Scientific Notation Quiz
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Questions and Answers

What are the steps to write a number in scientific notation?

  • Locate the original decimal's position, determine if the number is less than 1, move the decimal to obtain a number between 1 and 10, multiply by the appropriate power of 10
  • Move the decimal to obtain a number between 1 and 10, determine if the number is greater than or equal to 1 but less than 10, multiply by the appropriate power of 10, track the number of decimal places moved
  • Move the decimal to obtain a number between 1 and 10, determine if the number is less than 1, multiply by the appropriate power of 10, track the number of decimal places moved
  • Locate the original decimal's position, determine if the number is greater than or equal to 1 but less than 10, move the decimal to obtain a number between 1 and 10, multiply by the appropriate power of 10 (correct)

    • How do you convert a number to scientific notation if it is less than 1?

  • Move the decimal point to the right, keeping track of the number of decimal places moved
  • Divide by a power of 10 without moving the decimal point
  • Move the decimal point to the left, keeping track of the number of decimal places moved (correct)
  • Multiply by a power of 10 without moving the decimal point

    • In scientific notation, what should you do when multiplying two numbers with different exponents?

  • Multiply both exponents together
  • Keep both bases the same and add their exponents (correct)
  • Divide one exponent by the other
  • Subtract one exponent from the other

    • When dividing two numbers in scientific notation, what should you do with their exponents?

    <p>Subtract one exponent from the other</p> Signup and view all the answers

    Which step is necessary to determine if a number should be written in scientific notation?

    <p>See if it is greater than or equal to 1 but less than 10</p> Signup and view all the answers

    Match the following pairs.

    <h1>Negative Exponents = means very small number Positive Exponents = A special way of writing very large or very small numbers Scientific Notations = means very big number</h1> Signup and view all the answers

    Express in Scientific Notation.

    1. 138,000,000,000,000
    2. 0.00000000816
    3. 19,000,000,000
    4. 0.00000954

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    Study Notes

    Writing in Scientific Notation

    Scientific notation simplifies the representation of very large or small numbers, making them easier to compare, read, and calculate. To write a number in scientific notation, follow these steps:

    1. Locate the original decimal's position.
    2. Determine if the number is greater than or equal to 1, but less than 10.
    3. Move the decimal to obtain a number between 1 and 10, keeping track of the number of decimal places moved.
    4. Multiply the decimal number by the appropriate power of 10 obtained by counting the decimal places moved.

    Converting to Scientific Notation

    To convert a number to scientific notation, follow these rules:

    • If the number is greater than or equal to 1, but less than 10, no change is required.
    • If the number is less than 1, move the decimal to the right, making sure to keep track of the number of decimal places moved.
    • Multiply the new decimal number by the appropriate power of 10 obtained by counting the decimal places moved.

    Operations with Scientific Notation

    Scientific notation follows the same rules for addition, subtraction, multiplication, and division as any other number system. To perform operations:

    • Treat the decimal parts as usual.
    • For the exponents, follow these general rules:
      • For addition and subtraction of exponents, keep the base the same and add or subtract the exponents.
      • For multiplication, add the exponents.
      • For division, subtract the exponent of the divisor from the exponent of the dividend.

    Comparing Numbers in Scientific Notation

    Comparing numbers in scientific notation is simple because the exponents indicate the relative magnitude of the numbers. A larger exponent indicates a larger number, while a smaller exponent indicates a smaller number.

    Example:

    • To compare (1.2 \times 10^5) and (3.45 \times 10^6), you would notice that (10^6) is more than (10^5), meaning (3.45 \times 10^6) is larger than (1.2 \times 10^5).

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    Description

    Test your knowledge on writing, converting, performing operations, and comparing numbers in scientific notation. Understand the steps involved in converting, multiplying, and dividing numbers written in scientific notation. Learn how to compare numbers by analyzing their exponents.

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