Convert between units within a measurement system. |...

SECTION 1

Why Do We Need Unit Conversions?

Imagine you are baking cookies and the recipe says you need 2 cups of flour, but your measuring tool only shows ounces. What do you do? You convert (change from one unit to another). People have been doing this kind of math for thousands of years.

Long ago, different towns used different measurement systems. A "foot" in one city might be a different length than a "foot" in another. This caused huge problems for trade and building. Over time, countries agreed on standard systems so everyone could communicate clearly.

3000 BC

Ancient Egypt

Egyptians used body parts like the cubit (elbow to fingertip) to measure length. Different workers had different-sized arms, so measurements were not always the same!

1790

The Metric System Is Born

France created the metric system based on powers of 10. This made converting between units much easier—just move the decimal point.

1824

British Imperial System

Britain officially defined the imperial system with units like inches, feet, yards, and miles. The United States later adopted a version called the customary system.

1960

International System (SI)

Scientists worldwide agreed on the SI system (Système International), a modern version of the metric system used in nearly every country today.

Today, the SSAT expects you to convert between units in both the U.S. customary system (inches, feet, pounds, cups) and the metric system (millimeters, centimeters, meters, grams, kilograms). The big question is: how do you change from one unit to another without making mistakes?

SECTION 2

Core Principles of Unit Conversion

Before you start converting, you need to understand a few key ideas. These principles are the foundation of every unit conversion problem you will ever see.

Conversion Factor

A conversion factor is a fraction that equals 1. For example, since 12 inches = 1 foot, the fraction 12 in / 1 ft equals 1. Multiplying by 1 never changes the value—only the unit.

Multiply or Divide?

Going from a smaller unit to a bigger unit? Divide. Going from a bigger unit to a smaller unit? Multiply. Think: more small pieces fit into one big piece.

Stay Inside One System

On the SSAT, you will convert within one measurement system at a time. You won't need to change inches into centimeters. You only convert inches to feet, or grams to kilograms, and so on.

Metric Prefixes = Powers of 10

In the metric system, each prefix (kilo-, centi-, milli-) tells you a power of 10. "Kilo" means 1,000. "Centi" means 1/100. "Milli" means 1/1,000. This makes metric conversions as simple as moving a decimal point.

✦ KEY TAKEAWAY

Think of unit conversion like exchanging money. If 1 dollar = 4 quarters, then 3 dollars = 3 × 4 = 12 quarters. You multiply by the exchange rate. A conversion factor works the same way—it's the "exchange rate" between two units.

SECTION 3

Seeing the Relationships

The diagram below shows the most common U.S. customary length conversions you need for the SSAT. Notice how each arrow tells you the conversion factor between two units.

Cyan arrows (÷) move from smaller to larger units. Pink arrows (×) move from larger to smaller units. The number on each arrow is the conversion factor.

Look at the length section. To go from inches to feet, you divide by 12 because 12 inches fit inside 1 foot. To go back from feet to inches, you multiply by 12. The same idea works for every pair of units in the diagram. When you move to the right (toward a bigger unit), you divide. When you move to the left (toward a smaller unit), you multiply.

SECTION 4

The Math Behind Conversions

Every conversion uses one simple idea: multiply by a conversion factor that equals 1. Here is how to set it up.

CONVERSION FORMULA

New Amount = Original Amount × (Desired Unit ÷ Original Unit)

The fraction (Desired Unit ÷ Original Unit) is your conversion factor. Since both quantities are equal (for example, 1 ft = 12 in), the fraction equals 1.

