Podcast
Questions and Answers
What is the product of $(3 x 10^4) imes (2 x 10^3)$ expressed in standard form?
What is the product of $(3 x 10^4) imes (2 x 10^3)$ expressed in standard form?
When dividing $(5 x 10^6) / (1 x 10^2)$, what will the result be in standard form?
When dividing $(5 x 10^6) / (1 x 10^2)$, what will the result be in standard form?
Which of the following results represents a number outside the acceptable range for standard form?
Which of the following results represents a number outside the acceptable range for standard form?
If the result of a multiplication is $20 x 10^5$, what is the correct adjustment to put this in standard form?
If the result of a multiplication is $20 x 10^5$, what is the correct adjustment to put this in standard form?
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What is the outcome when dividing $(9 x 10^7) / (3 x 10^5)$ in standard form?
What is the outcome when dividing $(9 x 10^7) / (3 x 10^5)$ in standard form?
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Study Notes
Multiplying Standard Form Numbers
- To multiply numbers in standard form, multiply the coefficients and add the indices of the powers of 10.
- Example: (2.5 x 103) x (4 x 102) = (2.5 x 4) x 103+2 = 10 x 105 = 1.0 x 106
- Ensure the final answer is also in standard form. This means the coefficient should be a number greater than or equal to 1 and less than 10. If the coefficient is not between 1 and 10 adjust the power of 10 to get the correct standard form.
- Example:
- If the result is 25 x 106 you adjust it to 2.5 x 107
- If the result is 0.75 x 10-3, you adjust it to 7.5 x 10-4
Dividing Standard Form Numbers
- To divide numbers in standard form, divide the coefficients and subtract the indices of the powers of 10.
- Example: (8 x 105) / (2 x 102) = (8 /2) x 105-2 = 4 x 103
- The same rules for formatting apply as with multiplication. Ensure the final answer is in standard form (coefficient between 1 and 10).
- Example:
- If you get 15 x 10-4, you adjust to 1.5 x 10-3
- If you get 0.5 x 106, you adjust it to 5.0 x 105
Key Considerations
- Accurate calculation of indices (exponents) is crucial.
- Pay close attention to the signs when adding and subtracting the indices in multiplication and division operations.
- Always convert the answer to standard form.
Scientific Notation and Standard Form
- Scientific notation and standard form are closely related ways of expressing very large or very small numbers.
- Scientific notation always follows the form: $a \times 10^n$ where $1 \le a < 10$ and n is an integer.
- Standard form is another way of expressing these numbers in the form $a.bc \times 10^n$ (where the digits represent the number and n signifies the power of 10).
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Description
This quiz focuses on multiplying and dividing numbers in standard form. You will learn how to properly apply the rules for handling coefficients and exponents, ensuring your final answers are formatted correctly as per the standards. Test your understanding of these concepts with practical examples.
