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Multiplying and Dividing Decimals Study Guide (page 2)

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Updated on Apr 25, 2014

Dividing Decimals

Dividing Decimals by Whole Numbers

To divide a decimal by a whole number, bring the decimal point straight up into the answer (the quotient), and then divide as you would normally divide whole numbers.

Example:

1. Move the decimal point straight up into the quotient area:
2. Divide:
   
   
       
3. To check your division, multiply the quotient (0.128) by the divisor (4). If you get back the dividend (0.512), you know you divided correctly. 0.128
 

Dividing by Decimals

To divide any number by a decimal, first change the problem into one in which you're dividing by a whole number.

1. Move the decimal point to the right of the number you're dividing by (the divisor).
2. Move the decimal point the same number of places to the right in the number you're dividing into (the dividend).
3. Bring the decimal point straight up into the answer (the quotient) and divide.

 

Tip

Does your answer make sense? Remember that dividing by a decimal that has a value less than one will give you a bigger number!

 

Example:

1. Because there are two decimal digits in .03, move the decimal point two places to the right in both numbers:
2. Move the decimal point straight up into the quotient:
3. Divide using the new numbers:
        
           
   

Under the following conditions, you'll have to tack zeros onto the right of the last decimal digit in the dividend, the number you're dividing into:

Case 1. There aren't enough digits to move the decimal point to the right.
Case 2. The answer doesn't come out evenly when you divide.
Case 3. You're dividing a whole number by a decimal. In this case, you'll have to tack on the decimal point as well as some zeroes.

Case 1

There aren't enough digits to move the decimal point to the right.

Example

1. Because there are two decimal digits in 0.03, the decimal point must be moved two places to the right in both numbers. Since there aren't enough decimal digits in 1.2, tack a zero onto the end of 1.2 before moving the decimal point:
2. Move the decimal point straight up into the quotient:
3. Divide using the new numbers:

Case 2

The answer doesn't come out evenly when you divide.

Example:  

1. Because there is one decimal digit in 0.5, the decimal point must be moved one place to the right in both numbers:
2. Move the decimal point straight up into the quotient:
3. Divide, but notice that the division doesn't come out evenly
4. Add a zero to the end of the dividend (12.) and continue dividing:

Example:   

1. Because there is one decimal digit in 0.3, the decimal point must be moved one place to the right in both numbers:
2. Move the decimal point straight up into the quotient:
3. Divide, but notice that the division doesn't come out evenly:
4. Add a zero to the end of the dividend (1.0) and continue dividing:
5. Since the division still did not come out evenly, add another zero to the end of the dividend (1.00) and continue dividing:
6. By this point, you have probably noticed that the quotient is a repeating decimal. Thus, you can stop dividing and write the quotient like this:

Case 3

When you're dividing a whole number by a decimal, you have to tack on the decimal point as well as some zeros.

Example:  

1. There are two decimals in 0.02, so we have to move the decimal point to the right two places in both numbers. Because 19 is a whole number, put its decimal point at the end (19.), add two zeros to the end (19.00), and then move the decimal point to the right twice (1900.):
2. Move the decimal point straight up into the quotient:
3. Divide using the new numbers:

Division Shortcut

To divide a number by 10, just move the decimal point in the number one digit to the left. To divide a number by 100, move the decimal point two digits to the left. Just count the number of zeros and move the decimal point that number of digits to the left. If you don't have enough digits, tack zeros onto the left before moving the decimal point.

Example: Divide 12.345 by 1,000.

1. Since there are three zeroes in 1,000, move the decimal point in 12.345 three digits to the left.
2. Since 12.345 only has two digits to the left of its decimal point, add one zero at the left, and then move the decimal point:

Thus, 12.345 ÷ 1,000 = 0.012345

 

Tip

Write down how much money you earn per hour (include both dollars and cents). If you earn a monthly or weekly salary, divide your salary by the number of hours in a month or week to get your hourly wage. If you don't have a job right now, invent a wage for yourself—and make it generous. Divide your hourly wage by 60 to see how much money you earn each minute. Then multiply your hourly wage by the number of hours you work per week to find your weekly wage; round your answer to the nearest dollar.

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