U.S. Customary Conversion Factors

Common U.S. Customary Conversion Factors

Type	Relationship	Conversion Factor
Length	1 foot = 12 inches	12 in / 1 ft or 1 ft / 12 in
Length	1 yard = 3 feet	3 ft / 1 yd or 1 yd / 3 ft
Length	1 mile = 5,280 feet	5,280 ft / 1 mi or 1 mi / 5,280 ft
Weight	1 pound = 16 ounces	16 oz / 1 lb or 1 lb / 16 oz
Liquid Volume	1 pint = 2 cups	2 c / 1 pt or 1 pt / 2 c
Liquid Volume	1 quart = 2 pints	2 pt / 1 qt or 1 qt / 2 pt
Liquid Volume	1 gallon = 4 quarts	4 qt / 1 gal or 1 gal / 4 qt

Metric System Conversion Factors

METRIC PREFIX PATTERN

kilo- (× 1,000) → base unit → centi- (÷ 100) → milli- (÷ 1,000)

1 kilometer = 1,000 meters, 1 meter = 100 centimeters, 1 meter = 1,000 millimeters. The same prefixes apply to grams and liters.

Common Metric Conversion Factors

Type	Relationship	Conversion Factor
Length	1 kilometer = 1,000 meters	1,000 m / 1 km
Length	1 meter = 100 centimeters	100 cm / 1 m
Length	1 centimeter = 10 millimeters	10 mm / 1 cm
Mass	1 kilogram = 1,000 grams	1,000 g / 1 kg
Volume	1 liter = 1,000 milliliters	1,000 mL / 1 L

💡 Which fraction do I pick?

Always place the unit you want to cancel on the bottom of the fraction. The unit you want to keep goes on top. When you multiply, the old unit crosses out and you are left with the new unit.

SECTION 5

The Metric Staircase

The metric system is built on powers of 10, which means you can picture it like a staircase. Each step up means dividing by 10, and each step down means multiplying by 10. The diagram below shows how this works for meters.

The meter is the base unit in the center. Moving up the staircase (to larger units), divide by 10 at each step. Moving down (to smaller units), multiply by 10 at each step. The same pattern works for grams and liters—just swap the base unit.

On the SSAT, the three metric conversions you will use most often are kilo- to base (× 1,000 or ÷ 1,000), base to centi- (× 100 or ÷ 100), and base to milli- (× 1,000 or ÷ 1,000). Don't worry about hectometers or dekameters—they rarely appear on the test.

⚡ Quick Trick for Metric

Count how many "steps" you move on the staircase. Each step is one place value in the decimal. For example, from meters to centimeters is 2 steps down, so move the decimal 2 places to the right: 3.5 m → 350 cm.

SECTION 6

Worked Example: Step by Step

Let's walk through a full problem like one you might see on the SSAT.

Example: How many inches are in 4.5 feet?

Step 1 — Identify the unitsWe start with 4.5 feet and need to convert to inches. We are going from a bigger unit (feet) to a smaller unit (inches), so the answer should be a larger number.

Step 2 — Find the conversion factorWe know that 1 foot = 12 inches. Since we want to cancel feet and keep inches, we use the fraction 12 in / 1 ft.

Step 3 — Multiply4.5 ft × (12 in / 1 ft) = 4.5 × 12 = ?

Step 4 — CalculateBreak it into friendly pieces: 4 × 12 = 48, and 0.5 × 12 = 6. So 48 + 6 = 54.

4.5 feet = 54 inches

Step 5 — Check your answerDoes the answer make sense? We expected a bigger number because inches are smaller than feet. 54 is larger than 4.5, so we are on the right track. ✓

Example: Convert 2,500 grams to kilograms

Step 1 — Identify the unitsWe start with 2,500 grams and need to convert to kilograms. We are going from a smaller unit (grams) to a bigger unit (kilograms), so we expect a smaller number.

Step 2 — Find the conversion factor1 kilogram = 1,000 grams. We want to cancel grams, so we use 1 kg / 1,000 g.

Step 3 — Divide2,500 g × (1 kg / 1,000 g) = 2,500 ÷ 1,000 = 2.5

2,500 grams = 2.5 kilograms

Step 4 — Check your answer2.5 is smaller than 2,500, which makes sense because kilograms are a much bigger unit than grams. ✓

SECTION 7

Common Mistakes and How to Avoid Them

Lots of students lose easy points on conversion problems—not because the math is hard, but because of small slip-ups. Here are the most common mistakes and how to dodge them.

Common Conversion Mistakes

Mistake	Why It Happens	How to Fix It
Multiplying when you should divide	Students forget which direction they are going.	Ask: should my answer be bigger or smaller? Going to a larger unit = divide. Going to a smaller unit = multiply.
Using the wrong conversion factor	Mixing up facts, like thinking 1 yard = 4 feet.	Memorize the key facts: 12 in/ft, 3 ft/yd, 16 oz/lb, 2 c/pt, 2 pt/qt, 4 qt/gal.
Forgetting to move enough decimal places (metric)	Losing count of the zeros.	Use the staircase. Count the steps and move the decimal that many places.
Not checking the answer	Rushing to the next problem.	Spend 3 seconds asking: is my answer reasonable? If you get 0.5 feet for 60 inches, something is wrong.

✦ KEY TAKEAWAY

Think of it like pizza slices. If you cut a pizza into more slices, each slice is smaller—but you still have the same amount of pizza. When you convert 1 foot to 12 inches, the total length hasn't changed—you've just described it in more, smaller pieces.

SECTION 8

Multi-Step Conversions and What Comes Next

Sometimes a problem asks you to convert between units that are not directly next to each other. For example, converting inches to yards requires two steps: inches → feet → yards. You can also chain conversion factors together in one big multiplication. This is called dimensional analysis (a fancy name for a simple idea).

Conversion Skill Progression

Skill Level	What You Do	Example
Basic (this lesson)	One-step conversion between two units in the same system	5 ft → ? in (multiply by 12)
Intermediate	Two-step conversion chaining through a middle unit	72 in → ? ft → ? yd (÷ 12, then ÷ 3)
Advanced (future)	Convert between different systems (customary ↔ metric)	10 km → ? miles (requires cross-system factor)

On the SSAT, you will mostly see one-step and two-step conversions. If you master the conversion factors in this lesson, you'll have the tools to handle anything the test throws at you. In later math courses, you will use these same skills in science (converting grams to moles in chemistry) and in everyday life (figuring out how many gallons of paint to buy for a wall measured in square feet).

SECTION 9

Practice Problems

PROBLEM 1 — CONCEPTUAL

When you convert from a larger unit (like feet) to a smaller unit (like inches), should the number you get be larger or smaller than the number you started with? (A) Larger (B) Smaller (C) The same (D) It depends on the number (E) There is no way to tell

PROBLEM 2 — BASIC CALCULATION

How many ounces are in 3 pounds? (A) 36 (B) 42 (C) 48 (D) 54 (E) 60

PROBLEM 3 — INTERMEDIATE

A ribbon is 7,200 centimeters long. How many meters is that? (A) 7.2 (B) 72 (C) 720 (D) 7,200,000 (E) 0.72

PROBLEM 4 — APPLIED

Maria needs 10 cups of juice for a party. Juice comes in quart containers. How many quarts does she need to buy? (A) 2 (B) 2.5 (C) 3 (D) 4 (E) 5

PROBLEM 5 — CRITICAL THINKING

Jake runs 2 miles every morning. His friend Tomas says he ran 10,000 feet yesterday. Who ran farther, and by how many feet? (A) Jake, by 560 feet (B) Tomas, by 560 feet (C) Jake, by 1,760 feet (D) Tomas, by 1,760 feet (E) They ran the same distance

SUMMARY

Putting It All Together

Converting between units means changing how you describe a measurement without changing the measurement itself. You do this by multiplying or dividing by a conversion factor—a fraction that equals 1. In the U.S. customary system, memorize the key relationships: 12 inches = 1 foot, 3 feet = 1 yard, 5,280 feet = 1 mile, 16 ounces = 1 pound, and the liquid chain 2 cups = 1 pint, 2 pints = 1 quart, 4 quarts = 1 gallon.

In the metric system, everything is based on powers of 10. Use the metric staircase: kilo- (× 1,000), base unit, centi- (× 100), milli- (× 1,000). When going from a bigger unit to a smaller unit, multiply. When going from a smaller unit to a bigger unit, divide. Always check: does my answer make sense? If you follow these steps, you will handle every SSAT conversion problem with confidence.