Understanding Scientific Notation: 13 040 000

What is Scientific Notation?

Scientific notation is a way to represent very large or very small numbers using powers of ten. It is used in scientific and mathematical calculations where the number of digits in a number can make a calculation difficult.

Writing 13 040 000 in Scientific Notation

To write 13 040 000 in scientific notation, we need to express it as a number between 1 and 10 multiplied by a power of 10. First, we count the number of digits in the original number. In this case, there are 7 digits. Next, we move the decimal point to the left until we have a number between 1 and 10. In this case, we move the decimal point 6 places to the left, giving us 1.304. Finally, we add the power of 10. Since we moved the decimal point 6 places to the left, the power of 10 is 10^6. Therefore, 13 040 000 in scientific notation is 1.304 x 10^7.

Why Use Scientific Notation?

Scientific notation is used to make it easier to work with very large or very small numbers. For example, it is much easier to multiply 1.304 x 10^7 by 2 than it is to multiply 13 040 000 by 2. Scientific notation is also used to express the results of scientific experiments, which often involve very large or very small numbers. For example, the mass of the sun is approximately 1.989 x 10^30 kilograms.

Converting Scientific Notation to Standard Form

To convert a number in scientific notation back to standard form, we need to multiply the number before the "x" by 10 raised to the power after the "x". For example, to convert 1.304 x 10^7 to standard form, we multiply 1.304 by 10^7, giving us 13 040 000.

Practice Problems

Here are some practice problems to help you get comfortable with scientific notation: 1. Write 0.00000345 in scientific notation. 2. Write 5.6 x 10^8 in standard form. 3. Write 9.81 x 10^-7 in standard form.

Solution to 13 040 000 in Scientific Notation

To recap, 13 040 000 in scientific notation is 1.304 x 10^7.

Summary

Scientific notation is a way to represent very large or very small numbers using powers of ten. It is often used in scientific and mathematical calculations to make it easier to work with these numbers. If you need to convert a number in scientific notation to standard form, simply multiply the number before the "x" by 10 raised to the power after the "x".