 1, so multiplying by it doesn't change the value — only the units. Put the unit you want to cancel on the opposite side of the fraction so it divides out.

(Oʻzbekcha: oʻlchov birliklarini almashtirishda kerakmas birlik qisqarib ketadigan qilib koʻpaytiramiz.)

Worked Example (one step)

Convert 5 feet to inches (1 foot = 12 inches).

• 5 ft × (12 in / 1 ft) = 60 in. The "ft" cancels, leaving inches.
• Answer: 60 inches.

(Oʻzbekcha: "ft" yuqorida va pastda boʻlgani uchun qisqaradi, faqat "in" qoladi.)

Worked Example (chained)

Convert 90 km/h to meters per second (1 km = 1000 m, 1 h = 3600 s).

• 90 km/h × (1000 m / 1 km) × (1 h / 3600 s)
• = 90 × 1000 / 3600 m/s = 90000/3600 = 25 m/s.

Tip: line up the factors so every unwanted unit appears once on top and once on bottom. (Oʻzbekcha: har bir kerakmas birlik bir marta yuqorida, bir marta pastda boʻlsin.)

Practice

Convert 3 hours to seconds.

Key words — Kalit soʻzlar

• Unit conversion — birliklarni almashtirish
• Dimensional analysis — oʻlchamlar tahlili
• Conversion factor — almashtirish koeffitsiyenti
• Cancel (units) — (birliklarni) qisqartirish
• Numerator / Denominator — surat / maxraj
• Per — har biriga
• Rate — tezlik
• Equivalent — teng qiymatli
• Measurement — oʻlchov

Summary

• Multiply by conversion factors (fractions equal to 1) to change units.
• Arrange each factor so the unwanted unit cancels (top vs bottom).
• Chain several factors for multi-step conversions (e.g. km/h → m/s).