Numbers come in all shapes, sizes, and forms, such as fractions, decimals, and percentages. When a TASC Math question asks you to compare numbers or put a set of numbers in a certain order, it's easiest to do when they're all in the same form.
  • Converting fractions to decimals. To convert a fraction to a decimal, divide the numerator by the denominator. The quotient could result in a terminating, repeating, or non-terminating, non-repeating decimal.

    To represent repeating decimals, put a bar over the digits that repeat.

    TASC_2601

  • Converting decimals to fractions. If the decimal is terminating, meaning it ends, you put the given digits over a power of 10. If there are two digits, you put them over 102 and then simplify if possible. Check out this example:

    TASC_2602

    You can always check your work by dividing numerator by denominator to make sure you get the same decimal you started with. Here's another conversion example, this one with three digits:

    TASC_2603

    If the decimal is repeating, put the given repeating digits over 9s (depends on the number of digits that repeat). If there's one digit that repeats, then it goes over one 9; if there are two digits that repeat, they go over two 9s, so 99. Then simplify if possible. For example:

    TASC_2604

    Here's another example:

    TASC_2605

  • Converting percentages to decimals. To convert a percentage to a decimal, you must consider how you got that percentage in the first place. Percentage literally means per 100, so to go from a percent to a decimal, you move the decimal two places to the left. Mathematically this means you're dividing by 100. Take at look at these examples:

    TASC_2606

Practice questions

  1. Which of the following is listed in ascending order?

    TASC_2607

  2. Which of the following is in descending order?

    TASC_2608

Answers and explanations

  1. The correct answer is Choice (A).

    Comparing numbers in different forms can be difficult, so you want to rewrite them all into the same form (usually decimals is the easiest).

    TASC_2609

    .6 is already a decimal,

    TASC_2610

    and 350% = 3.5. Now that they're all in decimal form, you need to remember what ascending means: smallest to largest. This means the order should be

    TASC_2611

    Substituting back in the original values, you get:

    TASC_2612

    which is Choice (A).

  2. The correct answer is Choice (D).

    First rewrite each of the numbers into the same form (decimal form is probably the easiest).

    TASC_2613

    Now you can order them in descending order, which means from largest to smallest: 2.64, .7, .05, .03 and then substitute your original numbers back in:

    TASC_2614

    thus Choice (D) is correct.

About This Article

This article is from the book:

About the book authors:

Stuart Donnelly, PhD, earned his doctorate in mathematics from Oxford University at the age of 25. Since then, he has established successful tutoring services in both Hong Kong and the United States and is considered by leading educators to be one of the most experienced and qualified private tutors in the country. Nicole Hersey, PhD, is a lecturer at the University of Rhode Island, with a dual appointment to the School of Education and the Department of Mathematics. Ron Olson, MA, is an NBCT-certified teacher in Social Studies who teaches AP Government, Civics, and Contemporary World Problems at Clover Park High School in Lakewood, WA. In addition to his 35 years of teaching experience, he works as an AP US History workshop consultant for The College Board and has been the advisor for National Honor Society at his high school. Shannon Reed, MA, MFA, is a visiting lecturer at the University of Pittsburgh, where she teaches composition, creative writing, and business writing.

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