5.18: Fundamentals 17 - Conversion

Quantway Core · LibreTexts

0%

Contents

    Text

    Size
    100%
    Theme
    Typeface
    Line length
    Spacing

    From LibreTexts, under CC BY-NC 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    LEARNING GOALS

    By the end of this lesson, you should understand

    • a percent is out of a hundred.
    • 100% represents the entire quantity.
    • percentages are an important part of our everyday lives.
    • percentages are handy ways of writing fractions.
    • percentages can be compared more easily than fractions.

    By the end of this lesson, you should be able to

    • recognize and convey the meaning of a percent.
    • convert a percent to a fraction.
    • convert a percent to a decimal.
    • compare percentages in different ways.

    FUNDAMENTALS OF THE LESSON

    The word percent means “per hundred, or, “out of a hundred”, and is represented by the % symbol. Since percent means out of 100, we can think of percents as special kinds of fractions that have a denominator of 100. So, 1% means 1 out of 100, or one hundredth of a whole. One hundred percent (100%) represents the entire quantity, 100 out of 100, or 1 whole.

    Let’s take a look at 25%. This means 25 out of 100 and can be represented as the fractions: begin fraction 25 over 100 end fraction or begin fraction 1 over 4 end fraction. Both begin fraction 25 over 100 end fraction and begin fraction 1 over 4 end fraction can be represented as the decimal number 0.25. Percents, fractions, and decimals are all related. Often, we have to convert from one form to another to correctly understand a situation and solve a problem.

    Fraction → Percent

    One way to convert a fraction to a percentage is to find the equivalent fraction out of 100. Then, the numerator gives the amount of the percent. For example:

    begin fraction 1 over 4 end fraction equals begin fraction 1 times25 over 4 times25 end fraction equals begin fraction 25 over 100 end fraction equals 25 percent sign

    Note that begin fraction 1 over 4 end fraction and begin fraction 25 over 100 end fraction are equivalent fractions. They equal the same number.

    Fraction → Decimal → Percent

    Another way to convert a fraction to a percent is to convert the fraction to a decimal, and then convert the decimal to a percent.

    When a fraction has a denominator that is a power of 10 (for example: 10, 100, 1000), you can convert the fraction to a decimal by using place value. You can then convert the decimal to a percent by multiplying the decimal by 100 (or move the decimal point two places to the right). Then, attach a % symbol to the result. For example:

    begin fraction 7 over 10 end fraction open bracket r e a d s a s 7 t e n t h s close bracket equals 0 .70 equals 70 percent sign

    begin fraction 27 over 1000 end fraction open bracket r e a d s a s 27 t h o u s a n d t h s close bracket equals 0 .027 equals 2 .7 percent sign

    When a fraction has a denominator that is not a power of 10, convert the fraction to a decimal by dividing the numerator by the denominator. You can then convert the decimal to a percent by multiplying the decimal by 100 (or move the decimal point two places to the right). Then, attach a % symbol to the result. For example:

    begin fraction 1 over 4 end fractionor (1 divided by 4) = 0.25 = 25%

    begin fraction 5 over 8 end fraction or (5 divided by 8) = 0.625 = 6.25%

    TRY THESE

    1. Complete the chart below. In your own words, write how to convert decimals, fractions, and percentages in different ways.

    A. How do you change a percent into a decimal?

    B. How do you change a decimal into a percent?

    C. How do you change a decimal into a fraction?

    D. How do you change a fraction into a decimal?

    E. How do you change a percent into a fraction?

    F. How do you change a fraction into a percent?
    1. Fill in the chart below by converting to percents, decimals, and fractions.

    Percent

    Decimal

    Fraction

    12%

    0.12

    A

    35.5%

    0.355

    B

    C

    1.43

    1\(\dfrac{43}{100}\)

    0.2%

    0.002

    D

    12.5%

    E

    \(\dfrac{1}{8}\)

    345%

    3.45

    F

    Organizing Information

    The number of mobile phone users in the world is growing rapidly and by 2019, it was estimated that there would be over 5 billion users. A small survey was done to gather information about what type of mobile phones are currently being used by mobile phone users. The table in the next question shows the responses of 40 mobile phone users. The responses will help to provide information to cell phone carrier companies about certain brands of phones being used by the consumers.

