---
excerpt: "Fractions and decimals are two types of numbers that we frequently encounter in our daily lives. Converting between fractions and decimals has a lot of practical use and is essential for progressing toward advanced mathematics. In this lesson, we will demonstrate step-by-step how to convert fractions to decimals and vice versa with examples."
keywords: "decimal to fraction, .375 as a fraction, 0.05 as a fraction, 3/8 as a decimal, .625 as a fraction, fraction to decimal, fraction to decimal, decimal to fraction"
---

## Fractions and Decimals

Fractions and decimals are two forms used to represent parts of whole quantities. Usually, the context determines which form works best. For example, it would be strange if the price of a pizza box reads $$ \$11 \frac{2}{5}$$ instead of $11.40. On the other hand, it wouldn't make sense to say there are 2.75 pizzas left over from last night’s party instead of 2 and 3/4 of pizza.

![A Pizza box with the price indicated as eleven and two-fifths dollars::200px](/lessons/fraction-to-decimal/fraction.png)

When solving algebraic equations, geometry, etc. you’ll encounter both fractions and decimals in the mix, and knowing how to convert between the two forms is vital. This guide will teach you how to turn a decimal into a fraction and vice versa step-by-step.

## How to convert a decimal into a fraction?

Understanding place value in decimals gives better insight into the relationship between decimals and fractions. The place value chart below shows how the place value gets ten times smaller each time it shifts to the right. A whole unit divides into ten parts to make tenths, the tenths place divides further to give hundredths, and so on.

![A place value chart from tens place to thousandths, with arrows showing division by ten when shifting to the right of each place.::200px](/lessons/fraction-to-decimal/place-value-chart.png)
Now let’s consider the decimal number 0.21 on the place value chart.

![A place-value chart representing the decimal number 0.21::200px](/lessons/fraction-to-decimal/place-value-chart-2.png)
We have 2 tenths and 1 hundredth. If we add them up we get:

$$
\frac{2}{10} + \frac{1}{100} =
$$

$$
\frac{2}{10} \times \frac{10}{10} + \frac{1}{100} \times \frac{1}{1} =
$$

$$
\frac{20}{100} + \frac{1}{100}=\frac{21}{100}
$$

So the decimal 0.21 is $\frac{21}{100}$ as a fraction. As the number of digits in the decimal number increases, the calculations get more tedious. Hence, the following step-by-step approach is more popular.

Let’s apply this to a few examples.

<Snippet ribbon="Example">
<Question tag="Example 1. ">What is 0.375 as a fraction?</Question>
<Answer tag="Answer:">
<strong>Step 1.</strong> Consider the decimal as a fraction with a denominator of 1
$$
0.375 = \frac{0.375}{1}
$$
<strong>Step 2. </strong> Obtain an equivalent fraction with a whole number as the numerator

To convert 0.375 into a whole number, we need to shift the decimals 3 places to the left. Therefore, we multiply 0.375 by 10 three times, or simply by 1000.

$$
\frac{0.375}{1} \times \frac{1000}{1000}=\frac{375}{1000}
$$

<strong>Step 3.</strong> Write the fraction in its simplest form

The GCD of the numerator and denominator is 125. Divide the numerator and denominator by 125 to get:

$$
\frac{375 \div 125}{1000 \div 125} = \frac{3}{8}
$$

Hence, 0.375 as a fraction is $\frac{3}{8}$.
</Answer>
</Snippet>

<Snippet ribbon="Example">
<Question tag="Example 2. ">Write 0.05 as a fraction.</Question>
<Answer tag="Answer:">
<strong>Step 1.</strong> Consider the decimal as a fraction with a denominator of 1
$$
0.05 = \frac{0.05}{1}
$$
<strong>Step 2. </strong> Obtain an equivalent fraction with a whole number as the numerator

Note here that the digit 5 is in the hundredths place and should shift two places to the left. So we should multiply it by 100.

