Write the speed of light 299,792,458 m/s in scientific notation using 3 significant figures. b) Write the speed of light 299,792,458 m/s in scientific notation using 4 significant figures. Need asap and show work please and thank you
The Correct Answer and Explanation is:
) Speed of light in scientific notation (3 significant figures)
The speed of light is 299,792,458 m/s. To express this in scientific notation with 3 significant figures, we follow these steps:
- Identify the first three significant digits: The speed of light is 299,792,458, and the first three significant digits are 2, 9, and 9.
- Convert to a form where there is one non-zero digit to the left of the decimal point: To do this, we can write 299,792,458 as 2.99×1082.99 \times 10^82.99×108.
- Adjust for 3 significant figures: The number 2.99 includes three significant figures, so we do not need to round further.
Thus, the speed of light in scientific notation using 3 significant figures is:2.99×108 m/s\boxed{2.99 \times 10^8 \, \text{m/s}}2.99×108m/s
b) Speed of light in scientific notation (4 significant figures)
Now, we need to write the speed of light in scientific notation using 4 significant figures. Let’s go through the same process:
- Identify the first four significant digits: The speed of light is 299,792,458, and the first four significant digits are 2, 9, 9, and 7.
- Convert to scientific notation: We need to express this number so that only one non-zero digit is to the left of the decimal point. We can write 299,792,458 as 2.997×1082.997 \times 10^82.997×108.
- Adjust for 4 significant figures: The number 2.997 includes four significant figures, so no further rounding is needed.
Thus, the speed of light in scientific notation using 4 significant figures is:2.997×108 m/s\boxed{2.997 \times 10^8 \, \text{m/s}}2.997×108m/s
Explanation:
Scientific notation is a way to express large or small numbers as a product of a coefficient (a number between 1 and 10) and a power of 10. In this case, the number 299,792,458 m/s299,792,458 \, \text{m/s}299,792,458m/s is quite large, so using scientific notation makes it easier to work with.
- The exponent in the scientific notation (the power of 10) tells you how many places to move the decimal point.
- The significant figures refer to the number of meaningful digits that are considered reliable for measurement. The coefficient should be rounded to the desired number of significant figures to reflect the accuracy of the original number.
