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ft in cm

Unit
Conversions

Master the skill of converting between units within the same measurement system: length, weight, capacity, and time.

SSAT Middle Level

What Is a Unit Conversion?

A unit conversion changes a measurement from one unit to another without changing its actual size. For example, \(12\) inches and \(1\) foot describe the exact same length.

Why Do Conversions Matter?

SSAT Tests
Many quantitative questions require you to convert units before you can compare or calculate.
Real Life
Cooking recipes, travel distances, and science experiments all use different units for the same quantities.
Problem Solving
You cannot add \(3\) feet \(+\) \(8\) inches without first converting to the same unit.

Two Measurement Systems

U.S. Customary
Inches, feet, yards, miles, ounces, pounds, cups, gallons. Conversion factors vary (12, 3, 5280, 16, 8, 4...).
Metric
Millimeters, centimeters, meters, kilometers, grams, kilograms, milliliters, liters. Always powers of \(10\).

The Multiplication Rule

Bigger \(\rightarrow\) Smaller
Multiply (\(\times\))
Smaller \(\rightarrow\) Bigger
Divide (\(\div\))

Why Multiply or Divide?

Think of it this way: smaller units need more of them to describe the same amount. So when you move to a smaller unit, the number gets bigger: you multiply.

1 yard 1 ft 1 ft 1 ft
\(1 \text{ yard} = 3 \text{ feet} \rightarrow \text{multiply by } 3\)

Converting Down vs. Converting Up

Converting Down (to smaller) Converting Up (to bigger)
Direction Bigger unit \(\rightarrow\) Smaller unit Smaller unit \(\rightarrow\) Bigger unit
Operation Multiply Divide
Number gets Larger Smaller
Example \(2 \text{ ft} \times 12 = 24 \text{ in}\) \(36 \text{ in} \div 12 = 3 \text{ ft}\)

Essential Conversion Factors

Category U.S. Customary Metric
Length \(1\) ft \(= 12\) in, \(1\) yd \(= 3\) ft, \(1\) mi \(= 5{,}280\) ft \(1\) m \(= 100\) cm, \(1\) km \(= 1{,}000\) m
Weight / Mass \(1\) lb \(= 16\) oz, \(1\) ton \(= 2{,}000\) lb \(1\) kg \(= 1{,}000\) g
Capacity \(1\) cup \(= 8\) fl oz, \(1\) gal \(= 4\) qt \(1\) L \(= 1{,}000\) mL
Time \(1\) hr \(= 60\) min, \(1\) min \(= 60\) s, \(1\) day \(= 24\) hr

Step-by-Step Method

1
Identify the units: What unit do you have? What unit do you need?
2
Find the conversion factor: How many of the smaller unit fit in the bigger unit?
3
Decide: multiply or divide? Going to a smaller unit \(\rightarrow\) multiply. Going to a bigger unit \(\rightarrow\) divide.
4
Calculate and check: does the answer make sense? Smaller units should give a bigger number.

Example 1: Feet to Inches

Problem: Convert \(5\) feet to inches.

1
Units: Have feet, need inches.
2
Factor: \(1\) foot \(= 12\) inches.
3
Direction: Bigger \(\rightarrow\) smaller, so multiply.
4
Calculate: \(5 \times 12 = \) \(60\) inches. ✓ Bigger number, makes sense!

Example 2: Ounces to Pounds

Problem: A package weighs \(48\) ounces. How many pounds is that?

1
Units: Have ounces (smaller), need pounds (bigger).
2
Factor: \(1\) pound \(= 16\) ounces.
3
Direction: Smaller \(\rightarrow\) bigger, so divide.
4
Calculate: \(48 \div 16 = \) \(3\) pounds. ✓ Smaller number, makes sense!

Example 3: Two-Step Conversion

Problem: Convert \(2\) yards to inches.

\(2 \text{ yd}\)
\(\times 3\)
\(6 \text{ ft}\)
\(\times 12\)
\(72 \text{ in}\)

Metric: Powers of 10

Metric conversions are simpler because every step is a power of \(10\). Just move the decimal point!

km m cm mm
\(\times 1{,}000\)
\(\times 100\)
\(\times 10\)
Example: \(3.5 \text{ m} = 350 \text{ cm}\)
 Move the decimal 2 places right (\(\times 100\))

Time Conversions

Time conversions use the same multiply/divide rule, but with different factors at each step: \(60\), \(60\), and \(24\).

days
\(\times 24\)
 hours
\(\times 60\)
 minutes
\(\times 60\)
 sec

Common Mistakes

✕ Wrong Operation
Multiplying when you should divide (or vice versa). Always ask: "Should my answer be bigger or smaller?"
✕ Wrong Factor
Using \(10\) instead of \(12\) for feet-to-inches, or \(100\) instead of \(1{,}000\) for kg-to-g. Memorize key factors.
✕ Forgetting Multi-Step
Going from yards to inches requires two steps (yd \(\rightarrow\) ft \(\rightarrow\) in). Skipping a step gives the wrong answer.

Quick Reference Chart

Conversion Factor Example
Feet ↔ Inches \(\times 12 \text{ / } \div 12\) \(4\) ft \(= 48\) in
Yards ↔ Feet \(\times 3 \text{ / } \div 3\) \(7\) yd \(= 21\) ft
Pounds ↔ Ounces \(\times 16 \text{ / } \div 16\) \(2\) lb \(= 32\) oz
Gallons ↔ Quarts \(\times 4 \text{ / } \div 4\) \(3\) gal \(= 12\) qt
Meters ↔ Centimeters \(\times 100 \text{ / } \div 100\) \(2.5\) m \(= 250\) cm
Kilograms ↔ Grams \(\times 1{,}000 \text{ / } \div 1{,}000\) \(0.5\) kg \(= 500\) g
Hours ↔ Minutes \(\times 60 \text{ / } \div 60\) \(2.5\) hr \(= 150\) min

Question 1 of 5

How many inches are in \(3\) feet?

Question 2 of 5

A package weighs \(64\) ounces. How many pounds is that?

Question 3 of 5

Convert \(4{,}500\) grams to kilograms.

Question 4 of 5

How many inches are in \(2\) yards?

Question 5 of 5

A movie is \(150\) minutes long. How many hours and minutes is that?