UNDERSTANDING DECIMALS

UNDERSTANDING DECIMALS

Decimals, like fractions show a part of something. Money is a common example. Dollars and cents are separated by a decimal point: dollars (whole numbers) are to the left of the decimal point, cents (parts of a whole dollar) are to the right. When reading a decimal number, read the whole number, say "and" for the decimal point then read the decimal parts followed by their place value. (Numbers to the right of a decimal point are parts; the further the numbers extend to the right of the decimal point, the smaller the part.)

The location of the number in relation of the decimal point is called its place value.

1 3.1 = 3 10

1 3.01 = 3 100

1 3.001 = 3 1000

1 3.0001 = 3 10000

3 .1 = three and one tenth 3.01 = three and one hundredth 3.001 = three and one thousandth 3.0001 = three and one ten thousandth

Each additional place adds another zero to the fraction.

Example 1: Seven tenths

To translate words into decimal numbers

Step 1) write the whole number (if any)

Step 2) put in the decimal point

.

Step 3) determine the place value

of the decimal (10ths = 1 place) . __

Step 4) write the decimal in its place

. 7_

Example 2: Eleven and nine hundredths

Step 1) write the whole number Step 2) put in the decimal point Step 3) determine place value

(hundredths = 2 places) Step 4) write decimal in its place Step 5) fill in empty places with zeroes

11 11.

11.__ __ 11.__ 9 11. 0 9_

Practice:

1) six and nine tenths _______

2) ten and eight tenths

_________

3) fifteen and fifteen hundredths______ 4) twenty seven and five thousandths ________

5) one and three hundredths ______

6) one hundred fifty and nineteen ten

thousandths

_________

ADDING AND SUBTRACTING DECIMALS

When adding and subtracting decimals you may rewrite these problems vertically and add zeroes to keep columns straight.

Remember:

? to line up the decimal points and immediately put the decimal point in your answer space directly below those in the question.

? whole numbers go to the left of any decimal points. ? you may add a decimal point (and zeroes) to the right of any whole

number without changing its value.

? if an answer ends in one or more zeroes to the right of the decimal point, clean up your answer by eliminating them. If there are no numbers (other than zero) following the decimal point, you can eliminate it as well.

Example 1: 7 + .03 + .721 =

Step 1) rewrite, with added zeroes, and line up the decimal points

Step 2) bring down the decimal point Step 3) add (from right to left)

7.000 .030

+ .721 .

7.751

Example 2: 99.2 - .763 =

Step 1) rewrite (add zeroes) and line up decimal points

Step 2) bring down the decimal point Step 3) subtract (from right to left)

99.200 - .763

. 98.437

Example 3: 29.1 + 3 + .9 =

Step 1) rewrite with added zeroes

29.1

3.0

+ .9

Step 2) bring down the decimal point

.

Step 3) add

33.0

Step 4) clean up your answer by

removing the decimal point and zero

Answer: 33

Note: If you can work these problems without rewriting, you can save valuable time.

To subtract from a whole number, add a decimal point to the right of the whole number and as many zeroes as needed. Line up the decimal points in the problem, then, starting from the right, subtract. Borrow if necessary.

Work these problems: 1) .2 +.13 + .5 = _____

2) 7 - .28 = _____

3) .6 + 9 + .31 = _____

4) 85.03 - .0002 = ____

5) .868 - .518 = ______ 6) 17.1 - .139 = ____

7) 10.67 + 9.33 = _____

8) 9 + 3.4 + 0.7 = ______ 9) 7.5 - 1.095 = _____

10) 25.09 + .03 + 1.62 = _____ 11) 8.2 - .009 = ____

12) 73 + .0008 + .23 = ______

13) 6.7 + .67 + .067 = _______ 14) 14.54 - 9.76 = _____ 15) 82.62 ? 3.909 = _______

16) 1 - .005 = _____

17) 1.09 + .036 +.17 = ____ 18) 70.07 ? 1.24 = _____

19) 1.942 - .848 = _____

20) 83.006 - .47 = ________ 21) 123 ? 9.42 = ______

22) 4 + 8.917 + .44 + .9130 = ______

23) .2220 + 2 + .022 + 2.02 = __________

24) 7.005 + .35 + 15 + 3.2 = _________ 25) 20.35 +.0089 + 1.35 + .4 = __________

26) 9 - .635 = _______

27) 8.04 ? 7.961 = ________ 28) 210 - .3 = ________

29) .65 + 8 + 7.15 + .2 = ________

30) 2 + .1 + .36 + 7.640 = _____________

WORD PROBLEMS: ADDITION AND SUBTRACTION

1) Deanna carried boxes of nails weighing 23.2 pounds, 15.14 pounds and 6.70 pounds. Find the total weight.

2) On the way to work Sandy's odometer read 10,515.2. Coming home it read 10,579. How far did she travel?

3) The price of gasoline jumped from $2.19 per gallon to $4.37 per gallon in one month. How much was the increase?

4) When Bea started work, the thermometer read 72.3 degrees. By lunch it was 26.7 degrees warmer. How hot was it?

5) Clara's new spud wrench cost $33.78 plus $3.04 tax plus $4.37 shipping. How much did she pay?

6) Find the combined weight of 6 boxes of screws weighing 2.4 lbs., 5.1 lbs., 3.25 lbs., 1.9 lbs., 6.75 lbs., and 4.75 lbs.

7) From a stack of bricks weighing 3,714pounds, Aminah removed bricks weighing 647.5 Pounds. What was the weight of the remaining bricks?

8) Tamara cut 27.75 inches from a 36 inch piece of sheet metal. How much was left?

