To express Earth's diameter of 12,760,000 meters in scientific notation, we need to follow a step-by-step approach to convert the given number into a format of [tex]\( a \times 10^b \)[/tex], where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( b \)[/tex] is an integer.
Here are the steps:
1. Identify the non-zero digits in the number:
The given number is 12,760,000. The non-zero digits are 1, 2, 7, and 6.
2. Place the decimal point such that the number is between 1 and 10:
We move the decimal point 7 places to the left to get 1.276. This is because we have the number 12,760,000 and want to express it in a form where the number is between 1 and 10.
3. Count the number of places the decimal moved:
Since we moved the decimal 7 places to the left, we multiply by [tex]\( 10^7 \)[/tex].
4. Compose the final scientific notation:
Combining the mantissa 1.276 with the power of ten, we get [tex]\( 1.276 \times 10^7 \)[/tex].
Thus, Earth's diameter of 12,760,000 meters written in scientific notation is:
[tex]\[ 1.276 \times 10^7 \][/tex]
Among the given choices:
- [tex]\( 1.276 \times 10^{-7} \)[/tex] is incorrect as the exponent is negative.
- [tex]\( 12.76 \times 10^{-6} \)[/tex] is incorrect due to the wrong exponent.
- [tex]\( 1.276 \times 10^7 \)[/tex] is correct.
- [tex]\( 0.1276 \times 10^8 \)[/tex] is incorrect because the mantissa must be between 1 and 10.
Hence, the correct answer is:
[tex]\[ \boxed{1.276 \times 10^7} \][/tex]
