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Questions and Answers
What is the result of $2 \times 100.5$?
What is the result of $2 \times 100.5$?
The number 0.000045 can be written as $4.5 \times 10^{-5}$.
The number 0.000045 can be written as $4.5 \times 10^{-5}$.
True
Convert 900,000 to standard form.
Convert 900,000 to standard form.
9 × 10^5
The ordinary form of $3.1 \times 10^2$ is _____ .
The ordinary form of $3.1 \times 10^2$ is _____ .
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Match the following numbers with their standard form:
Match the following numbers with their standard form:
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What denotes a number in standard form?
What denotes a number in standard form?
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A number in standard form can have a negative exponent only if it represents a large number.
A number in standard form can have a negative exponent only if it represents a large number.
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Write 0.000005 in standard form.
Write 0.000005 in standard form.
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In standard form, if n is positive, it indicates a __________ number.
In standard form, if n is positive, it indicates a __________ number.
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Which of the following is NOT in standard form?
Which of the following is NOT in standard form?
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If you have the standard form 7.1 × 10², what is the ordinary number?
If you have the standard form 7.1 × 10², what is the ordinary number?
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When the decimal point moves to the left in a number, n is __________.
When the decimal point moves to the left in a number, n is __________.
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Study Notes
Writing Numbers in Standard Form
- Standard form expresses very large or very small numbers concisely.
- The form is a x 10n, where:
- 'a' is a number greater than or equal to 1 and less than 10.
- 'n' is an integer (whole number).
- A positive 'n' indicates a large number, where the decimal point is moved to the right 'n' places.
- A negative 'n' indicates a small number, where the decimal point is moved to the left 'n' places.
Converting to Standard Form
- Identify the value for 'a' by placing the decimal point in the original number so that 'a' is between 1 and 10.
- Count the number of places the decimal point moved.
- This count is the value of 'n'.
- If the decimal point moved to the right, 'n' is positive.
- If the decimal point moved to the left, 'n' is negative.
Converting from Standard Form
- Determine the sign and value of 'n'.
- Move the decimal point in 'a' to the right if 'n' is positive.
- Move the decimal point in 'a' to the left if 'n' is negative.
- Add zeros as placeholders as needed.
Examples
- 39,000 = 3.9 x 104
- 0.0000467 = 4.67 x 10-5
- 3.2 x 102 = 320
- 1.8 x 10-3 = 0.0018
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Description
This quiz focuses on expressing numbers in standard form, a method for representing very large or very small numbers concisely. It covers the structure of standard form, how to convert original numbers to this format, and vice versa. Test your understanding of identifying values and counting decimal point movements.