$$
\frac{0.05}{1} \times \frac{100}{100}=\frac{5}{100}
$$

<strong>Step 3.</strong> Write the fraction in its simplest form

The GCD of the numerator and denominator is 5.

$$
\frac{5 \div 5}{100 \div 5} = \frac{1}{20}
$$

Hence, 0.05 as a fraction is $$\frac{1}{20}$$.
</Answer>
</Snippet>

<Snippet ribbon="Example">
<Question tag="Example 3. ">What is 1.5 as a fraction?</Question>
<Answer tag="Answer:">
<strong>Step 1.</strong> Consider the decimal as a fraction with a denominator of 1
$$
1.5 = \frac{1.5}{1}
$$
<strong>Step 2. </strong> Obtain an equivalent fraction with a whole number as the numerator

$$
\frac{1.15}{1} \times \frac{10}{10}=\frac{15}{10}
$$

<strong>Step 3.</strong> Write the fraction in its simplest form

The GCD of the numerator and denominator is 5.

$$
\frac{15 \div 5}{10 \div 5} = \frac{3}{2} = 1\frac{1}{2}
$$

Note the last equation follows from rules for the conversion of improper
fractions to mixed fractions.
</Answer>
</Snippet>

## How to convert a fraction to decimal?

A fraction visually represents the division of the numerator by the denominator.

We can use the next example to understand how to turn a fraction into a decimal using division.

<Snippet ribbon="Example">
<Question tag="Example 4. ">3/8 as a decimal</Question>
<Answer tag="Answer:">
<strong>Step 1.</strong> Write the fraction in its simplest form
This step is optional, yet it will make calculations easier to work out by hand.

In this example ⅜ cannot be simplified any further, so we can move on to step 2.

<strong>Step 2.</strong> Divide the numerator by the denominator.
We have to divide 3 by 8. Let’s use long division to work it out.

Always ensure that the dividend is the denominator and the divisor is the numerator.
![The first step of long division of 3 by 8 with 3 labeled as dividend and 8 as the divisor::150px](/lessons/fraction-to-decimal/l_d_1.png)
<strong>Step 3.</strong> Obtain quotient after the remainder becomes 0

Continue the long division algorithm until there isn’t any remainder, as shown below.
![Illustration of steps of dividing 3 by 8 using the long division method](/lessons/fraction-to-decimal/division_3_over_8.png "3 steps for dividing 3 by 8 using the long division method")

Finally, we obtain that ⅜ is 0.375 as a decimal. Which tallies with the result we obtained in the very first example.

Note: The long division does not always yield a 0 remainder upon repeating, which happens with recurring decimals. In such cases, you can use the appropriate notation to represent the decimal.

</Answer>
</Snippet>

It’s time to challenge ourselves to see how well we are able to convert a fraction into a decimal and vice versa.

<Snippet ribbon="Question">
<Question tag="Review Question 1. ">Turn 0.625 into its decimal form</Question>
<Answer tag="Solution:">
<strong>Step 1.</strong> Consider the decimal as a fraction with a denominator of 1
$$
0.625 = \frac{0.625}{1}
$$

<strong>Step 2.</strong> Obtain an equivalent fraction with a whole number as the numerator

$$
\frac{0.625}{1} \times \frac{1000}{1000}=\frac{625}{1000}
$$

<strong>Step 3.</strong> Write the fraction in its simplest form

$$
\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}
$$

0.625 as a fraction is $\frac{5}{8}$.
</Answer>
</Snippet>

<Snippet ribbon="Question">
<Question tag="Review Question 2. ">Use a place value chart to write 3.5 as a fraction form</Question>
<Answer tag="Solution:">
<strong>Step 1.</strong> Write 3.5 on the place value chart

3 goes in the Unit's place, and 5 goes in the tenths place.
![A place value chart representing the decimal number 3.5::200px](/lessons/fraction-to-decimal/place-value-chart-3.png)

<strong>Step 2.</strong> Add all the values as fractions

3 is a whole number.

