1. Unit 3
Decimal Fractions

2. DECIMAL FRACTIONS Written with a decimal point
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, read number as whole number.
Say name of place value of last digit to right.
0.567 is read “five hundred sixty-seven thousandths”
To read a mixed decimal (a whole number and a decimal fraction), read whole number, read word and at decimal point, and read decimal.
is read “forty-five and seven hundred fifty-three hundred thousandths”

4. ROUNDING DECIMAL FRACTIONS
Rounding rules:
Determine place value to which number is to be rounded
Look at digit immediately to its right
If digit is less than 5, drop it and all digits to its right
If digit is 5 or more, add 1 to digit in place to which you are rounding. Then drop all digits to its right

5. ROUNDING EXAMPLES Round 14.763 to the nearest hundredth
6 is in the hundredths place value, so look at 3. Since 3 is less than 5, leave 6 alone and drop 3.
Ans: 14.76
Round to the nearest ten thousandth
5 is in the ten thousandths place value, so look at 7. Since 7 is greater than 5, raise 5 to 6 and drop all digits to its right.
Ans:

6. CONVERTING FRACTIONS TO DECIMALS
Fractions can be converted to decimals by dividing the numerator by the denominator
Express 5/8 as a decimal fraction:
Ans
Place a decimal point after the 5 and add zeros to the right of the decimal point.
Bring the decimal point straight up in the answer. Divide. 8 20 16 40

7. CONVERTING DECIMALS TO 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
Change to a common fraction:
0.015 is read as fifteen thousandths

8. ADDITION AND SUBTRACTION
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

9. ADDITION AND SUBTRACTION
Perform the following operations:
13.475
3.537
– 1.476
Ans
Ans

10. MULTIPLICATION
Multiply decimals using same procedures as with whole numbers
Count total number of digits to right of decimal points in both numbers being multiplied
Begin counting from last digit on right in answer and place decimal point same number of places as there are total in both of the numbers being multiplied

11. MULTIPLICATION Multiply 62.4  1.73:
Since 62.4 has 1 digit to right of decimal and 1.73 has two points to right of decimal, answer should have 3 digits to right of decimal point
62.4
1.73
1 872
43 68
62 4
= Ans

12. DIVISION 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

13. DIVISION
Divide by 6.4:
Move decimal point 1 place to right in 6.4
Move decimal point 1 place to right in 2.432
Place decimal point straight up in the answer
Divide 2
5 12
.38 Ans

14. POWERS Product of two or more equal factors Appear slightly smaller
Located above and to right of number being multiplied

15. The power 3 means to multiply .4 by itself 3 times
POWERS
Evaluate each of the following powers:
.43
(2.5 × 3)2
The power 3 means to multiply .4 by itself 3 times
.43 = .4 × .4 × .4 = .064 Ans
Parentheses first: 2.5 × .3 = .75
(.75)2 = .75 × .75 = Ans

16. ROOTS
A quantity that is taken two or more times as an equal factor of a number
Finding a root is opposite operation of finding a power
Radical symbol () is used to indicate root of a number
Index indicates 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

17. FINDING ROOTS Determine the following roots:
This means to find the number that can be multiplied by itself to equal 64. Since 8 × 8 = 64, the = 8 Ans
This means to find the number that can be multiplied by itself three times to equal 27. Since 3 × 3 × 3 = 27, = 3 Ans
Note: Roots that are not whole numbers can easily be computed using a calculator

18. 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

19. ORDER OF OPERATIONS
Parentheses and grouping symbols (square root) first:
(1.2)2 + 6 ÷ 2
Powers next:
 2
Divide:
Add:
4.44 Ans

20. PRACTICE PROBLEMS Write the following numbers as words. a. 0.0027
Round to each of the following place values:
TENTHS
HUNDREDTHS
THOUSANDTHS
TEN
HUNDRED
MILLIONTHS

21. PRACTICE PROBLEMS (Cont)
Express each of the following as decimal fractions:
4. Express each of the following as fractions in lowest terms:
a b c
5. Perform the indicated operations: a b
c –
d – 16.97

22. PRACTICE PROBLEMS (Cont)
f × 3.46
g  .4
h  2.5 i
j. (12.2 × .2)2

23. Solutions Writing Rounding Twenty-seven ten thousandths
One hundred forty-three and forty-five hundredths
One and seven thousand three hundred sixty-eight millionths
Rounding
10.2
10.24
10.236

24. Solutions Convert to decimal Decimal to Fraction 0.5 0.875 0.9375 a b

25. Solutions Order of operations 0.7217 9.026 2.103 28.33 4.158 88.6798
0.03
6.13
0.027
5.9536 4
5.32
3.82