# SAT Math : How to convert decimals to scientific notation

## Example Questions

### Example Question #11 : How To Convert Decimals To Scientific Notation

Convert the decimal into scientific notation:

Explanation:

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 six places to the right. Since the number is less than zero, the exponent is negative:

### Example Question #12 : How To Convert Decimals To Scientific Notation

Convert the decimal into scientific notation:

Explanation:

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:

### Example Question #13 : How To Convert Decimals To Scientific Notation

Convert the decimal into scientific notation:

Explanation:

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 three places to the right. Since the number is less than zero, the exponent is negative:

### Example Question #14 : How To Convert Decimals To Scientific Notation

Convert the decimal into scientific notation:

Explanation:

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 three places to the right. Since the number is less than zero, the exponent is negative:

### Example Question #1281 : Sat Mathematics

Convert the decimal into scientific notation:

Explanation:

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:

### Example Question #1282 : Sat Mathematics

Express the product  in scientific notation.

is

Explanation:

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.

### Example Question #1283 : Sat Mathematics

Raise  to the third power and express the result in scientific notation.

Explanation:

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:

### Example Question #1284 : Sat Mathematics

Express the result in scientific notation:

Explanation:

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:

### Example Question #1285 : Sat Mathematics

Express the result in scientific notation: .

Explanation:

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.

### Example Question #11 : How To Convert Decimals To Scientific Notation

Which of the following represents the quotient

in scientific notation?