$$
3 + \frac{5}{10} =
$$

$$
\frac{3}{1} \times \frac{10}{10} + \frac{5}{10} \times \frac{1}{1}=
$$

$$
\frac{30}{10} + \frac{5}{10} = \frac{35}{10}
$$

<strong>Step 3.</strong> Write the fraction in its simplest form

The GCD of 35 and 10 is 5. Hence we can simplify by dividing the numerator and denominator by 5.

$$
\frac{35\div 5}{10 \div 5}= \frac{7}{2}= 3\frac{1}{2}
$$

Hence, 3.5 as a fraction is $\frac{7}{2}$ or $3\frac{1}{2}$ as a mixed number.
</Answer>
</Snippet>


How to convert fractions to decimals and vice versa

---
excerpt: "Inequalities are used in mathematics to represent restrictions or constraints placed on variables. From the derivation of theorems to optimization and engineering, inequalities are essential to anyone interested in mathematics. Linear inequalities are a great place to start as they are simple yet help you build a solid understanding of higher-order inequalities. In this post, we’ll cover the algebraic method to solve two-step linear inequalities along with practical examples."
description: "Learn how to solve linear inequalities with step-by-step examples. We cover both single-step and two-step inequalities, and how to present solutions using interval notation and inequality arrows."
---

## Linear Inequalities vs Linear Equations?

Linear Equations are used to describe the equality between two expressions. For example 2x + 1 = x - 3. It is a way of mathematically saying something is <strong>equal to</strong> something. Sometimes the relationship can be different or more complicated. Common relationships we use to compare quantities in everyday life include, greater than, less than, not equal, between, etc. We use inequalities to represent these sorts of relationships mathematically. You may already be aware of some of the standard symbols used:

<NumberedList>
  <li>
    <div>
      Greater than $\gt$
    </div>
  </li>
  <li>
    <div>
     Less than $\lt$
    </div>
  </li>
  <li>
    <div>
      Not equal $\neq$
    </div>
  </li>
  <li>
    <div>
      Greater than or equal $\ge$
    </div>
  </li>
  <li>
    <div>
      Less than or equal $\le$
    </div>
  </li>
</NumberedList>
If the two expressions that are being compared are linear, then the relationship is known as linear inequalities.

![A balance that compares expressions::200px](/lessons/inequalities/inequality_balance.png)

## Real-world example of how linear inequalities are used to represent constraints or limitations

<Snippet ribbon="Example">
<Question tag="Example 1. "> An uber charges a fixed fee of 50 for a ride, plus a rate of 6 per hour. How many hours can you go without exceeding 125?</Question>
<Answer tag="Answer:">
The variable here is the number of hours traveled. Let’s use <strong>x</strong> to represent it. 

The expression that represents the cost of a ride of $x$ hours is:
$$
50 + 6x
$$

Since this expression has to be <strong>less than or equal to 125</strong>, we can use the following inequality to describe the constraint:
$$
50 + 6x \le 125
$$

</Answer>
</Snippet>

## Solving Linear Inequalities

The algebraic approach to solving inequalities uses the same fundamentals that are used to solve linear equations. The main steps involved are:
<NumberedList>
  <li>
    <div>
      $\text{Assign the variable/s (for contextual questions only)}$
    </div>
  </li>
  <li>
    <div>
     $\text{Build the inequality from the context (for contextual questions only)}$
    </div>
  </li>
  <li>
    <div>
      $\text{Rearrange and Simplify like terms}$
    </div>
  </li>
  <li>
    <div>
      $\text{Isolating the variable}$
    </div>
  </li>
</NumberedList>

There are a few important points that you need to keep in mind when rearranging terms and manipulating inequalities as compared to equations. It can be summarized by the rules below:

<BulletList>
  <li>
    <div>
      $\text{Multiplying or dividing an inequality by a negative number reverses the sign of inequality.}$
    </div>
  </li>
  <li>
    <div>
     $\text{Obtaining the reciprocal can reverse the sign of the inequality}$
    </div>
  </li>
</BulletList>
We can use a simple example to verify rule #1 above.

