Understanding Standard Notation And Solving For 1.986 X 106

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What is Standard Notation?

Standard notation is a mathematical representation of numbers using powers of 10. It is also known as scientific notation and is commonly used in science, engineering, and other fields that deal with very large or very small numbers. In standard notation, a number is expressed as a product of a decimal number between 1 and 10 and a power of 10. The power of 10 indicates the number of digits the decimal point needs to be moved to the left or right to get the original number.

How to Write a Number in Standard Notation?

To write a number in standard notation, follow these steps: 1. Identify the decimal point in the number. 2. Count the number of digits between the decimal point and the end of the number. 3. If the decimal point is to the right of the first digit, move it to the left of the first digit and add a negative exponent equal to the number of places you moved the decimal point. 4. If the decimal point is to the left of the first digit, move it to the right of the first digit and add a positive exponent equal to the number of places you moved the decimal point.

Solving for 1.986 x 106 in Standard Notation

Let's apply the steps above to solve for 1.986 x 106 in standard notation. Step 1: Identify the decimal point in the number. The decimal point is after the last digit, which is 6. Step 2: Count the number of digits between the decimal point and the end of the number. There are no digits between the decimal point and the end of the number. Step 3: If the decimal point is to the right of the first digit, move it to the left of the first digit and add a negative exponent equal to the number of places you moved the decimal point. Since there is no decimal point to the right of the first digit, we don't need to move it. Step 4: If the decimal point is to the left of the first digit, move it to the right of the first digit and add a positive exponent equal to the number of places you moved the decimal point. The decimal point is already to the left of the first digit. We don't need to move it. Therefore, 1.986 x 106 in standard notation is 1.986 x 10^6.

Why Use Standard Notation?

Standard notation is useful because it allows us to represent very large or very small numbers in a compact and easy-to-read form. For example, the distance between the Earth and the Sun is approximately 149.6 million kilometers. Writing this number in standard notation gives us 1.496 x 10^8 kilometers, which is much easier to read and compare with other numbers.

Practice Problems

Here are some practice problems to help you master writing numbers in standard notation: 1. Write 0.0000000000075 in standard notation. 2. Write 420,000 in standard notation. 3. Write 8.9 x 10^4 in decimal form.

Solution to Practice Problems

1. 0.0000000000075 in standard notation is 7.5 x 10^-12. 2. 420,000 in standard notation is 4.2 x 10^5. 3. 8.9 x 10^4 in decimal form is 89,000.

Conclusion

In conclusion, standard notation is a useful tool for representing very large or very small numbers. To write a number in standard notation, identify the decimal point, count the number of digits between the decimal point and the end of the number, and move the decimal point to the left or right as needed. Practice problems can help you master this skill and improve your understanding of standard notation.