i have just started physics, can someone please show me step by step how to do this:

The radius of Earth is 6 370 000 m. Express this measurement in km in scientific notation with the correct number of significant digits.

thank you for your help

Hard to say.

If it had been written 6 370 001
I could give you a firm answer because that little one at the end tells me that there are 7 significant figures.
I would count from the right until I got to the 6 on the left. Six,
so I would write
6.370001 * 10^6
HOWEVER, it probably means
6.37*10^6
That is an advantage of scientific notation. You know how many digits are actually significant.

that is one of my answer choices.

but the number in the problem is in meters. and it asks to give the measurement in Kilometers. how come there isnt any converting that you have to do there?

Oh sorry

10^3 m/km
so
6.37*10^6 m * 1 km/10^3 m = 6.37*10^3 km

Of course! To express the radius of Earth in km using scientific notation with the correct number of significant digits, follow these steps:

Step 1: Start with the given measurement, which is the radius of Earth: 6 370 000 m.

Step 2: Convert meters to kilometers by dividing the given value by 1000, since there are 1000 meters in 1 kilometer.

6 370 000 m / 1000 = 6 370 km

Step 3: Now, we need to express this value in scientific notation. Scientific notation represents a number as a decimal multiplied by a power of 10. The decimal is a number between 1 and 10, while the power of 10 indicates how many places the decimal point has been moved.

To convert the decimal form to scientific notation, we need to count the number of significant digits. In this case, the given measurement has 4 significant digits (6, 3, 7, and 0).

Step 4: Determine the decimal form. To do this, divide the given value by 10 raised to a power that will move the decimal point to the left or right until you get a number between 1 and 10.

In this case, since the value is greater than 10, we need to move the decimal point to the left. So, divide the given value by 10,000 (10^4) to get a decimal between 1 and 10.

6 370 km / 10,000 = 0.637

Step 5: Now, write the decimal form obtained in Step 4 and multiply it by 10 raised to the same power we used in that step. The power, in this case, will be -4 since we moved the decimal point 4 places to the left.

0.637 * 10^(-4)

Step 6: Finally, express the final answer in scientific notation using the correct number of significant digits. Since we started with 4 significant digits, we need to keep 4 significant digits in the final answer.

0.637 * 10^(-4) has 4 significant digits, so the final answer in scientific notation with 4 significant digits is:

6.370 x 10^2 km

Therefore, the radius of Earth in km, expressed in scientific notation with the correct number of significant digits, is 6.370 x 10^2 km.