Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately 5,880,000,000,000 miles. Suppose a star is 13.6 light-years from Earth. In scientific notation, how many miles away is it?
I entered the numbers in my calculator, which you could
have done just as well,
and came up with 7.9968 x 10^13
We don't use calculators, is the issue.
To express the distance in scientific notation, we need to convert 5,880,000,000,000 into scientific notation.
Scientific notation is a way of writing numbers that are very large or very small in a concise and standardized form. It consists of two parts: a coefficient and an exponent of 10.
In this case, the coefficient is obtained by expressing the given number between 1 and 10, and the exponent of 10 represents the number of times we need to multiply the coefficient by 10.
To convert 5,880,000,000,000 into scientific notation, we need to move the decimal point 12 places to the left:
5,880,000,000,000 = 5.88 × 10^12
Since the star is 13.6 light-years away, we can now express its distance in scientific notation by multiplying the coefficient by 13.6:
5.88 × 10^12 × 13.6 = 79.968 × 10^12
When we multiply 79.968 by 10^12, we need to adjust the exponent accordingly:
79.968 × 10^12 = 7.9968 × 10^13
Therefore, the star is approximately 7.9968 × 10^13 miles away in scientific notation.