## Proof of Rule #1
Consider two numbers <strong>a</strong> and <strong>b</strong>. The diagram shows the positions of these numbers on the number line. 
![Two numbers a and b marked on a number line::200px](/lessons/inequalities/inequalities_rule1_1.png)

Since <strong>b</strong> is on the right side of <strong>a</strong> in the number line, we can represent it using the following inequality:
$$
a \lt b
$$
Now if we consider the negative values of <strong>a</strong> and <strong>b</strong> on a number line, their positions will be at a distance of <strong>a</strong> and <strong>b</strong> respectively on the left of 0 on the number line. 

![A number line with the postiive and negative values of a and b marked::200px](/lessons/inequalities/inequalities_rule1_2.png)

So visually it is clear, since <strong>-b</strong> is on the left of <strong>-a</strong> on the number line, the inequality that describes the relationship of their sizes would be:
$$
-a \gt -b
$$
If you compare the two inequalities that compare <strong>a</strong> and <strong>b</strong>, and <strong>-a</strong> and <strong>-b</strong>, it is evident that if you multiply (or divide) by a negative number the sign of the inequality flips. 

Before we prove <strong>rule #2</strong>, let’s try an example of solving two step inequalities.

<Snippet ribbon="Example">
<Question tag="Example 2."> Solve $-12x -18 + 7x \le -3 $</Question>
<Answer tag="Answer:">
<strong>Step 1:</strong> Simplify like terms
On the left-hand side of the inequality, we have two like terms of x. 
$$
-12x + 7x - 18 \le -3
$$
$$
-5x - 18 \le -3
$$

<strong>Step 2:</strong> Isolate the variable
The variable here is x. To isolate the x term we have to first remove -18 from the left-hand side of the inequality by adding 18 to both sides of the inequality.
$$
-5x - 18 + 18 \le -3 + 18
$$
$$
-5x \le 15
$$
Next, we have to remove -5 by dividing both sides by -5. 
$$
x \ge -3
$$
Note that the sign of the inequality flipped because we divided by a negative number. (Rule #1)

</Answer>
</Snippet>

## The proof for rule #2

Let’s consider two positive numbers a and b, where b is greater than a. The inequality that depicts that is : 
$$
b \gt a
$$
Next let’s consider <strong>c</strong> and <strong>d</strong>, which are the reciprocals of <strong>b</strong> and <strong>a</strong> respectively. In a fraction, as the denominator gets larger the size of the fraction reduces. We can use this concept to prove that <strong>c</strong> will be smaller than <strong>d</strong>. Now that evaluates to the inequality:
$c \lt d$, 
Which in turn means that, 
$$
\frac{1}{b} \lt \frac{1}{a}
$$
This is proof of rule #2. This rule only applies if a and b are <strong>both positive</strong>  or <strong>both negative</strong>.
It’s time to apply the newly gained knowledge to problem-solving. 

<Snippet ribbon="Example">
<Question tag="Example 3."> 
In a triathlon event, Sarah swims 1.5 km, cycles 40 km, and runs 15 km. Her average cycling speed is twice her average swimming speed, and her average running speed is 1.5 times her average swimming speed. If she finishes the race in less than 3$\frac{1}{3}$ hours, what can we say about her average speeds?
</Question>
<Answer tag="Solution:">
<strong>Step 1.</strong> Assign the variables.

Here the variables are Sarah's running speed, cycling speed, and swimming speed. 
If her swimming speed is <strong>s</strong> then:
$$
\text{Swimming Speed -- } s
$$
$$
\text{Cycling Speed -- } 2s
$$
$$
\text{Running Speed -- } 1.5s
$$

<strong>Step 2.</strong> Build the inequality from the context.

