# SAT Math : Decimals

## Example Questions

### Example Question #1 : How To Convert Decimals To Scientific Notation

Convert 0.0004640 into scientific notation.

The value is already in scientific notation

Explanation:

When written in scientific notation, a number will follow the format in which is between one and ten and is an integer value.

To find , take the first non-zero digit in your given number as the ones place. In 0.0004640 this would be the first 4. All subsequent digits fall into the tenths, hundredths, etc. places.

To find , we must count the number of places that is removed. In 0.0004640, the first digit of  is in the ten-thousandths place. This indicates that will be .

Together, the final scientific notation will be .

### Example Question #1 : How To Convert Decimals To Scientific Notation

Write  in scientific notation.

Explanation:

We want to move the decimal point to the place just after the first non-zero number, in this case 6, and then drop all of the non-significant zeros. We need to move the decimal point five spaces to the right, so our exponent should be negative.  If the decimal had moved left, we would have had a positive exponent.

In this case we get 6.009 * 105.

### Example Question #1 : How To Convert Decimals To Scientific Notation

is equal to which of the following?

Explanation:

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:

### Example Question #1 : How To Convert Decimals To Scientific Notation

is equal to which of the following?

Explanation:

The easiest way to do this is to convert each of your answer choices into scientific notion and compare it to .

For each of the answer choices, this would give us:

When you convert, you add for each place that you move to the left and subtract for each place you move to the right. (Note that this is opposite of what you do when you multiply out the answer. We are thinking in "reverse" because we are converting.)

### Example Question #45 : Decimals

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

### Example Question #46 : Decimals

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 #47 : Decimals

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 #48 : Decimals

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

### Example Question #1 : Other Decimals

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

### Example Question #41 : Decimals

Convert the decimal into scientific notation: