Chapter 2- Decimals

What will be covered?

• Place Value Chart

• Comparing Decimals

• Rounding Decimals

• Add and Subtract Decimals

• Multiply and Divide Decimals

• Order of Operations with Decimals

• Fraction to Decimal

Place Value Chart

Comparing Decimals

• Line up the decimals vertically.

• Start at the left and compare corresponding digits. If the digits are the same, move one place to the right.

• When two digits are different, the larger number is the one with the larger value.

Example: Comparing Decimals

• List from Smallest to Largest

1.834, 1.83, 1.381, 1.38, 1.8

1.834

1.83

1.381

1.38

1.8

0

0

00

Answer:

1.38, 1.381, 1.8,1.83, 1.834

Example 2: Compare Decimals

• List from smallest to largest15.002, 15.02, 15.001, 15.018, 15.0019

15.002

15.02

15.001

15.018

15.0019

0 0

0

0

0 Answer:15.001, 15.0019, 15.002, 15.018, 15.02

Rounding Decimals•Circle the digit value to round to,

and draw an arrow to the number to the right

•If the value is 5 or greater, round the digit value up one

•If the value is less than 5, drop the values to right of digit

Example: Rounding DecimalRound 137.8945 to the nearest hundredths

1 3 7.8 9 4 5 5 or Greater? No

Then drop values

137.89

Round 0.3899 to the nearest thousandth

0.3 8 9 9 0.39

Examples: More on rounding

Round to the nearest whole number. This is the same thing as rounding to the nearest ones place.

8. 7 6 59.0 or 9

4 9 5.2 4 5 495.00 or 495

Adding and Subtracting Decimals

• Write the numbers to be added vertically and line up the decimal points. Extra zeros may be placed to the right of the decimal points if needed.

• Add or subtract all the digits with the same place value, starting with the right column and moving to the left.

• Place the decimal point of the sum or difference in line with the decimal points of the numbers added.

Examples on Adding Decimals

3.1 + 2.16 =

3.1

2.16+

0

5.26

Example: Adding Decimals

Step 1

15.3

+1.1109

Step 2

15.3000

+1.1109

Step 3

15.3000+1.110916.4109

Example: Subtracting Decimals

• Subtract 15.87 – 1.649Step 1

15.87

- 1.649

Step 2

15.870- 1.649

Step 3

15.870- 1.64914.221

Multiplying Decimals Steps

• Set up in multiplying form – don’t worry about lining up decimals or trailing zeros

• Multiply

• Count decimals places in both multiplied numbers

• Move decimal point in final answer

Example: Multiplying Decimals

• Multiply 21.7 x .23Step 1

21.7

X .23

Step 2

21.7X .23 651+4340 4991

Step 3

3 Decimal Places

4.991

More Examples on Multiplication

5.261 x 45 =

Step 1

5.261

45x

Step 2

5.261

45

26305

210440

236745

x

+

Step 3

236. 745

Dividing a Decimal by a Whole Number

• Set up the division problem

• Place the decimal point for the quotient directly above the decimal point in the dividend.

• Then, divide if the numbers were whole numbers.

• Validate by multiplication.

Dividing by a Whole Number

8 17 28.. The decimal points are aligned,

one above the other.

2.16

Divide as you normally divide whole numbers.

161284848

0

Dividing by a Decimal

Dividing by a Decimal

1. Make the divisor a whole number by moving the decimal point to the right. Mark that position with a caret (). Count the number of places the decimal point moved.

2. Move the decimal point in the dividend to the right the same number of places. Mark that position with a caret.

3. Place the decimal point of your answer directly above the caret marking the point of the dividend.

4. Divide as with whole numbers.

When dividing a decimal by another decimal, the division problem is converted into an equivalent problem that has a whole number as a divisor.

Dividing by a Decimal

Example: Divide 4.209 ÷ 1.83.

1.83 4.20 9

2.3

Move each decimal point to the right two places.. .

Mark the new position by a caret ().1.83 4.20 9

Place the decimal point of the answer directly above the caret. .

366

549549

0

Divide as normal.

Dividing by a Whole NumberExample: Divide 263.82 ÷ 7 and round to the nearest

hundredths.

7 263.8237.688 Carry out the division to the

thousandths place, and then round.

2153494842

6256

60Note that the remainder is not zero.

0

An extra zero was added to carry out the division to the required place.

37.688 is rounded to 37.69 (the nearest hundredths).

0.3 x 0.5 + ( 0.4) 3 – 0.036

0.3 x 0.5 + ( 0.4x 0.4x 0.4) – 0.036

.15 + 0.064 – 0.036

0.150+ 0.064 0.150+ 0.064

0.214

0.214-0.036

0.178

Validate0.0360.178

0.214

Order of Operations

Fraction to Decimal

Fraction to Decimal

Validation: