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 one place 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. 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.

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. 

First, express  itself as a number in scientific notation. Move the decimal point to the right until it follows the first nonzero digit - the "4" - as seen below:

Since the decimal point was moved 9 places to the right to form the number 4, the number, expressed in scientific notation, is .

Consequently, 

This can be rewritten applying the Power of a Product Property, as follows:

Applying the Power of a Power Property, we get 

Since , this number is not in scientific notation. We can adjust this by noting that 

,

substituting, and applying the Product of Powers Property:

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

First, express  itself as a number in scientific notation. Add the implied decimal point to the end of the number, and move it to the left until it follows the first nonzero digit - the "2" - as seen below:

Since the decimal point was moved 7 places to the left to form the number 2, the number, expressed in scientific notation, is .

Consequently, 

This can be rewritten applying the Power of a Product Property, as follows:

Applying the Power of a Power Property, we get 

This number is in the correct scientific notation, making this the correct response.

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

Split the fraction as follows:

Apply the Quotient of Powers Rule:

However,  is not in scientific notation, since .

Adjust by noting that ; substitute and apply the Product of Powers Rule:

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

Split the quotient as follows:

Applying the Quotient of Powers Rule:

However,   is not in scientific notation, since . Adjust by noting that ; substituting and applying the Product of Powers Rule:

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:

,

the correct response.

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. 

First, rewrite 200,000,000 as a number in scientific notation. A number in scientific notation takes the form , where  and is an integer.

200,000,000 can be rewritten by adding the implied decimal point to the end of the number, and move it to the left until it follows the first nonzero digit - the "2" - as seen below:

Since the decimal point was moved 8 places to the left to form the number 2, the number, expressed in scientific notation, is .

Therefore, . By the Negative Exponent Rule , 

, so

Applying the Power of a Product Property, we get

Applying the Negative Exponent Rule and the Power of a Product Property on the right, we get

Therefore, .

Applying the Power of a Product Property:

Applying the Product of Powers Property:

Since , this is not in scientific notation; adjust it by noting that

substituting, and applying the Product of Powers Property: