# LESSON | Converting Units & Solving Problems Involving Conversion

LESSON | The Complete Guide to Converting Units & Solving Problems Involving Conversion
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## The Complete Guide to Converting Units & Solving Problems Involving Conversion

In this post, you'll learn how to solve problems that involve converting units and how to convert measurements from one unit to another in both the English and Metric systems. Since these systems are used by a lot of people, having a good understanding of them will help you solve these problems more accurately. in everyday life.

## CONVERSION OF MEASUREMENTS FROM ONE UNIT TO ANOTHER

Converting between different units of measurement for the same amount is called "conversion of units." This is usually done by multiplying conversion factors. Conversion Factor is a number that is used to change one set of units to another by multiplying or dividing. This includes both the English System, which uses different parts of the body or other tools to measure, and the Metric System, which uses a decimal system.

The conversion could be from the same system, either from English to English or from Metric to Metric. It could also be from the English System to the Metric System or the other way around.

The table of conversion is needed to convert one unit to another unit.
MEASURES (ENGLISH, METRIC AND EQUIVALENT)
Units of Length in English System Units of Length in the Metric System System to System Conversions for Length
$1 foot( ft) = 12 inches (in)$
$1 yard (yd) = 3 feet (ft)$
$1 yard (yd) =36 inches (in)$
$1 mile (mi) = 5,280 feet (ft)$
$1, 000 millimeter (mm) = 1 meter$
$100 centimeters (cm) = 1 meter$
$10 decimeter (dm) = 1 meter$
$1 dekameter (dam) = 10 meters$
$1 hectometer (hm) = 100 meters$
$1 kilometer (km) = 1000 meters$
$1 in = 2.54 cm$
$1 meter ≈ 3. 28 ft$
$1 foot ≈ 0.30 m$
$1 yard ≈ 0.91 m$
$1 km ≈ 0.62 mi$

Units of Mass in English System Units of Mass in the Metric System System to System Conversions for Mass
$1 ounces (oz) = 437.5 grains$
$1 pound (lb) = 16 ounces (oz)$
$1 ton (T) = 2, 000 lb$
$1 gram (g) = 1, 000 milligram (mg)$
$1 gram (g) = 100 centigram (cg)$
$1 kilogram (kg)= 1000 grams (g)$
$1 metric ton (t) = 1, 000 kg$
$1 oz ≈ 28.3 g$
$1 lb ≈0.45 kg$

Units of Area in English System Units of Area in the Metric System System to System Conversions for Mass
$1 {ft^2} = 144 in^2$
$1 {yd^2} = 9 {ft^2}$
$1 acre = 43, 560 ft^2$
$1 {mi^2} = 640 acres$
$1 cm^2 = 100 {mm^2}$
$1 {dm^2} = 100 {cm^2}$
$1 {m^2} = 100 {dm^2}$
$1 are (a) = 100 {m^2}$
$1 hectare (ha) = 100 a$
$100 hectares (ha) = 1 {km^2}$
$1 in^2 ≈ 6.45 {cm^2}$
$1 m^2 ≈ 1.196 {yd^2}$
$1 ha ≈ 2.47 acres$

Units of Volume in English System Units of Volume in the Metric System System to System Conversions for Volume
$1 ft^3 = 1, 728 in^3$
$1 yd^3 = 27 ft^3$
$1 cord = 128 ft^3$
$1 cc = 1 cm^3$
$1 mL = 1 cm^3$
$1 L = 1, 000 mL$
$1 hL = 100 L$
$1 kL = 1, 000 L$
$1 in^3 ≈ 16.39 mL$
$1 liter ≈ 1.06 qt$
$1 gallon ≈ 3.79 liters$
$1 m3 ≈ 35.31 ft^3$
$1 quart ≈ 0.95 L$

Units of Fluid Volume in English System Units of Time in the Both System System to System Conversions for Temperature
$1 tablespoon (T) = 3 teaspoons (tsp)$
$1 fluid ounce (fl oz) = 2T 1$
$cup (c) = 8 fl oz$
$1 pint (pt) = 2 c$
$1 quart (qt) = 2 pt$
$1 gallon (gal) = 4 qt$
$1 gal = 128 fl oz 1$
$barrel = 42 gallon$
$1 millisecond=1000 microseconds$
$1 second = 1000 millisecond$
$1 minute = 60 seconds$
$1 hour = 60 minutes$
$1 day ≈ 24 hours (hrs)$
$1 month ≈ 30 days$
$1 year ≈ 365 days$
$1 banking year = 360 days$
$1 decade = 10 years$
$1 score = 20 years$
$1 millennium = 1, 000 years$
$°F \to °C$
$°C = {5 \over 9} (°F – 32)$
$°C \to °F$
$°F = {9 \over 5}°C + 32$
$°K \to °C$
$°K = °C + 273$