Extra Effort 9) One morning Camille made 4 wheel barrow trips carrying a combined weight of

277.5 lbs. If the first 3 trips weighed 51.3 lbs., 65.61 lbs., and 87.5 lbs. respectively, what was the weight of the fourth?

MULTIPLYING DECIMALS

To multiply decimals it is easier to rewrite the problems vertically, lining up the last numbers on the right side, then work the problem. (You may choose to write the problem in whole numbers as you would any multiplication problem and then insert the decimal points.) Multiply as you would with any problem, then determine where to put the decimal point in your answer. Instead of bringing down the decimal point as you do for addition and subtraction, count the total number of places to the right of the decimal points in your problem and then put that same number of places to the right of the decimal point in your answer. (Begin at the right and move to the left). Then eliminate unnecessary zeroes and/or decimal points at the end of any answer.

Example 1: 26.25 x 3.1 = Step 1) rewrite Step 2) multiply

Step 3) count the number off decimal places in the problem

Step 4) insert the decimal point

26.25 x 3.1 2625 7875_ 81375

there are 3 places in the problem

81.375

Work these problems: 1) 6 x .3 = _______

2) .25 x 7 = _______

3) .031x 9 = ______

4) 75 x .45 = _______

5) 1.8 x .47 = _______

6) 5.03 x 8 = ______

7) 6.61 x 1.4 = _______ 8) .9 x 23.2 = ________ 9) 651 x .06 = _______

10) 200.2 x .707 = ________ 11) .836 x .28 = ________ 12) .056 x 5.6 = _________

If there are fewer numbers in your answer than there are decimal places in the question, add zeroes to the left until you have enough numbers.

Example 2: .075 x .03

Step 1) rewrite Step 2) multiply

.075 x .03 225

Step 3) count decimal places

there are 5 places in the problem : add 2 zeroes

Step 4) insert the decimal point .00225

Work these problems:

13) .08 x .8 = _________ 14) .678 x .123 = _______ 15) .06 x .553 = ________

16) .15 x .47 = ________ 17) .121 x .36 = ________ 18) 1.85 x .03 = ________

19) .301 x .21 = _______ 20) .306 x .3 = _________ 21) .4 x .346 = _________

22) .507 x .12 = ________ 23) .074 x .3 = _________ 24) .0112 x .313 = ___________

Decimal points and/or zeroes at the right end of answers are unnecessary. Eliminate them before writing your final answer.

Example 3: 5 x .2 = 1.0 Eliminate the zero and the decimal point. Final answer: 1

Work these problems: 25) .515 x .6 = _________ 26) 7.2 x 30 = _________ 27) .234 x 5 = ________ 28) 1.45 x .22 = ________ 29) 48.3 x 40 = ________ 30) .625 x 1.2 = _______ 31) .28 x .365 = ________ 32) .005 x .6 = _________ 33) 31.50 x .16 = _______ 34) 32.1 x 20 = _________ 35) 2.6 x 4.5 = _________ 36) .117 x .90 = ________

DIVIDING DECIMALS

Important things to remember:

1. Eliminate any decimal places outside the dividing box by moving the decimal point all the way to the right (creating a whole number)

2. Whatever you do to numbers outside the box, you must do inside the box (move decimal point if needed)

3. When steps 1 & 2 are completed, look for the decimal point inside the box and transfer it directly above into the answer space.

4. If you cannot divide a number inside the box, hold its answer space with a zero. 5. Once you begin dividing, you must put a number in the answer space for every

number in the dividing box. 6. Add zeroes after the last number inside the box if necessary 7. After solving, clean up your answer by eliminating any zeroes standing alone

before the decimal point (ex. 0.123) or any decimal point at the end of an answer. ( ex. 345. ) 8. Some numbers repeat. Carry them out to 5 places and then round back to 4 places.

______ Example 1: 4)3.5

Step 1) make sure that the number outside the box is a whole number (4 is a

whole number ? no change is required)

Step 2) replicate any changes inside the box (no changes made in this example)

Step 3) put a decimal point in the answer space directly above the one inside the

problem

_ .___

4)3.5

_ .875___

Step 4) divide (add zeroes as needed)

4)3.500

32

30

28

20

_______

20

Example 2: .80)6.48

_______

Step 1) make .8 a whole number

.80)

(move decimal point to the right as far as possible)

Step 2) do the same inside the box Step 3) transfer decimal point to answer space

____._ 80)648.

______ )6.48

Step 4) divide (adding zeroes as necessary)

_ _ 8.1__ 80)648.0

640 80 80

Hint: When setting up division problems, the ? symbol reads "divided by" so the number following the ? goes outside the box.

Practice:

1) .590 ? 5 =

______ 2) 2) 8.3

3) 57.75 ? 7 =

_____ 4) 8) 2.8

______ 5) 24) 3.6

6) 5.52 ? 4 =

______ 7) 8) 1.8

_____ 8) 40) 6.4

9) 13.8 ? 6 =

______ 10) 3)148.8

11) 9.32 ? 4 =

12) 4.374 ? 3 =

_____ 13) .4) .12

14) .42 ? 6 =

______ 15) .018 ) .2474

16) .576 ? .64 =

17) 5 ? .4 =

___ 18) .16) 5

19) .35 ? .7 =

20) .3 ? .8 =

21) 8.748 ? .06 = 22) .19 ? .04 =

______ 23) .16 ) .0848

____ 24) .16) .07

______ Example 3: .3)21

Step 1) move decimal point to the right to make 3 a whole number

_______

.3)21

______

Step 2) do the same to the inside number

3)21.0

Step 3) put the decimal point in the answer space __ _.__

3)210.

Step 4) divide

__70._

3)210.

21

0

0

Step 5) clean up your answer 70. = 70

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