### All SAT Math Resources

## Example Questions

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

Convert 0.0004640 into scientific notation.

**Possible Answers:**

The value is already in scientific notation

**Correct answer:**

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 : Decimals

Write in scientific notation.

**Possible Answers:**

**Correct answer:**

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 * 10^{–}^{5}.

### Example Question #2 : Decimals

is equal to which of the following?

**Possible Answers:**

**Correct answer:**

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 #3 : Decimals

is equal to which of the following?

**Possible Answers:**

**Correct answer:**

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:

(Which is, thus, the answer.)

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 #1 : How To Convert Decimals To Scientific Notation

Convert the decimal into scientific notation:

**Possible Answers:**

**Correct answer:**

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 #2 : How To Convert Decimals To Scientific Notation

Convert the decimal into scientific notation:

**Possible Answers:**

**Correct answer:**

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 #3 : How To Convert Decimals To Scientific Notation

Convert the decimal into scientific notation:

**Possible Answers:**

**Correct answer:**

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 #4 : How To Convert Decimals To Scientific Notation

Convert the decimal into scientific notation:

**Possible Answers:**

**Correct answer:**

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 #5 : How To Convert Decimals To Scientific Notation

Convert the decimal into scientific notation:

**Possible Answers:**

**Correct answer:**

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 #6 : How To Convert Decimals To Scientific Notation

Convert the decimal into scientific notation:

**Possible Answers:**

**Correct answer:**

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

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