1-Step Conversions

Conversions

1-Step Conversions:

When we are able to convert directly from one unit to another unit without having to first convert to a third unit, this is known as a 1-step conversion. The steps for a 1-step conversion are as follows:

1. Determine what is your given.

2. Determine the unit you want to convert to.

3. Determine an equivalence relationship between your given and the unit you want to convert to. You may need a chart or handout to determine these equivalence relationships.

4. Put your given over 1 and multiply it by a fraction using your equivalence relationship such that the given unit of measure cancels and the unit you want to convert to is left in the numerator. Simplify your final answer.

Example: Converting from Feet to Inches

Convert 5 feet to inches.

1. Our given is the 5 feet.

2. The unit we want to convert to is inches.

3. Our equivalence relationship between our given and the unit we want to convert to is 1 foot = 12 inches. Anything over its equivalent is equal to one. Therefore, both and are equal to one.

4. To convert from 5 feet to inches, we want to eliminate the unit “feet” and be left with the unit inches. Since the 5 feet is in the numerator, we want to multiply it by something that has the unit feet in the denominator. Therefore, we will multiply x so that the feet cancel and we are left with the unit we want to convert to which is inches.

= = 60 inches

Guided Practice: Convert 8 feet to inches.

1. What is your given?

2. What is the unit you want to convert to?

3. What is the equivalence relationship between your given and the unit you want to convert to?

4. Complete the following: = = ___ inches

Example: Converting from Inches to Feet

Convert 84 inches to feet.

1. Our given is the 84 inches.

2. The unit we want to convert to is feet.

3. Our equivalence relationship is 1 foot = 12 inches.

4. To convert from 84 inches to feet, we want to eliminate the unit “inches” and be left with the unit feet. Therefore, we will multiply so that the inches cancel and we are left with feet.

= = 7 Feet

Guided Practice:

Convert 108 inches to feet.

2. What unit do you want to convert to?

3. What is your equivalence relationship?

4. Complete the following: = = ___ Feet Example: Converting from inches to feet and inches

Convert 99 inches to feet and inches.

We could convert the 99 inches just to feet using either a decimal or a fraction for our final answer.

= = 8.25 Feet

= = Feet = 8 ¼ Feet

However, if we want to convert the 99 inches into feet and inches, then we will need to take the following steps:

1. Our given is the 99 inches.

2. The unit we want to convert to is feet and inches.

3. Our equivalence relationship is 1 foot = 12 inches.

4. To first convert the 99 inches to feet we want to eliminate the inches and be left with feet. To then convert from feet to feet and inches, we then divide the 12 into the 99 feet to get 8 with a remainder of 3. The 8 represents the number of whole feet since every 12 inches is one foot and the 3 we put over our divisor 12 to get the fractional part for a total of 8 ¾ feet. We then convert the fractional part to inches. Therefore, we get the following:

= = 8 Feet 3 inches

Guided Practice:

Convert 105 inches to feet and inches.

3. What is your equivalence relationship?

4. Complete the following: ___Feet __Inches

Multiple Step Conversions:

When there is not a direct conversion from one unit to another unit, then we must use multiple step conversions. Multiple step conversion is very much like the 1- step conversion except that there will be more than one equivalence relationship and step 4 will be repeated a number of times until we get to the unit we want to convert to. We will also need to figure out a path to conversion. Here are the steps for Multiple Step Conversions:

1. Determine what is your given.

2. Determine the unit you want to convert to.

3. Determine all the equivalence relationships to get to the unit you want to convert to. You may need a chart or handout to determine these equivalence relationships.

4. Determine a path to conversion.

5. Put the given over 1 and multiply it by a fractions using your equivalence relationships such that all units of measure cancel except the unit you want to convert to. The unit you want to convert to should be left in the numerator. Simplify your final answer.

Example: Converting Gallons to Ounces

Determine the number of ounces in one gallon.

1. Our given is one gallon.

2. The unit we want to convert to is ounces.

3. Our equivalence relationships are as follows:

1 gallon = 4 quarts 1 quart = 2 pints

1 pint = 2 cups

1 cup = 8 ounces

4. The path to conversion is as follows: convert from gallons to quarts, from quarts to pints, from pints to cups and from cups to ounces.

5. Using your equivalence relationships and your path to conversion set up your set up your fractions that you will need to multiply so that you eliminate all your units of measure except the unit you want to convert to. Remember that the unit you want to convert to should be left in the numerator. Simplify your final answer.

If you have a gallon of milk at home you should be able to verify that one gallon is in fact equivalent to 128 ounces.

Guided Practice:

Determine the number of seconds in a day.

