1. PRESENTATION 6 Decimal Fractions

2. DECIMAL FRACTIONS A decimal fraction is written with a decimal point
Decimals are equivalent to common fractions having denominators which are multiples of 10
The chart below gives the place value for each digit in the number 1 • 2 3 4 5 6 7
UNITS
TENTHS
HUNDREDTHS
THOUSANDTHS
TEN
HUNDRED
MILLIONTHS

3. READING DECIMAL FRACTIONS
To read a decimal fraction, read the number as a whole number
Say the name of the decimal place of the last digit to right
Example: is read “five hundred thirty-two thousandths”

4. READING DECIMAL FRACTIONS
To read a mixed decimal (a whole number and a decimal fraction), read the whole number, read the word “and” at the decimal point, and read the decimal
Example: is read “one hundred thirty-five and seven hundred eighty-seven ten-thousandths”

5. ROUNDING DECIMAL FRACTIONS
Rounding rules:
Determine the place value to which the number is to be rounded
Look at the digit immediately to its right
If the digit is less than 5, drop it and all digits to its right
If the digit is 5 or more, add 1 to the digit in the place to which you are rounding, then drop all digits to its right
Note: The ≈ sign means “approximately equal to”

6. ROUNDING DECIMAL FRACTIONS
Example: In determining rivet hole locations, a sheet metal technician computes a dimension of inches precision is needed for laying out the hole locations. Round the dimension to two decimal places.
Locate the digit in the second decimal place (0)
The third-decimal place digit, 3, is less than 5 and does not change the value, 0
Therefore, inches rounds to 1.50 inches
inches ≈ 1.50 inches

7. EXPRESSING FRACTIONS AS DECIMALS
Fractions can be converted to decimals by dividing the numerator by the denominator
Example: Express 3/8 as a decimal fraction
Place a decimal point after the 3 and add zeroes to the right of the decimal point
Place the decimal point for the answer directly above the decimal point in the dividend. Divide.
The fraction 3/8 equals 0.375

8. EXPRESSING DECIMALS AS FRACTIONS
To change a decimal to a fraction, use the number as the numerator and the place value of the last digit as the denominator
Example: Change to a common fraction
The number is read as sixty-five thousandths
Write the denominator as 1,000 and 65 as the numerator

9. ADDITION AND SUBTRACTION OF DECIMALS
To add and subtract decimals, arrange numbers so that decimal points are directly under each other
Add or subtract as with whole numbers
Place decimal point in answer directly under the other decimal points

10. ADDITION AND SUBTRACTION OF DECIMALS
Example: Add
Arrange the numbers so that the decimal points are directly under each other
Add zeroes so that all numbers have the same number of places to the right of the decimal point

11. ADDITION AND SUBTRACTION OF DECIMALS
Add each column of numbers
Place the decimal point in the sum directly under the other decimal points

12. ADDITION AND SUBTRACTION OF DECIMALS
Example: Subtract 44.6 –
Arrange the numbers so that the decimal points are directly under each other
Add zeroes so that the numbers have the same number of places to the right of the decimal point

13. ADDITION AND SUBTRACTION OF DECIMALS
Subtract each column of numbers
Place the decimal point in the difference directly under the other decimal points

14. MULTIPLYING DECIMALS
Multiply decimals using the same procedure as with whole numbers
Count the number of decimal places in both the multiplier and multiplicand
Begin counting from the last digit on the right of the product and place the decimal point the same number of places as there are in both the multiplicand and multiplier

15. MULTIPLYING DECIMALS Example: Multiply 60.412  0.53
Align the numbers on the right
Multiply as with whole numbers

16. MULTIPLYING DECIMALS
Since has 3 digit to the right of the decimal and has 2 digits to the right of the decimal, the answer should have 5 digits to the right of decimal point
Move the decimal point 5 places from the right

17. DIVIDING DECIMALS
Divide using the same procedure as with whole numbers
Move the decimal point of the divisor as many places as necessary to make it a whole number
Move the decimal point in the dividend the same number of places to the right
Divide and place the decimal point in the answer directly above the decimal point in the dividend

18. DIVIDING DECIMALS Example: Divide 0.3380 by 0.52
Move decimal point 2 places to the right in the divisor
Move the decimal point 2 places to the right in the dividend
Place decimal point in the quotient directly above the dividend and divide

19. DIVIDING BY POWERS OF 10
Since division is the inverse of multiplication, dividing by 10 is the same as multiplying by or 0.1
Dividing a number by 10, 100, 1,000, and so on is the same as multiplying by 0.1, 0.01,
To divide by 10, 100, 1,000, move the decimal point in the dividend as many places to the left as there are zeroes in the divisor

20. POWERS OF DECIMALS
Two or more numbers multiplied to produce a given number are factors of the given number
A power is the product of two or more equal factors
An exponent shows how many times a number is taken as a factor. It is smaller than the number, above the number, and to the right of the number

21. POWERS OF DECIMALS Example: Evaluate 0.83
The power 3 means to multiply 0.8 by itself 3 times
It is read “0.8 to the third power” or “0.8 cubed”
0.8 ×0.8 × 0.8 × = 0.512

22. POWERS OF DECIMALS Example: Evaluate (1.4 × 0.3)2
Perform the operation in parentheses first
1.4 × 0.3 = 0.42
Raise the result to the power of 2
0.42 × 0.42 =

23. ROOTS
The root of a number is a quantity that is taken two or more times as an equal factor of a number
Finding a root is the opposite or inverse operation of finding a power
The radical symbol () is used to indicate the root of a number
Index indicates the number of times a root is to be taken as an equal factor to produce the given number
Note: Index 2 for square root is usually omitted

24. ROOTS Example: Evaluate
This means to find the number that can be multiplied by itself to equal 144
Since 12 × 12 = 144, the is 12
This means to find the number that can be multiplied by itself three times to equal 125
Since 5 × 5 × 5 = 125, the is 5

25. ORDER OF OPERATIONS Order of operations including powers and roots is:
Parentheses
Fraction bar and radical symbol are used as grouping symbols
For parentheses within parentheses, do innermost parentheses first
Powers and Roots
Multiplication and division from left to right
Addition and subtraction from left to right

26. ORDER OF OPERATIONS Example: Multiply:
Add:
– 1.37 = – 1.37
Subtract:
11.02 – 1.37 = 9.65

27. PRACTICAL PROBLEMS
A certain 6-cylinder automobile engine produces 1.07 brake horsepower for each cubic inch of piston displacement
Each piston displaces cubic inches
Find the total brake horsepower of the engine to the nearest whole horsepower

28. PRACTICAL PROBLEMS
Determine the total number of cubic inches for the 6 cylinders
Determine the total horsepower
The total horsepower is 186