METRIC PREFIXES
Giga (G) Mega (M) Kilo (k) Hecto (h) Deka (da, D) Gram(g) Meter(m) Liter(L) Deci (d) Centi (c) Milli (m) Micro (μ) Nano (n)
$10^9$ $10^6$ $10^3$ $10^2$ $10^1$ $1$ $10^{-1}$ $10^{-2}$ $10^{-3}$ $10^{-6}$ $10^{-9}$

## 6 Steps on How to Convert A Unit of Measurement to Another Unit

1. Compare the two units.

2. Find the conversion factors that gives the appropriate ratio to the given unit.

3. Write the conversion as a fraction, where the denominator is in the same unit as the given unit.

4. Write a multiplication problem with the original number and the fraction.

5. Cancel out similar units that appears on the numerator and denominator.

6. Solve.

### Convert Lengths or Distance

a. Convert $108 \rm {inches}$ into $\rm {feet}$.
Given: $108 \rm {inches}$
First, you will find the conversion factors that gives the appropriate to the given unit.

$$12 \rm {inches} =1 \ rm {ft}$$

Secondly, Write the conversion as a fraction

$${1 \rm {ft} \over 12 \rm {in}}$$

Then, write a multiplication problem with the original

$$108 \rm {in} x {1 \rm {ft} \over 12 \rm {in}}$$

After that, Cancel out similar units that appears on the numerator and denominator

$108{\rm{ \bcancel{in} }}x{\rm{ }}\frac{{{\rm{1 ft}}}}{{17{\rm{ \bcancel{in}}}}}$

Lastly, Solve!

$${1 \rm {ft} \over 12}=9 \rm {ft}$$

Therefore $108 \rm {in}$ is $9 \rm {ft}$

Let's have another example. Just follow the steps above.

b. Convert 39 decimeters into millimeters
Given: $39 \rm {dm}$

Solution: $39{\rm{ dm }}x{\rm{ }}\frac{{1{\rm{ m}}}}{{10{\rm{ dm}}}}x{\rm{ }}\frac{{1000{\rm{ mm}}}}{{1{\rm{ m}}}} = \frac{{39000{\rm{ mm}}}}{{10}} = 3900{\rm{ mm}}$

### Convert Mass

a. Convert $7.2$ pounds into ounces
Solution: $7.2lb{\rm{ x }}\frac{{16oz}}{{1lb}} = 115.2oz$

b. Convert $3.5$ kilogram into grams.
Solution: $3.5kg{\rm{ x }}\frac{{1000g}}{{1kg}} = 3500g$

### Convert Area

a. Convert $1.7$ acre to square yard
Solution: $1.7acre{\rm{ x }}\frac{{43560f{t^2}}}{{1acre}}{\rm{ x }}\frac{{1y{d^2}}}{{9f{t^2}}} = \frac{{74052y{d^2}}}{9} = 8228y{d^2}$

### Convert Volume

a. Convert 2.4 cubic yard to cubic feet.
Solution: $2.4y{d^3}{\rm{ x }}\frac{{27f{t^3}}}{{1y{d^3}}} = 64.8f{t^3}$

### Convert Time

Convert $1/2$ month to hours.
Solution: $0.5{\rm{ month x}}\frac{{30{\rm{ days}}}}{{1{\rm{ month}}}}{\rm{ x }}\frac{{24{\rm{ hr}}}}{{1{\rm{ day}}}} \approx 360{\rm{ hrs}}$

### Try this Unit Conversion Calculator

This unit converter is a free and easy to use tool for converting units of measurements.

It converts length, area, volume, weight, speed, density and temperature. It also converts between different units of measurement.

The converter is available in metric or imperial units. You can type in the unit you want to convert into the search bar or click on the links below to find your desired unit.

## Conclusion: Use these Tips to Succeed at Unit Conversions with Ease

When changing from one unit of measurement to another, it is very important to know the table of conversion because this will be your guide.

There are some measurements in the table that can't be changed directly, so we should know which conversion factor is the easiest to use.

You need to know and be good at converting units before you can use the different problem-solving strategies to solve problems that involve converting units.

Unit conversions are a necessary skill in the workplace. Whether you are a student, engineer, or an accountant, you will need to know how to convert units of measurement.

Use these tips to succeed at unit conversions with ease:

• Use a calculator or an online conversion tool.
• Memorize the metric system conversion chart!
• Pay attention to units of measurements in context.
• Think about what units you want and what units you have before starting the conversion process.
• Never forget that there are always two values when converting from one unit to another - one from the original and one from the destination unit!