Decimals

Decimals Place Value• Like fractions, decimals show part of a whole. You see them all the time! • The decimal point separates the ones place and the tenths place.• The decimal says the word “and”.• Decimal representation

• Tenths (1/10) = 0.1• Hundredths (1/100) = 0.01• Thousandths (1/1000) = 0.001

Examples:• 4/10 = 0.4• 39/100 = 0.39• 76/100 = 0.76• 150/1000 = 0.150 = 0.15• 1 6/10 = 1.6• 8 23/100 = 8.23• Express the decimal “zero point two” as a reduced fraction. = 1/5• Convert the decimal value 0.6 to a fraction. = 6/10 = 3/5• To the nearest hundredth, what is 20% of 0.1? = 0.02

-----------------------------------------------------------------------------------------

1000’s 100’s 10’s 1’s 1/10ths 1/100ths 1/1000ths

1000 100 10 1 0.1 0.01 0.001

Fractions in the decimal form

Fractions in the visual form

Rounding DecimalsSteps to follow when rounding decimals.

1. Look at the digit to the right of the place being rounded.2. The digit remains the same if the digit to the right is 0, 1, 2, 3, or 4.3. Round up if the digit to the right is 5, 6, 7, 8, or 9.4. The deciding digit and every digit to the right is not changed to a zero as in whole number rounding.5. Putting zeros on the end of a decimal number does not change the value of the number, but it does change the way the number is read.

Example 1 --> Round 4.3 to the nearest whole number. (?)

• Underline place value being rounded• Draw arrow over the deciding digit

<|----|-----|-----|---|---|----|-----|-----|-----|-----|>4.0 4.5 5.0

4.1 4.3

4.3 rounds to 4

Example 2 –> Round 0.263 to the nearest tenth. (?)

• Steps

• Underline place value being rounded

• Draw arrow over the deciding digit

<|----|-----|-----|---|---|----|-----|-----|-----|-----|>.20 .25 .30

.263

0.263 rounds to 0.3

Example 3 –> Round 9.875 to the nearest hundredth. (?)•Steps

•Underline place value being rounded

•Draw arrow over the deciding digit

<|----|-----|-----|---|---|----|-----|-----|-----|-----|>9.870 9.875 9.880

9.875 rounds to 9.88

Example 4 –> What digit is in the thousandths place in the number 15487.6329? = 2

Adding & Subtracting Decimals

Steps to follow when adding & subtracting decimals.

1. Line up the numbers by the decimal point.

2. Add zeros to make the same number of places behind the decimal point in all numbers in the problem.

3. Add or subtract beginning on the far right side of the problem.

4. Place the decimal point in the answer by bringing the decimal point straight down from the problem to the answer.

Example 1 –> 21.99 + 56.18 + 8.1 = ?

21.99

56.18

+ 08.10

=====

86.27

=====

Example 2 –> 6.17 + 109.99 + 78 = ?

006.17

109.99

+078.00

========

194.16

========

Example 3 56.02 - 29.76 = ?

415 9 12

56.02

-29.76

======

26.26

======

Example 4 71.00 - 3.99 = ?

6 10 9 10

71.00

-03.99

======

67.01

======

1. If the problem is written across, copy it so that the first number is inside the division sign.

2. Move the decimal point of the number on the outside of the division sign all the way to the right so that it becomes a whole number.

3. Move the decimal point on the inside number the SAME number of places to the right as you did on the outside number. Add 0s if you need to move beyond the end of the number.

4. Put the decimal point for your answer directly above the one in your inside number.

5. Divide the same way you do with whole numbers. After the decimal point, answer with a 0 any time a number is too small to be divided.

6. If there is a remainder, add 0s to the number inside the division sign-one at a time, bring them down, and divide until there is no remainder or until there are 4 decimal places in your answer.

Steps to follow when dividing decimals. Example 1 -->

.3 6.3 3 0

6.0 5 5

3 6

3 0

3 3

3 0

3 0

.3633 06 =

:

.0 6.

3 0

0

)

Dividing Decimals

Example 2 –> .25 / .5 = ?

__.5________

.5 ) .2.5

25

======

0

======

Example 3 .0081 / .13 = ?

__.062..___

.13) .00.81

0

======

8 1

- 78

------------

30

-26

------------

4…

======

Example 4 71.00 - 3.99 = ?

6 10 9 10

71.00

-03.99

======

67.01

======

Multiplying DecimalsSteps to follow when multiplying decimals.

1. Multiply as you normally would2. Count the number of digits behind a decimal point in the problem.3. Put the decimal point in the answer. If your problem had 2 digits

behind a decimal point, your answer should have 2 digits behind a decimal point.

4. Add zeros if needed.

Example 1 2.1 x 3.9 = ?• Step 1. 21 x 39 = 819• Step 2. 2 digits behind decimal point• Step 3. After adding decimal point

behind two digits, answer changes to 8.19

Example 2 .021 x 3.9 = ? (a) 0.0819 (b) 0.8190 (c) .0819

Example 3 0.021 x 0.39 = ? (a) 0.00819 (b) 0.0819 (c) 0.819

Example 4 0.021 x 0.0039 = ? (a) 0.0000819 (b) 0.000819 (c) 0.00819