High School
SAT
ACT
University
MCAT
LSAT
DAT
Wize High School Algebra I Textbook (Common Core) > Foundations of Algebra

📝Review: Percentages

📝Review: Ratios, Rates, and ProportionsPrevious Section
📝Review: Powers & ExponentsNext Section
Popular Courses
Find My Course
0:00 / 0:00

Representing Numbers as Fractions, Decimals, and Percentages

Whenever we are talking about a part of a whole, meaning a fractional amount, there's always more than one way to represent these quantities.

Try to come up with as many ways as possible to represent the idea of A HALF. Be creative!
Some suggestions:
  • 1/2
  • 12\frac{1}{2}
  • 0.50.5
  • 50%50\%
  • 510\frac{5}{10}
  • or
As you can see, there are many ways to represent a number -- you can use a fraction, a decimal, a percentage, or a picture. It's important that you know how to represent a number using all of these formats, and know how to convert between these formats!

PAGE BREAK

Fractions, Decimals, and Percentages

Fractions, decimals, and percentages are different ways we can use to represent numbers, especially when the number is not whole.

Example 1
Represent the number depicted in this picture (pink rectangles as a part of the whole) using a fraction, a decimal, and a percentage.
  • Fraction: There are 3 pink rectangles and 8 rectangles in total, so this number as a fraction is38\boxed{\dfrac{3}{8}}. So, we can say that 3/8 ("three eights" or "three out of eight") of the rectangles are shaded in pink.
  • Decimal: There are 3 pink rectangles and 8 rectangles in total, so this number as a decimal is 3÷8=0.3753\div8=\boxed{0.375}. So, we can say that 0.375 of the rectangles are shaded in pink.
  • Percentage: There are 3 pink rectangles and 8 rectangles in total, so this number as a percentage is 3÷8×100%=37.5%3\div8\times 100\%=\boxed{37.5\%}. So, we can say that 37.5% of the rectangles are shaded in pink.

PAGE BREAK

Example 2
Jack completes a Marathon race in 3 hours and 54 minutes.
a) Represent Jack's race time in hours as a fraction, and as a decimal.
  • Fraction: We can keep the 3 hours as a whole number and convert the 54 minutes to a fraction of an hour. Since there are 60 minutes in an hour, 54 minutes is 5460\dfrac{54}{60} of an hour, but 5460\dfrac{54}{60} simplifies to 910\dfrac{9}{10}. So, Jack's race time in hours is 3 910 hours\boxed{3~\dfrac{9}{10}\text{ hours}} (or 3910 hours\boxed{\dfrac{39}{10}\text{ hours}} as an improper fraction).
  • Decimal: We can keep the 3 hours as a whole number and convert the 54 minutes to a decimal of an hour. Since there are 60 minutes in an hour, 54 minutes is 54÷60=0.954\div 60=0.9 of an hour. So, Jack's race time in hours is 3.9 hours\boxed{3.9\text{ hours}}.
b) What is 54 minutes as a percentage of an hour?
Since there are 60 minutes in an hour, 54 minutes is 54÷60×100%=90%54\div 60\times 100\%=90\% of an hour.


c) What is 54 minutes as a percentage of Jack's race time?
Let's convert Jack's race time, which is 3 hours and 54 minutes, into minutes.

3×60 minutes+54 minutes=234 minutes3\times 60\text{ minutes}+54\text{ minutes}=234\text{ minutes}

So, 54 minutes is 54÷234×100%≈0.231%54\div234\times100\%\approx\boxed{0.231\%} of Jack's race time.

Practice: Representing Numbers in Different Ways

The shaded part in the following circle represents a number. What is that number as a fraction, a decimal, and a percentage of the whole?



0:00 / 0:00

Converting Between Fractions, Decimals, and Percentages

From Fraction to Decimal to Percentage


From Percentage to Decimal to Fraction


0:00 / 0:00

Example: Rewriting Decimals as Fractions

Rewrite the following decimal numbers as fractions

a) 1.651.65

Write the decimal as a fraction over 1: 1.651\dfrac{1.65}{1}

Multiply top and bottom by 100 (2 zeros) because there are 2 numbers after the decimal point: 1.65 ×1001    ×100=165100\dfrac{1.65~\colorTwo{\times100}}{1~~~~\colorTwo{\times100}}=\dfrac{165}{100}

Reduce the fraction by dividing out the common factor of 5 from the top and from the bottom: 165100=3320\displaystyle \frac{\cancel{165}}{\cancel{100}}=\frac{33}{20}

Therefore, 1.65=33201.65={\dfrac{33}{20}}.

PAGE BREAK
b) −5-5

−5-5 is just an integer, so we can write it as a fraction over 1: −51\dfrac{-5}{1}

When there's one negative sign in a fraction, we usually write it in front like this −51\boxed{-\dfrac{5}{1}}.

Wize Tip
Most commonly, you will see −ab\displaystyle -\frac{a}{b} rather than −ab or a−b\displaystyle \frac{-a}{b}\ \text{or}\ \frac{a}{-b}, but all three mean the same thing!

PAGE BREAK
c) −0.302-0.302

i) Write the decimal as a fraction over 1: −0.3021\dfrac{-0.302}{1}

ii) Multiply top and bottom by 1000 (3 zeros) because there are 3 numbers after the decimal point: −0.302×10001   ×1000=−3021000\dfrac{-0.302\colorTwo{\times1000}}{1~~~\colorTwo{\times1000}}=\dfrac{-302}{1000}

iii) Reduce the fraction by dividing out the common factor of 2 from the top and from the bottom: −3021000=−151500\displaystyle \frac{\cancel{-302}}{\cancel{1000}}=\frac{-151}{500}

When there's one negative sign in a fraction, we usually write it in front like this −151500\boxed{-\dfrac{151}{500}}.

PAGE BREAK
d) −0.0013-0.0013

i) Write the decimal as a fraction over 1: −0.00131\dfrac{-0.0013}{1}

ii) Multiply top and bottom by 10000 (4 zeros) because there are 4 numbers after the decimal point: −0.0013×100001   ×10000=−1310000\dfrac{-0.0013\colorTwo{\times10000}}{1~~~\colorTwo{\times10000}}=\dfrac{-13}{10000}

iii) −13-13 and 1000010000 don't share any common factors other than 1, so there's nothing to reduce.

When there's one negative sign in a fraction, we usually write it in front like this −1310000\boxed{-\dfrac{13}{10000}}.

PAGE BREAK
e) 00

01 or 02 or 0any non-zero integer\displaystyle \frac{0}{1}\text{ or } \frac{0}{2} \text{ or } \frac{0}{\text{any non-zero integer}}

Practice: Rewriting Decimals as Fractions

Rewrite the following decimals as fractions

a) 1.251.25

b) −0.160-0.160

c) −0.0005-0.0005

Enter your final answer as an improper fraction, make sure to simplify your answer.

Practice: Converting between Fractions, Decimals, and Percentages

Fill in the following table with the missing fraction, decimal, or percentage.
Fraction (simplified form, leave as improper fraction if needed))DecimalPercentage (include the % sign)
2/5
0.056
-13.55%
128%
-0.085