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The order of magnitude of a number expressed in scientific notation is
- a)number of decimal places
- b)number of digit before decimal
- c)all digits in the number
- d)power of ten
Correct answer is 'D'. Can you explain this answer?
Verified Answer
The order of magnitude of a number expressed in scientific notation is...
- To convert a regular number to scientific notation, we first rewrite it as a decimal, then multiply it by a power of 10.
- There is an infinite number of ways to do this for any given number, but we always prefer the one that has only a single digit in front of the decimal point.
Most Upvoted Answer
The order of magnitude of a number expressed in scientific notation is...
- Scientific notation is the method of writing, or of displaying real numbers as a decimal number between 1 and 10 followed by an integer power of 10.
- To convert a regular number to scientific notation, we first rewrite it as a decimal, then multiply it by a power of 10.
- There is an infinite number of ways to do this for any given number, but we always prefer the one that has only a single digit in front of the decimal point.
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The order of magnitude of a number expressed in scientific notation is...
Understanding Order of Magnitude in Scientific Notation
The order of magnitude of a number is a way to express its size in relation to powers of ten. When a number is expressed in scientific notation, it takes the form of:
- a × 10^n
Where:
- "a" is a coefficient (a number typically between 1 and 10)
- "n" is the exponent (the power of ten)
Key Explanation
- The exponent "n" indicates the order of magnitude of the number.
- This means that the order of magnitude gives a clear idea of how large or small a number is by referring to the power of ten it is associated with.
Why Option D is Correct
- Power of Ten: The order of magnitude is defined by the exponent in the scientific notation. For example, in the number 3.2 × 10^5, the "5" is the order of magnitude, indicating that the number is on the order of hundreds of thousands.
- Comparison: Different numbers can be compared easily using their orders of magnitude. For instance, 4.5 × 10^3 and 6.1 × 10^5 can be compared quickly by looking at the exponents (3 and 5), revealing that the latter is significantly larger.
Conclusion
Understanding the order of magnitude helps in estimating the scale of large or small numbers effectively. Thus, the correct answer to the question of the order of magnitude of a number expressed in scientific notation is indeed option D: Power of ten.
The order of magnitude of a number is a way to express its size in relation to powers of ten. When a number is expressed in scientific notation, it takes the form of:
- a × 10^n
Where:
- "a" is a coefficient (a number typically between 1 and 10)
- "n" is the exponent (the power of ten)
Key Explanation
- The exponent "n" indicates the order of magnitude of the number.
- This means that the order of magnitude gives a clear idea of how large or small a number is by referring to the power of ten it is associated with.
Why Option D is Correct
- Power of Ten: The order of magnitude is defined by the exponent in the scientific notation. For example, in the number 3.2 × 10^5, the "5" is the order of magnitude, indicating that the number is on the order of hundreds of thousands.
- Comparison: Different numbers can be compared easily using their orders of magnitude. For instance, 4.5 × 10^3 and 6.1 × 10^5 can be compared quickly by looking at the exponents (3 and 5), revealing that the latter is significantly larger.
Conclusion
Understanding the order of magnitude helps in estimating the scale of large or small numbers effectively. Thus, the correct answer to the question of the order of magnitude of a number expressed in scientific notation is indeed option D: Power of ten.
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