To convert the distance between London and New York, which is 5,567,000 meters, into standard form, follow these steps:
1. Identify a number between 1 and 10 by placing the decimal point after the first non-zero digit. For the given number 5,567,000, the first non-zero digit is '5'. Placing the decimal point here, we get 5.567000.
2. Count the number of places the decimal point has moved from its original position to the new position. Initially, the decimal point is at the end of the number (5,567,000.0). Moving it to after the first digit '5' involves shifting it 6 places to the left.
3. Express the movement of the decimal point as a power of 10. Since the decimal point moved 6 places to the left, the power of 10 will be positive 6.
Therefore, the distance in standard form is:
[tex]\[ 5.567 \times 10^{6} \][/tex]
Finally, rounding 5.567 to one decimal place to match the significant figures often used in scientific notation, we get:
[tex]\[ 5.6 \times 10^{6} \][/tex]
So, the distance between London and New York in standard form is:
[tex]\[ 5.6 \times 10^{6} \][/tex] meters.
