Unit Conversions

What is a Unit Conversion? A unit conversion is a changing of

one unit to another.1 foot = _____ inches

1 meter = _____ centimeters

1 pound = _______ ounces

1 minute = ______ seconds

1 hour = ________ minutes

1 day = __________ seconds

1 gram = ___________ milligrams

What is a Metric Unit?

Metric units are the universally excepted units around the world (except for the US). They are the easiest to convert.

Metric Unit Examples: meters liters grams

Base Units – all other metric units are based off of these (km, cm, ml, kg)

Metric Unit Conversions

1 km= 1000 m100 cm= 1 m1000 mm = 1 m10 mm = 1 cm

These also work for liters and grams. Just replace the base unit (m) with a (g) or (l).

CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

Non-Metric (English) Unit Conversions

 Length:12 inches (in) = 1 foot (ft)

3 feet  = 1 yard (yd) 5280 feet = 1 mile (mi)

  Capacity:3 teaspoons (tsp) = 1 tablespoon (tbsp)

 16 tbsp = 1 cup (c)8 ounces (oz) = 1 c

2 c = 1 pint (pt)2 pt = 1 quart (qt)

4 qt = 1 gallon (gal)

Weight:16 ounces (oz) = 1 pound

(lb)2000 lb = 1 ton

 

Dimensional Analysis

Dimensional Analysis

A mathematical way to convert one unit to another. This works for metric units and non-metric (English) units.

This works by taking the unit you are given and multiplying it by a conversion factor.

Unit conversion factor?

A unit conversion factor is a fraction whose numerator and denominator are equivalent measures. Some common unit conversion factors are given below. You can also use the reciprocal of these.

Example 1: Convert 3m to cm

Given Conversion Factor

= 300cm

For meters to cancel out, meters in the conversion factor must be on the opposite side of the fraction (fence).

3m 100 cm1m

Multiply every number on top of the fence and divide by the bottom.

 

Example 2: Convert 1516 g to kg

conversion factor

1.516 kg

1516 g 1 kg

1000 g

 

Whiteboard Problem 1

John runs 5 kilometers a day to stay in shape. How many meters is this?

Whiteboard Problem 2

The volume of Alvin’s drink is 750 mL. How many liters is this?

Whiteboard Problem 3

Stacey took a jump-shot when she was 7200mm away from the hoop. Convert this length to km.

Example 4: Beth has to walk 2 miles to school every morning. How many miles does she have to walk in ft?

= 10,560 ft

2 mi 5280 ft

1 mi

 

Whiteboard Problem 4

The Reno High School football team is 3.2 ft away from the goal line. How many inches does the ball have to travel for them to score a touchdown?

English to Metric Unit conversions

Common Conversion Factors 5280 ft = 1 mile 12 in = 1 ft 1 mile = 1600 m 1 in = 2.54 cm 3 ft = 1 yard

English to Metric conversion factors

Example 5: William grew 2 inches over the summer, and is now 5 ft tall. How tall is William in cm?

5 ft 12 in

1 ft2.54 cm1 in

= 152. 4 cm 

Whiteboard Problem 5

Convert 50 inches to m.

Whiteboard Problem 6

1. Convert 45 inches to cm.

2. Convert 8 m to inches.

Whiteboard Problem 7

1. Convert 10ft to cm.

2. Convert 5 km to in.

Data Storage Unit Conversions

In the cases when used to describe data storage, bits/bytes are calculated as follows:

1 byte = 8 bits1 kilobyte (K / Kb) = 1,024 bytes1 megabyte (M / MB) = 1,024 kilobytes1 gigabyte (G / GB) 1,024 megabytes 1 terabyte (T / TB) = 1,024 gigabytes

A bit or binary digit is the basic unit of information in computing and telecommunications; it is the amount of information that can be stored by a digital device or other physical system that can usually exist in only two distinct states.

Whiteboard Problem 8

The Nintendo 64 featured a 64-bit chip. How many bytes of data could the Nintendo 64 store? (1 byte = 8 bits)

Whiteboard Problem 9

Frederick needs to buy a 1TB External Hard Drive to back up his files. How many Kb of information can this hard drive store?

Challenge Problem

The human brain will store 100 trillion bits in its lifetime. 8 bits equal 1 byte, and 1,024 bytes equal 1 kilobyte, and 1,024 kilobytes equal one megabyte. How many million megabytes can your brain store?