The word relationship we have is that:
$$
\text{Swim time} + \text{Run time} + \text{Cycle time} \lt 3\frac{1}{3} \text{hours}
$$
Using the formula : 
$$
\text{Time} = \frac{\text{Distance}}{\text{Speed}} 
$$
we can represent the relationship mathematically as follows:

$$
\frac{1.5}{s} + \frac{15}{1.5s} + \frac{40}{2s} \lt \frac{10}{3}
$$

<strong>Step 3.</strong> Simplify like terms
By simplifying the fractions we get:
$$
\frac{1.5}{s} + \frac{10}{s} + \frac{20}{s} \lt \frac{10}{3}
$$
$$
\frac{1.5}{s} + \frac{10}{s} + \frac{20}{s} \lt \frac{10}{3}
$$
$$
\frac{31.5}{s} \lt \frac{10}{3}
$$

<strong>Step 4.</strong> Isolate the variable

The variable here is s. To isolate the term we could obtain the reciprocal on both sides in order to get <strong>s</strong> on the numerator.
$$
\frac{s}{31.5} \gt \frac{3}{10}
$$

Note that the sign of the inequality flipped because of Rule #2, and it was applicable because we know for certain that the speed "s" is <strong>always positive</strong>.

Finally, multiply both sides by 31.5
$$
s \gt \frac{3 \times 31.5}{10}
$$
$$
s \gt 9.45
$$

Hence, we can say that 
<BulletList>
  <li>
    <div>
      $\text{Sarah's average swimming speed is above 9.45 km/h.}$
    </div>
  </li>
  <li>
    <div>
     $\text{Average cycling speed is above 18.90 km/h.}$
    </div>
  </li>
  <li>
    <div>
      $\text{Sarah's average running speed is greater than 14.18 km/h.}$
    </div>
  </li>
</BulletList>

</Answer>
</Snippet>

## Understanding the Solution Set: Inequality Arrows and Interval Notation

Inequality arrows are a method of representing solutions to an inequality visually. There are several conventions that are followed when using arrows:
![inequalities represented using inequality arrows::200px](/lessons/inequalities/inequalities_arrows.png)
Interval notation is a common way to represent the solution set of a linear inequality or a system of linear inequalities. It provides a compact and convenient way of writing down the set of all values that satisfy the inequality(ies).

<center>
  <FancyTable1>
  | Solution      |Interval Notation |  
  | :---        |       ---: |
  | $x \gt a$      |<center> $({a,\infty}) $ </center>     |
  | $x \lt a$   | <center> $(-\infty, a) $   </center>|
  | $x \ge a$   | <center>$[a, \infty) $</center> |
  | $b \lt x \le a$   | <center>$(b, a] $ </center>  |
  </FancyTable1>
</center>

The square bracket is used to indicate a closed-interval while the parenthesis is used for an open-interval.

<Snippet ribbon="Question">
<Question tag="Quiz on two step inequalities"> 
Solve the inequality: 
$$
2x - 5x \le 5 - 26
$$
and present the solution using the interval notation and inequality arrows.
</Question>
<Answer tag="Solution:">

<strong>Step 1.</strong> Simplify like terms

$$
2x - 5x \le 5 - 26
$$
$$
-3x \le -21
$$
<strong>Step 2.</strong> Isolate the variable

The variable here is x. To isolate the term we have to divide both sides of the inequality by -3. Remember that according to rule#1 the sign of the inequality reverses. 
$$
-3x \le -21
$$
$$
x \ge 7
$$
Representing this using inequality arrows:

In the interval notation, the solution x >=7 would be [7, inf]

<center>
  <FancyTable1>
  | Solution      |Interval Notation |<center>Inequality arrows</center>|  
  | :---        |:---:    |        ---: |
  | $x \ge 7$      |<center> $[{7,\infty})$ </center>     | ![solution represented using inequality arrows::50px](/lessons/inequalities/quiz_inequality_arrows.png)|
  </FancyTable1>
</center>
</Answer>
</Snippet>

Learn how to solve linear inequalities with step-by-step examples. We cover both single-step and two-step inequalities, and how to present solutions using interval notation and inequality arrows.

What are linear inequalities and How do they relate to linear equations?

