To convert a decimal into scientific notation, move the decimal point until you get to the left of the first non-zero integer. The number of places the decimal point moves is the power of the exponent, because each movement represents a "power of 10". The exponent will be positive if the original number is greater than zero, and negative if the original number is less than zero.

For this example, move the decimal point four places to the right. Since the number is less than zero, the exponent is negative:

When rounding to the nearest thousand, look to the hundreds place to determine whether you need to round up or down. You always round down when the digit is between 0 and 4, and up when it is between 5-9. Therefore, the rounded number is 902,000. When using scientific notation, the first number in the notation must be less than 10. In this case, that number is 9.

From there, the decimal goes immediately after. Then count how many places the decimal would have to be moved in order to convert back to the original number (5 places).

When the decimal is moved to the left when writing it in scientific notation, the exponent is positive. When moved to the right to write the number in scientific notation, the exponent is negative.

To convert a decimal into scientific notation, move the decimal point until you get to the left of the first non-zero integer. The number of places the decimal point moves is the power of the exponent, because each movement represents a "power of 10". The exponent will be positive if the original number is greater than zero, and negative if the original number is less than zero.

For this example, move the decimal point two places to the right. Since the number is less than zero, the exponent is negative:

To convert a decimal into scientific notation, move the decimal point until you get to the left of the first non-zero integer. The number of places the decimal point moves is the power of the exponent, because each movement represents a "power of 10". The exponent will be positive if the original number is greater than zero, and negative if the original number is less than zero.

For this example, move the decimal point two places to the right. Since the number is less than zero, the exponent is negative:

A number in scientific notation takes the form , where and is an integer.

To convert 3,880,000,000,000 to scientific notation, place the implied decimal point after the final zero and move it to the left as many places as is necessary until it is after the first nonzero digit - in this case the "3". Note that the point is moved 12 places to the left.

The number in front is 3.88, the number formed. The exponent of 10 is 12 - positive since the point was moved to the left. Therefore, the number, in scientific notation, is .

To convert a decimal into scientific notation, move the decimal point until you get to the left of the first non-zero integer. The number of places the decimal point moves is the power of the exponent, because each movement represents a "power of 10". The exponent will be positive if the original number is greater than zero, and negative if the original number is less than zero.

For this example, move the decimal point four places to the right. Since the number is less than zero, the exponent is negative:

A number in scientific notation takes the form , where and is an integer.

To multiply two numbers that are in scientific notation, first, use commutativity to multiply the numbers:

Applying the Product of Powers Rule on the powers of 10:

However, since , this number is not in scientific notation. Adjust by noting that , then applying the Product of Powers Rule again:

A number in scientific notation takes the form , where and is an integer.

To find , apply the Power of a Product Rule, then the Product of Powers Rule, as follows:

However, since , this number is not in scientific notation. Adjust by noting that , then applying the Product of Powers Rule again:

A number in scientific notation takes the form , where and is an integer. Of the five choices, all of which can be shown to be equal in value to the given product, only and have in the correct range. However, in scientific notation, decimals are used, and not fractions. This makes the correct choice.

We need to convert into a number of the form .

The trick is, however, figuring out what should be. When you have to move your decimal point to the right, you need to make the decimal negative. (Note, though, when you multiply by a negative decimal, you move to the left. We are thinking in "reverse" because we are converting.)

Therefore, for our value, . So, our value is: