Very Large Numbers

The Sun is about 150000000 kilometers away. A number with that many zeros is hard to read and easy to copy wrong. Scientific notation writes it as a number that is at least 1 and less than 10, times a power of ten: 1.5 × 10^8.

A number in scientific notation has two parts. The first part is a number that is at least 1 and less than 10, so it has exactly one nonzero digit before the decimal point. The second part is a power of ten, and its exponent tells you how big the number is. To write 45000 this way, move the decimal point four places to the left, so that it sits after the 4. The number becomes 4.5 × 10^4. The exponent 4 is the number of places the point moved.

To write a large number in scientific notation, place the decimal point after the first nonzero digit. Count how many places the point moved. That count is the exponent of the 10. In 45000 = 4.5 × 10^4, the point moved four places, so the exponent is 4.