# PSAT Math : How to convert decimals to scientific notation

## 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

Express 770,000,000,000 in scientific notation.

Explanation:

Write the number with a decimal point and without commas:

Counting the number of places, move the decimal point to the left until it is after the first nonzero digit:

The resulting number is 7.7; the number of places the decimal point moved to the left was 11. In scientific notation, this number is .

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

Convert  into scientific notation.

Explanation:

To convert a number into scientific notation, the decimal must be moved until our base number is greater than 1 and less than 10. Next, we must count the number of places we moved it and multiply it by 10 to that number. Thus, our answer is:

### Example Question #4 : How To Convert Decimals To Scientific Notation

12 grams of oxygen are equal to  atoms. Which of the following comes closest to the mass, in grams, of one million atoms of oxygen?

Explanation:

In scientific notation, one million atoms is equal to  atoms. To find the mass  of this many atoms, we can solve the proportion statement

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

Define an operation  as follows:

For all real numbers

Which of the following is equal to  ?

Explanation:

Substitute and execute the operations:

Move the decimal point right five places to get it after the first nonzero digit; the scientific notation equivalent is

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

Define an operation  as follows:

For all real numbers

Which of the following is equal to  ?

Explanation:

Substitute and execute the operations:

Move the decimal point right two places to get it after the first nonzero digit; the scientific notation equivalent is

### Example Question #7 : How To Convert Decimals To Scientific Notation

Define an operation  as follows:

For all real numbers

Which of the following is equal to  ?

Explanation:

Substitute and execute the operations:

Move the decimal point right four places to get it after the first nonzero digit; the scientific notation equivalent is

### Example Question #21 : Decimal Operations

Represent  in scientific notation.

Explanation:

Trick: Count how many times you move the decimal to get 3.452.  We moved the decimal 6 times to the right so the exponent above 10 will be -6.  If we move the decimal to the left then our exponent would be positive.

Another way to remember whether the exponent will be negative or possitive is whether or not the original number is less than or greater than one. If the original number is less than one, when you put it in scientific notation the exponent above the 10 will be negative. On the other hand, if the original number is greater than one, then the exponent above the 10 will be positive.

### Example Question #9 : How To Convert Decimals To Scientific Notation

can be represented by which of the following notations?