DECIMAL NUMBERS

Introduction to Decimal Numbers

• A number written as a decimal has 3 parts:Whole # partThe decimal pointDecimal part

• The position of the digit in the decimal number determines the digit’s value.

Place Value Chart

.

ones

tens

hund

reds

thou

sand

s

tent

hs

hund

redt

hs

thou

sand

ths

ten-

thou

sand

ths

Hun

dred

-tho

usan

dths

Whole number part Decimal part

Decimal point

Writing a Decimal Number in Words

• Write the whole number part• The decimal point is written “and”• Write the decimal part as if it were a whole

number• Write the place value of the last digit

Ex: Write 6.32 in words

Six and thirty-two hundredths

Ex: Write 0.276 in words

Zero and two hundred seventy-six

thousandths

Or two hundred seventy-six thousandths

Writing Decimal Numbers in Standard Form

• Write the whole number part

• Replace “and” with a decimal point

• Write the decimal part so that the last non-zero digit is in the identified decimal place value

• Note: if there is no “and”, then the number has no whole number part.

Ex: Write in standard form “eight and three hundred four ten-

thousandths”

8 . 3 0 40

Ex: Write in standard form “seven hundred sixty-two thousandths”

Note: no “and” no whole part

0 . 7 6 2

• Your turn to try a few

Decimal Addition & Subtraction

To add and subtract decimal numbers, use a vertical arrangement lining up the decimal points (which in turn lines up the place values.)

Ex: Add 16.113 + 15.21 + 2.0036

16.11315.21 2.0036

000

put in 0 place holders

+

6623.33

Ex: Subtract 24.024 – 19.61

24.02419.610

put in 0 place holders-

414.4

31

1 1

Ex: Subtract 16 – 9.6413

16 9.6413

. put in the decimal point

put in 0 place holders0000

-

5 9 9 91

7853.

1

6

• Your turn to try a few

Decimal Multiplication

Decimal numbers are multiplied as if they were whole numbers. The decimal point is placed in the product so that the number of decimal places in the product is equal to the sum of the decimal places in the factors.

Ex: Multiply 1.2 x 0.04

Think 12 x 4 12 x 4 = 48

1.2 has 1 decimal place

0.04 has 2 decimal places

Therefore the product of 1.2 and 0.04 will have 1 + 2 = 3 decimal places

48.0 1.2 x 0.04 = 0.048

Ex: Multiply 3.1 x 1.45

Think 31 x 145 31 x 145 =4495

3.1 has 1 decimal place

1.45 has 2 decimal places

Therefore the product of 3.1 and 1.45 will have 1 + 2 = 3 decimal places

4 4 9 5. 3.1 x 1.45 = 4.495