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\ \times\ 10^n where 1\ < \ a\ < \ 10 and is a one-digit number.
To express the number in the form of a × 10^n, we need to determine the values of a and n.
Given that light takes less than 0.000000003 of a second to travel a one-meter distance, we can represent this as 0.000000003 seconds.
To convert this number into the desired form, we shift the decimal point to the right until we have a number between 1 and 10. For every shift to the right, we increase the exponent n by 1.
0.000000003 -> 3 × 0.000000001
Therefore, a = 3 and n = -9.
In the desired form, 0.000000003 seconds is written as 3 × 10^-9.
To express the number in the form of a × 10^n, we need to convert it to scientific notation.
The given number is less than 0.000000003 of a second, which can be written as 3 × 10^(-9) seconds.
Therefore, the number can be expressed as 3 × 10^(-9), where 3 is a one-digit number and 10^(-9) represents the power of 10.
To express a number in the form of a multiplied by 10 raised to the power of n, where 1 < a < 10 and a is a one-digit number, we need to count the number of decimal places the original number moves to the left.
Given that it takes light less than 0.000000003 of a second to travel a one-meter distance, we can rewrite this number as 3 × 10^(-9) seconds.
Explanation:
- The original number 0.000000003 has eight zeros after the decimal point.
- So, we can rewrite it as 3 × 10^(-9), where 3 is the one-digit number, and -9 indicates that it moves nine decimal places to the left.
Therefore, the number 0.000000003 can be expressed in the form of a × 10^n as 3 × 10^(-9).