3. What are your equivalence relationships?

4. What is your path to conversion?

5. Complete the following: Conversions that use Formulas:

Some conversions use formulas to convert from one unit to another unit. For our purposes, we will be concerned only with the formulas to convert temperatures from Fahrenheit to Celsius and from Celsius to Fahrenheit. If we let F = Fahrenheit and C = Celsius here are the formulas:

C = 5(F – 32)/9

F=1.8C+32

When working these formulas we will only be working on the right side of the equations to crunch the numbers. When crunching these numbers, we will need to know our order of operation. Here is a quick review of our order of operation:

Parenthesis (Simplify what is inside of the parenthesis.)

Exponents

Multiplication

Division

Subtract

Multiplication and division are done at the same time working from left to right. Therefore, you may have to do a division before you do a multiplication. Addition and subtraction are also done at the same time working from left to right. To remember the steps you can use the mnemonic PEMDAS: Please Excuse My Dear Aunt Sally.

Many times you may need to round your final answer. Do not do any rounding until you get to the final answer. If you are asked to round to a certain place value, go to the right one additional place value, if that number is 5 or greater, then round the up one digit. If the number to the right is not 5 or greater then truncate the number (eliminate all numbers to the right) .

Example: round 5345.467 to the nearest hundredth

The number 6 is in the hundredth place value. The number to the right of the 6 is the number 7 which is 5 or greater. Therefore, we will round up one digit.

Example: round 3459.76125 to the nearest thousandth

The number 1 is in the hundredth place value. The number to the right of the 1 is the number 2 which is not 5 or greater. Therefore, we will truncate our answer (eliminate all numbers to the right of the number 1).

Steps to Convert from Fahrenheit to Celsius or from Celsius to Fahrenheit:

The steps to convert from Fahrenheit to Celsius and from Celsius to Fahrenheit are the same. 1. Determine the correct formula to use.

To convert from Fahrenheit to Celsius: C = 5(F – 32)/9

To convert from Celsius to Fahrenheit: F=1.8C+32

2. Substitute the given number of degrees for the appropriate variable on the right side of your equation.

3. Crunch the numbers on the right side of the equation. Remember your order of operation (PEMDAS).

4. Round your final answer to the appropriate place value if asked to do so.

Converting from Fahrenheit to Celsius:

Convert 76 degrees Fahrenheit to Celsius. Round your final answer to the nearest tenth.

1. Since we want to convert to Celsius, we will want to use the following formula: C = 5(F – 32)/9.

2. Substitute 76 for F in the formula.

C = 5(76 – 32)/9

a. Our first order of operation is parenthesis. Therefore, we will simplify what is inside our parenthesis. 76 – 32 = 44

Our formula now is

C = 5(44)/9 b. Our next order of operation is exponent, but we don’t have any exponents. Therefore, we move on to multiplication and division working from left to right. We first multiply 5x44 to get 220. We then divide 220/9 to get 24.444444444. C = 24.444444444 degrees Celsius

4. We now need to round our final answer to the nearest tenth. The second 4 is in the tenth place value. The number to the right of that 4 is another 4 which is not 5 or greater, therefore, we will truncate our answer to get 24.4 degrees.

76°F = 24.4°C

Guided Practice:

Convert 64 degrees Fahrenheit to Celsius. Round your final answer to the nearest tenth.

1. Which formula is appropriate for this problem?

2. Substitute 64 for F in your formula.

3. Crunch the numbers on the right side of the equation. Remember your order of operation (PEMDAS). What is the answer you got for C?

4. Round your final answer to the nearest tenth. C= _____

Converting from Celsius to Fahrenheit:

Convert 40 degrees Celsius to Fahrenheit. Round your final answer to the nearest tenth if necessary. 1. Since we are converting to Fahrenheit, we will want to use the following formula: F = 1.8C+32

2. Substitute 40 for C in the formula.

F = 1.8(40) + 32

a. Our first order of operation is parenthesis. However, we have nothing to simplify in our parenthesis. Our next order of operation is exponent, but we have no exponents. Therefore, we move on to multiplication and division working from left to right. We multiply 1.8x40 = 72.0 = 72

Our formula now is F = 72 + 32

b. We now add 72 + 32 = 104. F = 104 degrees Fahrenheit = 104°F

4. It is not necessary to round our final answer since our final answer is a whole number. Therefore, 40°C = 104°F.

Guided Practice

Convert 32 degrees Celsius to Fahrenheit. Round your final answer to the nearest tenth.

1. Which formula is appropriate for this problem? 2. Substitute 32 for C in your formula.

3. Crunch the numbers on the right side of the equation. Remember your order of operation (PEMDAS). What is the answer you got for F?

4. Round your final answer to the nearest tenth. F= _____