Question

What is the mass of Saturn's moon Titan in scientific notation?

Answer 1

Step-by-step explanation

Let's assume that we must write a considerably large number in scientific notation (like the mass in kilograms of a planet or a natural satellite like Titan). The number is the following (with letters instead of digits):

We have to write it as a decimal number smaller than 10 multiplied by a power of 10. First we need to count the number of digits between the second digit (counting from the left) and the one in the unit. In this case this means counting all the digits between b and l including both.

There are 11 digits, this means that the exponent on the power of 10 will be 11. Then we divide the number we have by this power of 10. Remember that dividing by a power of 10 with an exponent n moves the decimal dot n places to the left:

Then the number on scientific notation will be this decimal number multiplied by the corresponding power of 10. In this case since the number has a lots of digits we can round it. Let's say we round it to the nearest hundreth so the final number in scientific notation is:

`M=a.bc\cdot10^(11)`

And that's how you can write any number in scientific notation.

For the mass of Titan if you can find it in decimal form and you convert it to scientific notation you'll get:

`1.3452\cdot10^(23)\text{ kg}`