Roughly, it takes light less than 0.000000003 of a second to travel a one-meter distance. Express this number in the form of a × 10^n where 1 < a < 10 and is a one-digit number.
To express the number in the desired form, we need to move the decimal point to a position between 1 and 10. Starting with the given number, 0.000000003, we can express it as 3 × 10^(-9).
To express the number in the form of a × 10^n, we need to move the decimal point to the right until there is one digit to the left of it. In this case, we start with 0.000000003 and move the decimal point 10 places to the right:
0.000000003 -> 0.00000000003
Now, there is only one digit to the left of the decimal point, so we have 3 × 10^(-10). This number is in the desired form, with 3 being a one-digit number between 1 and 10, and -10 being the exponent.
To express the number in the form of a × 10^n, where 1 < a < 10 and a is a one-digit number, we need to convert the given time in seconds (0.000000003) to scientific notation.
1. Start by counting the number of decimal places until the first non-zero digit. In this case, we have 9 decimal places (0.000000003).
2. Move the decimal point 9 places to the right to obtain a number between 1 and 10. This gives us 3.0 in scientific notation (3.0 × 10^0).
3. Finally, since the decimal point was moved 9 places to the right, we need to adjust the exponent accordingly. In this case, the exponent will be -9, as the decimal point was moved to the right.
Therefore, the number 0.000000003 expressed in the form of a × 10^n is 3.0 × 10^-9.