    Types of smartphone owned

    I

    A

    I

    A

    W

    I

    A

    A

    I

    W

    W

    A

    I

    A

    I

    F

    W

    I

    A

    F

    I

    A

    F

    I

    I

    W

    I

    A

    I

    A

    A

    I

    W

    F

    W

    F

    I

    W

    A

    I
           

    I = iPhone

    A = Android

    W = Windows phone

    F = Amazon Fire

    3. Use the data in the table above to answer the following questions.

    A. What percentage of phone users owned an iPhone?

    B. What percentage of phone users owned an Android?

    C. What percentage of phone users owned an iPhone or an Amazon Fire phone?

    D. What percentage of phone users owned a Windows phone?

    NEXT STEPS

    Understanding and Using Percents, Fractions, and Decimals

    Almost everyday we encounter a percent. For example, when we shop at a store and see a 30% off sale. Or, when listening to a basketball game and hearing about a team making 85% of their free-throw shots. Percents are used all the time in money calculations, like when credit card companies advertise that their credit card pays 2% cash back on purchases, or when people in a state are told that 7.65% of their paycheck goes towards federal and state taxes.

    Read the following situations carefully. Use the given information to solve the problems.

    4. Taylor put one dollar in the vending machine for a $0.85 candy bar and did not get change back. What percent of Taylor’s dollar did she lose?

    5. Sam bought a new car for $17,500. A 5.5% down payment was required. How much did Sam have to pay for the down payment? Hint: How can we use 5.5% to answer this question? Would it help to write the percentage in a different form?

    6. Steph made 27 out of 45 three point shots in a basketball game. What percentage of 3-point shots did Steph make?

    7. Thirty shirts have to be sold for a T-shirt company to make its daily profit projection. Six shirts have been sold so far. What percentage of shirts are left to sell?

    FURTHER APPLICATIONS

    8. A policy at a restaurant states that servers must “tip-out” a certain dollar amount of the tips they earn to the host and the kitchen staff. From the tips they receive, the server must give 5% of the food bill to the kitchen staff and 1% of the tip to the host. If the total food bill was $30, and a $6 tip was left, what was the “tip-out” amount given to the kitchen staff and to the host? Explain your work.

    9. Pam scored 92% on her last math test. If she answered 23 questions correctly, how many problems were on the test? (Note: assume each problem was worth the same amount, 1 point). Explain your work.

    Questions: Conversions—Percents, Decimals, and Fractions

    1. Express the decimal 0.25 as a percentage.
    2. Express the decimal 0.3333 as a percentage.
    3. Express the decimal 3.53 as a percentage.
    4. Express the decimal 0.0035 as a percentage.
    5. Express the decimal 5 as a percentage.
    6. Express the percent 70% as a decimal.
    7. Express the percent 51% as a decimal.
    8. Express the percent 781% as a decimal.
    9. Express the percent 0.55% as a decimal.
    10. Express the percent 60% as a fraction in lowest terms.
    11. Express the percent 125% as a fraction in lowest terms.
    12. Express the fraction \(\dfrac{1}{3}\) as a percentage. Round to the nearest tenth of a percent, if needed.
    13. Express the fraction \(\dfrac{12}{8}\) as a percentage. Round to the nearest tenth of a percent, if needed.
    14. Fill in the blank to find another expression for 2%. ______ for every 100
    15. Fill in the blank to find another expression for 3%. ______ for every 50
    16. Fill in the blank to find another expression for 8%. 1 for every _____
    17. Fill in the blank to find another expression for 4%. 0.5 for every _____
    18. Which represents the greater percent: begin fraction 325 over 500 end fraction o r begin fraction 600 over 1000 end fraction
    19. Mary has 60 candy bars to sell. She has sold 75% of the candy bars so far. How many candy bars has Mary sold? Round to the nearest bar.
    20. Barry sold 180 newspapers out of 200. Paul sold 85% of his 260 newspapers.

    A. Who sold the most newspapers?

    B. Who sold the greatest percentage of newspapers?

    This page titled 5.18: Fundamentals 17 - Conversion was last modified on Wed, 15 May 2024 07:37:22 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Carnegie Math Pathways (WestEd) .