---
excerpt: "As a math student, understanding temperature conversions is a fundamental skill that will come in handy in real-life situations. Fahrenheit and Celsius are the two most commonly used units of temperature measurement, and being able to convert between them is a crucial skill. In this article, we will guide you through the process of converting Fahrenheit to Celsius and vice versa. This lesson will provide you with practical examples and a clear explanation of the conversion formula, so you can confidently tackle any unit conversion problem that comes your way."
---

## Fahrenheit and Celsius

Temperature is a fundamental physical quantity that we encounter in our daily lives, from checking the weather forecast to setting our home thermostats. However, depending on location, scientific context, or practical considerations, the temperature can be measured using different units. Fahrenheit, Celsius, and Kelvin are the most commonly used temperature scales, with Kelvin mainly used in scientific applications. Being able to convert between these units is a valuable skill that can come in handy in real-life situations, and also serves as an excellent way to understand unit conversions in general.
![Fahrenheit and Celsius applications cover image::400px](/lessons/temperature_conversion/temperature_conversion.png)
## Celsius to Fahrenheit Conversion

In the United States, it is natural to use Fahrenheit when referring to temperature. However, for most of the rest of the world, Celsius is the unit used. In everyday speech, we often use the term “degrees” instead of specifying Fahrenheit or Celsius. This can lead to confusion when traveling around the world. 

We can use the following formula for converting Celsius to Fahrenheit.
$$
\degree\text{F} = \frac{9}{5}\text{C} + 32
$$
Let's understand how to apply the formula by working out the conversion of 38.5 celsius to fahrenheit problemstep by step.

<Snippet ribbon="Example">
<Question tag="Example 1."> What is 38.5 celsius in fahrenheit?
![38.5 c to f thermometer::400px](/lessons/temperature_conversion/38.5_celsius_example.png)</Question>
<Answer tag="Answer:">
<strong>Step 1:</strong> Substitute 38.5 c into the formula

We need to replace C by 38.5 in the following formula: 
$$
\degree\text{F} = \frac{9}{5}\text{C} + 32
$$
$$
\degree\text{F} = \frac{9}{5}\times 38.5 + 32
$$

<strong>Step 2:</strong> Determine the temperature in Fahrenheit

Now we can simplify
$$
\degree\text{F} = \frac{9}{5}\times 38.5 + 32
$$
$$
\degree\text{F} = 69.3 + 32
$$
$$
\degree\text{F} = 101.3
$$
</Answer>
Hence, the temperature of 38.5 degrees Celsius is 101.3 degrees Fahrenheit.
</Snippet>

Now that you know how to work with the formula let's try to extending this understanding to a practical scenario. 

<Snippet ribbon="Question">
<Question tag="Question 1."> 
Imagine you are planning a trip to Toronto, Canada, in the middle of October. You check the weather forecast and see that the temperature will be around 19 degrees Celsius. As someone who is used to the Fahrenheit scale, you want to know what to expect in terms of weather. Can you convert the 19 degrees celsius to fahrenheit to help you prepare for your trip?
![weather card for converting 19 c to f::300px](/lessons/temperature_conversion/weather_19_c_to_f.png)
</Question>
<Answer tag="Solution:">

<strong>Step 1.</strong> Apply the conversion formula

We need to replace C by 19 in the following formula: 
$$
\degree\text{F} = \frac{9}{5}\text{C} + 32
$$
$$
\degree\text{F} = \frac{9}{5}\times 19 + 32
$$

<strong>Step 2:</strong> Determine the temperature in Fahrenheit

Now we can simplify
$$
\degree\text{F} = \frac{9}{5}\times 19 + 32
$$
$$
\degree\text{F} = 34.2 + 32
$$
$$
\degree\text{F} = 66.2
$$

Hence, the temperature of 19 degrees Celsius is 66.2 degrees Fahrenheit.

</Answer>
</Snippet>

## Fahrenheit to Celsius Conversion
Once you know how to convert from celsius to Fahrenheit, it’s quite straightforward to go the other way around. We can start from the formula that was used to convert from celsius to fahrenheit and make the celsius parameter the subject. 
Below are the steps to derive the formula for converting from Fahrenheit (F) to Celsius (C):
$$
\degree\text{F} = \frac{9}{5}\text{C} + 32
$$
$$
\degree\text{F} - 32 = \frac{9}{5}\text{C}
$$
$$
\degree\text{C} = \frac{5}{9}(\text{F} - 32)
$$

<Snippet ribbon="Example">
<Question tag="Example 2."> When body temperature rises above 102.2 degrees Fahrenheit, it can be a sign of a serious infection. What is 102.2$\degree\text{F } \text{ in } \degree\text{C}$?
![Practical example of converting fever 102.2 f to c::300px](/lessons/temperature_conversion/fahrenheit_to_celsius_example.png)</Question>
<Answer tag="Solution:">
<strong>Step 1.</strong> Apply the conversion formula

We need to replace F by 102.2 in the following formula: 
$$
\degree\text{C} = \frac{5}{9}(\text{F} - 32)
$$
$$
\degree\text{C} = \frac{5}{9}(102.2 - 32)
$$

<strong>Step 2:</strong> Determine the temperature in Fahrenheit

Now we can simplify
$$
\degree\text{C} = \frac{5}{9}(102.2 - 32)
$$
$$
\degree\text{C} = \frac{5}{9}(70.2)
$$
$$
\degree\text{C} = 39
$$

Hence, according to the conversion formula we can say that a temperature higher than 39 $\degree\text{C}$ can be a sign of serious infection.

</Answer>
</Snippet>

## The rise and drop of temperature
In describing weather conditions it is quite common to mention the increase and decrease of temperature in degrees. However, it's essential to understand that the unit of measurement can significantly impact the magnitude of change. For instance, a 15-degree change in temperature can mean vastly different things depending on the unit used. Based on the conversion formula the change in Celsius, $\Delta\text{C}$, for a given change in Fahrenheit ,$\Delta\text{F}$, is given by :
$\Delta\text{C} = \frac{5}{9}\times\Delta\text{F} $. 
This is an important conversion that everyone should be familiar with.

<Snippet ribbon="Question">
<Question tag="Question 2."> 
If New York City is expected to experience a temperature rise of 27°F in the following week.<br></br>
a) What is the equivalent increase in Celsius? <br></br>
b) If the temperature in New York was 20$\degree\text{C}$, what would it be after the increase in Fahrenheit and Celsius?
</Question>
<Answer tag="Solution:">

<strong>Step 1.</strong> Apply the conversion formula

Let's consider the rise in celsius to be $\Delta\text{C}$ and $\Delta\text{F}$ the rise in Fahrenheit
$$
\Delta\text{C} = \frac{5}{9}\times\Delta\text{F}
$$

Since $\Delta\text{F}$ is 27, we get:
$$
\Delta\text{C} = \frac{5}{9}\times 27
$$
Hence,
$$
\Delta\text{C} = 15\degree
$$
Therefore, the expected rise in temperature in celsius is 15$\degree\text{C}$.

<strong>Step 2:</strong> Determine the temperature after the increase, in $\degree\text{F} \text{ and } \degree\text{C}$

Since the temperature is 20$\degree\text{C}$ initially, after an increase of 15$\degree\text{C}$ the temperature will be  35$\degree\text{C}$.

We can now convert 35c to fahrenheit:
$$
\degree\text{F} = \frac{9}{5}\times 35 + 32
$$
$$
\degree\text{F} = 63 + 32
$$
$$
\degree\text{F} = 95\degree
$$

Hence, the temperature after the increase would be 35$\degree\text{C}$ or 95$\degree\text{F}$.

</Answer>
</Snippet>





Lessons

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What are linear inequalities and How do they relate to linear equations?

Unlocking Fahrenheit to Celsius and Celsius to Fahrenheit Conversion: A Comprehensive Guide and Practice Lessons