Convert between Percent, Fractions and Decimals

Convert between Percent, Fractions and Decimals exercise

• Describe how to convert a decimal number or a fraction into a percent.

  Hints

  As you know, $\frac12$ and $0.5$ are the same.

  You probably know how to write this as a percent.

  The picture on the right shows how to convert the fraction $\frac 38$ into its decimal form.

  Solution

  If you need to compare numbers, it's helpful if all the numbers appear in the same form.

  Compare Like Forms

  • fractions $~\leftrightarrow~$ fractions
  • decimals $~\leftrightarrow~$ decimals
  • percents $~\leftrightarrow~$ percents

  If the numbers are given to you in different forms, you will need to convert them.

  To convert a decimal number into percent:

  1. multiply the decimal by $100$
  2. put a percent sign behind the number
  3. $0.125\xrightarrow{\times 100}12.5\%$

  To convert a fraction into percent:

  1. calculate the decimal form of the fraction by dividing the numerator by the denominator
  2. use the steps you learned to change a decimal into a percent
  3. that means: $\frac38=0.375\xrightarrow{\times 100}37.5\%$

• Help Toni convert the customer's strange order.

  Hints

  Did you know you can also reducing fractions using factors? To simplify a fraction to its lowest terms, divide the numerator as well as the denominator by a common factor. Repeat until there are no more common factors.

  Solution

  To convert a percent into a fraction, we write the percent as a fraction divided by $100$ and then simplify the fraction by dividing the numerator as well as the denominator by the Greatest Common Factor.

  • $50~\%=\frac{50}{100}=\frac12$

  To convert a percent into a decimal, either you transform it to a fraction first and then divide the numerator by the denominator, or you take away the percent sign and divide the resulting number by 100.

  • $50~\%=\frac{50}{100}=50 \div 100= 0.5$
  • $50~\%= 50 \div 100= 0.5$

  To convert a decimal to a fraction, count the number of places in the numerator you need to move the decimal point to get a whole number, and then add the same number of zeros to the right of $1$ in the denominator. Afterwards, simplify the fraction by dividing the numerator as well as the denominator by the Greatest Common Factor.

  • $0.125=\frac{125}{1000}=\frac18$

  To convert a decimal to a percent, multiply it by $100$ and add a percent sign to the end.

  • $0.125=0.125 \times 100 \%=12.5\%$

  To convert a fraction to a decimal, you divide the numerator by the denominator.

  • $\frac {3}{8}=3 \div 8= 0.375$.

  To convert a fraction to a percent, you must first convert the number to a decimal by dividing the numerator by the denominator. Then, multiply it by $100$ and add a percent sign at the end.

  • $\frac {3}{8}=3 \div 8= 0.375=0.375 \times 100 \%=37.5\%$

• Convert each number from its current form to percent form.

  Hints

  You can simplify a fraction by dividing the numerator and the denominator by the GCF: $\frac{10}{20}=\frac{10\div 10}{20\div 10}=\frac12$.

  Solution

  There are $4$ percent values given. We can convert percent into a fraction by writing $8\%$ as $\frac8{100}$. This fraction can be simplified to $\frac2{25}$ by dividing the numerator and denominator by $4$. You can convert percent into decimal form by dividing the percent by $100$. In our example above, we have $8\%=0.08$.

  1. $75~\%=0.75~\longleftrightarrow~75\%=\frac{75}{100}=\frac34$
  2. $25~\%=0.25~\longleftrightarrow~25\%=\frac{25}{100}=\frac14$
  3. $40~\%=0.40~\longleftrightarrow~40\%=\frac{40}{100}=\frac25$
  4. $55~\%=0.55~\longleftrightarrow~55\%=\frac{55}{100}=\frac{11}{20}$

• Change fractions or decimals into percent form.

  Hints

  All the percentages should add up to $100\%$.

  To convert a decimal number into percent, multiply by $100$, and then write a percent sign at the end of the resulting number.

  To transform a fraction to percent:

  • Convert the fraction into a decimal, and then multiply by $100$
  • or scale raise terms so that the denominator is equal to $100$ as shown in the picture

  Solution

  Toni's guest orders a pizza with the following ingredients:

  Olives: $\frac15=\frac{1\times 20}{5\times 20}=\frac{20}{100}=20\%$

  Onions: $0.30\xrightarrow{\times 100}30\%$

  Pepperoni: $\frac3{20}=0.15\xrightarrow{\times 100}15\%$

  Chili Peppers: $0.35\xrightarrow{\times 100}35\%$

• Explain the meaning of percent.

  Hints

  $100¢$ are in $\$1$.

  Here we have a customary percent sign.

  $1\%$ of $\$1$ is $1¢$.

  Solution

  We can remember the meaning of percent for example by conversion from cent to dollar:

  • $100¢$ are in $\$1$
  • $\frac1{100}$ of $\$1$ is $1¢$

  So percent means per hundred.

  If Toni divides his pizza in $100$ even slices, we can say that one slice equals $1\%$ of the pizza.

• Prepare your own pizza.

  Hints

  Each value is given as a fraction. If possible, simplify each fraction.

  The pizza is divided in $10$ slices. Write each fraction with the denominator $10$. The number of slices is written in the numerator.

  Solution

  Since the pizza is divided into $10$ slices, we should try to convert each fraction so that we get $10$ in the denominator. Then, we can easily compare the fractions to each other.

  • $\frac3{15}=\frac15=\frac2{10}$, or $2$ slices with pepperoni
  • $\frac{16}{40}=\frac{16\div 4}{40\div 4}=\frac4{10}$, or $4$ slices with cheese
  • $\frac{15}{50}=\frac{15\div 5}{50\div 5}=\frac3{10}$, or $3$ slices with mushrooms
  • $\frac{3}{30}=\frac{3\div 3}{30\div 3}=\frac1{10}$, or $1$ slice with bacon