Decimals:

 

Estimation:

Addition: 

Rounding – round decimal to greatest  nonzero place of smallest number.  Add the rounded numbers.

Front End – Add the nonzero front digits.  Write zeros for the other digits.

The exact sum will be between these estimates!!!

Clustering – When a number of addends cluster around a certain number, an estimate for the sum may be obtained by multiplying that number by the number of addends.

 

Subtraction:

Rounding – Round the decimals to the greatest nonzero place of the smaller number.  Subtract the rounded numbers.

Front end – Subtract the nonzero front digits.  Write zeros for these other digits. 

The exact difference will be between these estimates!!!

 

Multiplication:

Round each factor to its greatest place value.  Multiply the rounded factors.

 

Division:

Write the decimal point in the quotient.  Decide in which place the first nonzero digit of the quotient begins.  Find the first nonzero digit of the quotient.  Write zeros for the remaining digits.

 

Moving the decimal point This only works with multiples of ten!!!!

 

  1. To multiply a decimal by a multiple of 10 or 100, multiply the factors as if they were whole numbers;  to obtain the final product, drop a zero from that product for each place the decimal point in the decimal factor was moved to the right in order to make it a whole number.
  2. Same as multiplication – but move to the left. 
  3. For both multiplication and division the decimal point is moved the same number of places as there are zeros in 10, 100, and 1000.

 

For example: 10 x 3.626 = 36.28;  100 x 3.628 = 362.8; and

1000 x 3.628 = 3626;  20 x 0.4 = 8;  200 x 0.4 = 80

For example: 4321 divided by 10 = 432.1;  4321 divided by 100 = 43.21;  4321 divided by 1000 = 4.321

  1. When there are not enough places to move the decimal point as far to the left as needed, zeros are written as placeholders to the right of the decimal point until the quotient has the correct number of places.

For example: 4 divided by 1000 = 0.0004

 

Be able to predict if the divisor will be 10, 100, or 1000

For example:  2.08 divided by ? = 0.208.

Use the rule.  How many place did the point move?  One – so the answer is 10.

1.8 divided by ? = 0.018.  Use the rule.  The point moved two places so the answer is 100.

59 divided by ? = 0.059.  The point moved three places so the answer is 1000.

 

Be able to find the missing factor.

? times 0.309 = 309.  The answer is 1000 because the point moved three places right.

? times 0.028= 0.28.  The answer is 10 because the point moved one place right.

100 times?  = 350.  The answer is 3.5 because the point moved two places right in the answer.

1000 times ? = 1580.  The answer is 1.58 because the point moved three places right in the answer.

 

Multiplying Decimals that aren’t multiples of ten:

1.       Be sure there are the same number of decimal places in the product as in the decimal factors.  Mark them off from right to left.

2.     When there are not enough nonzero digits to fill all the decimal places needed in the product, write zeroes in those places so that the value of the product is correct and the decimal point is properly placed.

 

 

 

 

Dividing Decimals by whole numbers:

1.       It’s just like dividing money except there’s no dollar sign.  Insert the point in the quotient before you start directly over the point in the quotient.  Follow the steps for division.  Does Mc Donalds serve cheeseburgers?  Be sure to start in the correct place.

2.     Instead of a remainder, add up to two zeros to the right end of the dividend.  If there’s still a remainder, just drop it.