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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