Question
Writing Express 0.0000268 in scientific notation. Use pencil and paper. How can negative powers of 10 make small numbers easier to write and compare?
Question content area bottom
Part 1
0.0000268equals
enter your response here
(Use scientific notation. Use the multiplication symbol in the math palette as needed.)
Question content area bottom
Part 1
0.0000268equals
enter your response here
(Use scientific notation. Use the multiplication symbol in the math palette as needed.)
Answers
GPT-4o mini
To express the number 0.0000268 in scientific notation, follow these steps:
1. Move the decimal point to the right until you have a number between 1 and 10. In this case, we move the decimal point 5 places to the right, which gives us 2.68.
2. Count how many places you moved the decimal. Since we moved it 5 places to the right, the power of 10 will be negative.
3. Write the number in the format \( a \times 10^n \), where \( a \) is the number you obtained and \( n \) is the power of 10.
So, we can express 0.0000268 as:
\[
2.68 \times 10^{-5}
\]
### Part 2: Understanding Negative Powers of 10
Negative powers of 10 are particularly useful for representing very small numbers. Here’s how they help:
- **Simplicity**: Instead of writing multiple zeros, using negative powers allows us to write small numbers concisely. For example, instead of writing 0.0000001, we can simply write \( 1 \times 10^{-7} \).
- **Comparison**: It makes it easier to compare small numbers. For instance, if you have \( 3.2 \times 10^{-5} \) and \( 2.5 \times 10^{-4} \), you can easily see that \( 2.5 \times 10^{-4} \) is larger because the exponent (or power) of 10 is greater, indicating it is further to the right on the number line.
In summary, negative powers of 10 simplify writing and comparing very small quantities in a consistent and straightforward manner.
1. Move the decimal point to the right until you have a number between 1 and 10. In this case, we move the decimal point 5 places to the right, which gives us 2.68.
2. Count how many places you moved the decimal. Since we moved it 5 places to the right, the power of 10 will be negative.
3. Write the number in the format \( a \times 10^n \), where \( a \) is the number you obtained and \( n \) is the power of 10.
So, we can express 0.0000268 as:
\[
2.68 \times 10^{-5}
\]
### Part 2: Understanding Negative Powers of 10
Negative powers of 10 are particularly useful for representing very small numbers. Here’s how they help:
- **Simplicity**: Instead of writing multiple zeros, using negative powers allows us to write small numbers concisely. For example, instead of writing 0.0000001, we can simply write \( 1 \times 10^{-7} \).
- **Comparison**: It makes it easier to compare small numbers. For instance, if you have \( 3.2 \times 10^{-5} \) and \( 2.5 \times 10^{-4} \), you can easily see that \( 2.5 \times 10^{-4} \) is larger because the exponent (or power) of 10 is greater, indicating it is further to the right on the number line.
In summary, negative powers of 10 simplify writing and comparing very small quantities in a consistent and straightforward manner.