Question

Explain how to write a large number in scientific notation.

Answer 1

To write a large number in scientific notation, place the decimal after the first non-zero digit to find the coefficient (which should be between 1 and 10), then multiply by 10 raised to the power of the number of places the decimal was moved.

Step-by-step explanation:

Expressing Large Numbers in Scientific Notation-

Scientific notation is a method used to write very large or very small numbers in a more compact form. To express a number in scientific notation, you first identify the coefficient which falls between 1 and 10, and then determine the appropriate power of ten.

Here is a step-by-step example to convert the number 79,345 into scientific notation:

1. Place the decimal after the first non-zero digit. For 79,345, the decimal point would be placed after the 7 to get 7.9345.
2. Count how many places the decimal point has moved from its original position. In our example, it has moved 4 places to the left so our exponent will be 4.
3. Write the number in scientific notation as the coefficient times 10 raised to the power of the exponent. Thus, 79,345 is written as 7.9345 × 10⁴.

Similarly, to write very large numbers such as 1,230,000,000 or 840,000,000,000,000 in scientific notation, repeat these steps to find they are respectively 1.23 × 10⁹ and 8.40 × 10¹⁴. The exponent indicates the number of times the decimal point was moved to the left to create a coefficient between 1 and 10.

Answer 2

You move the decimal point of a number until the new form is a number from 1 up to 10 (N), and then record the exponent (a) as the number of places the decimal point was moved. Whether the power of 10 is positive or negative depends on whether you move the decimal to the right or to the left. Moving the decimal to the right makes the exponent negative; moving it to the left gives you a positive exponent.

Step-by-step explanation: