5. Kendra finds the dimensions of a sticky note. She uses a meter stick to determine that the dimensions are 1.25 * 10 ^ 4 - 8 meters wide
1 point
by 2.5 * 10 ^ 5 - 6 meters long. Use scientific notation to write the dimensions in millimeters.
1.25 * 10 ^ 4 - 10 by 2.5 * 10 ^ 4 - 8 millimeters
1.25 * 10 ^ x - 11 by 2.5 * 10 ^ 2 - 9 millimeters
1.25 * 10 deg - 6 by 2.5 * 10 ^ 5 - 4 millimeters
1.25 * 10 ^ 2 - 5 by 2.5 * 10 ^ n - 3 millimeters
The correct answer is:
1.25 * 10^4 - 8 meters is equal to 1.25 * 10^7 - 3 millimeters.
2.5 * 10^5 - 6 meters is equal to 2.5 * 10^8 - 3 millimeters.
So the dimensions in millimeters are 1.25 * 10^7 - 3 by 2.5 * 10^8 - 3 millimeters.
7. Subtract 4.66 * 10 ^ s - 5 - 7.34 * 10 ^ x - 7 *
- 4.5866 * 10 ^ 0.5
2.68 * 10 ^ 4 * 2
4.5866 * 10 ^ - 5
- 2/68 * 10 ^ 2
To subtract these numbers in scientific notation, we need to make sure the exponents are the same. Let's simplify each term separately:
4.66 * 10^s - 5 - 7.34 * 10^x - 7 - 4.5866 * 10^0.5 - 2.68 * 10^4 * 2 - 4.5866 * 10^-5 - 2/68 * 10^2
First, let's deal with the exponents:
1. 10^s - 5 has an exponent of -5.
2. 10^x - 7 has an exponent of -7.
3. 10^0.5 can also be written as the square root of 10, which is approximately 3.1623, so it has an exponent of 0.5.
4. 2.68 * 10^4 times 2 is 5.36 * 10^4, which has an exponent of 4.
5. 10^-5 is the same as 1 divided by 10^5, which has an exponent of -5.
6. 2/68 * 10^2 is the same as 1/34 * 10^2, which simplifies to 0.02941 * 10^2, or 2.941 * 10^0, which has an exponent of 0.
Now let's subtract:
4.66 * 10^-5 - 7.34 * 10^-7 - 4.5866 * 10^0.5 - 5.36 * 10^4 - 4.5866 * 10^-5 - 2.941 * 10^0
Since we have the same exponents, we can simply subtract the coefficients:
4.66 - 7.34 - 4.5866 - 5.36 - 4.5866 - 2.941
Adding everything together, the result is approximately -19.399.
Therefore, the subtracted expression simplifies to:
-19.399 * 10^0
To convert the given dimensions in meters to millimeters using scientific notation, follow these steps:
1. Convert 1.25 * 10^4 - 8 meters to millimeters:
- Note that 1 meter is equal to 1000 millimeters.
- Multiply 1.25 by 1000 to convert it to millimeters: 1.25 * 1000 = 1250.
- The exponent remains the same, so it becomes 10^4 - 8.
- Therefore, the width in millimeters is 1.25 * 10^4 - 8 millimeters.
2. Convert 2.5 * 10^5 - 6 meters to millimeters:
- Multiply 2.5 by 1000 to convert it to millimeters: 2.5 * 1000 = 2500.
- The exponent remains the same, so it becomes 10^5 - 6.
- Therefore, the length in millimeters is 2.5 * 10^5 - 6 millimeters.
Putting it all together, the dimensions of the sticky note in millimeters using scientific notation are:
Width: 1.25 * 10^4 - 8 millimeters
Length: 2.5 * 10^5 - 6 millimeters