Math 40
Prealgebra
Section 5.1 – Introduction to Decimals
5.1 Introduction to Decimals
There is 1 part shaded out of a total of 10.
Fraction:
1
10
1
 0.1
10
Decimal: 0.1
There is 1 part shaded out of a total of 100.
1
 0.01
100
Fraction:
1
100
Decimal: 0.01
15 . 3487
Whole Number Part
Fractional Part
Decimal Point
Place Values
Let’s look at the number,
365.24219
(three hundred sixty-five and twenty-four thousand two hundred nineteen hundred-thousandths)
Each digit of the number has a specific place value, as shown in the chart below.
tenths
hundredths
thousandths
ten-thousandths
hundred-thousandths
millionths
9
decimal point
1
ones
2
tens
4
hundreds
2
thousands
.
ten thousands
5
hundred thousands
6
millions
3
1,000,000
100,000
10,000
1,000
100
10
1
.
1
10
1
100
1
1000
1
10000
1
100000
1
1000000
Whole Number Part
.
Fractional Part
1
2015 Worrel
Math 40
Prealgebra
Section 5.1 – Introduction to Decimals
How to Read a Decimal Number
1. Pronounce the whole number part (the part left of the decimal point) as you would
any whole number.
2. Say the word “and” to indicate the presence of the decimal point.
3. State the fractional part (the part right of the decimal point) as you would any whole
number, followed by the name of the place value of the rightmost digit.
Note:
When reading or writing numbers, the word “and” should not be used unless indicating the
presence of a decimal point.
Example 1: Pronounce the given decimal number. Write your answer out in words.
Solution:
789.1345
789 . 1345
seven hundred eighty-nine and one thousand three hundred forty-five ten-thousandths
seven hundred eighty-nine and one thousand three hundred forty-five ten-thousandths
You Try It 1: Pronounce the given decimal number. Write your answer out in words.
1,982.35
Example 2: Explain why “four hundred and thirty-four and two tenths” is an incorrect pronunciation of the
decimal number, 434.2.
Solution: “four hundred and thirty-four and two tenths”
The word “and” is used twice in the pronunciation. Remember, the word “and” should only be used
to indicate the presence of a decimal point. It should appear at most one time in a pronunciation of a
number. The correct pronunciation of 434.2 is “four hundred thirty-four and two tenths.”
You Try It 2: Pronounce the given decimal number. Write your answer out in words.
Example 3: Pronounce the given decimal number. Write your answer out in words.
Solution:
286.9
5,678.123
5,678 . 123
five thousand, six hundred seventy-eight
and one hundred twenty-three thousandths
five thousand, six hundred seventy-eight and one hundred twenty-three thousandths
2
2015 Worrel
Math 40
Prealgebra
Section 5.1 – Introduction to Decimals
You Try It 3: Pronounce the given decimal number. Write your answer out in words.
Example 4: Pronounce the given decimal number. Write your answer out in words.
Solution:
nine hundred ninety-five
7,002.207
995.4325
995 . 4325
and four thousand three hundred twenty-five ten-thousandths
nine hundred ninety-five and four thousand three hundred twenty-five ten-thousandths
You Try It 4: Pronounce the given decimal number. Write your answer out in words.
500.1205
Changing a Decimal to an Improper Fraction
1. Create a fraction.
2. Place the entire number in the numerator without the decimal point.
3. Put the place value of the last digit in the denominator.
Example 5: Change the following decimal numbers to improper fractions.
a) 1.2345
b) 27.198
Solution: a) 1.2345
b) 27.198
 1 
the place value of the last digit is the ten-thousandths 

 10000 
12345 12345
12345


10000
10000
 1 
the place value of the last digit is the thousandths 

 1000 
27198 27198
27198


1000
1000
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2015 Worrel
Math 40
Prealgebra
Section 5.1 – Introduction to Decimals
You Try It 5: Change 17.205 to an improper fraction.
Note:
Another way to figure out the denominator, is to put a 1 in the denominator, count the
number of digits after the decimal point, and put the same number of zeros in the
denominator.
EX) 23.786
there are 3 digits after the decimal point

23786

23786
1000
there are 3 zeros after the 1
Example 6: Change each of the following decimals to fractions reduced to lowest terms.
a) 0.35
b) 0.125
 1 
the place value of the last digit is the hundredths 

 100 
35 35
35  5
7
7




100 100  5 20
20
Solution: a) 0.35
 1 
the place value of the last digit is the thousandths 

 1000 
125 125
125  125 1
1




1000 1000  125 8
8
b) 0.125
You Try It 6: Change 0.375 to a fraction reduced to lowest terms.
4
2015 Worrel
Math 40
Prealgebra
Section 5.1 – Introduction to Decimals
REVIEW from Section 1.1: Steps for Rounding Numbers
1. Circle the number in the place value you wish to round (this is your rounding digit)
2. Look at the digit to the right of your rounding digit, underline it (this is your testing digit)
a) If the test digit is less than 5 (meaning it is 0, 1, 2, 3, or 4), the rounding digit stays
the same and all digits to the right of it turn into zeros.
b) If the test digit is 5 or more (meaning 5, 6, 7, 8, or 9), you add 1 to the rounding digit
and all digits to the right of it turn into zeros.
Note: Zeros at the very end of a number, after the decimal point, are not needed.
Ex) 3.75000  3.75
Example 7: Round the number 37.9475 to the nearest thousandth.
Solution:
37.9475
rounding digit
testing digit
Since the testing digit, 5, is 5 or more, we will add 1 to the rounding digit and turn all digits to the
right into zeros. 37.9475  37.9480 But remember, if we have zeros at the very end of a number,
after the decimal point, we do not need them.
So, 37.9475  37.948
You Try It 7: Round the number 9.2768 to the nearest hundredth.
Example 8: Round the number 2.7963 to the nearest hundredth.
Solution:
2.7963
rounding digit
testing digit
Since the testing digit, 6, is 5 or more, we will add 1 to the rounding digit and turn all digits to the
right into zeros. Note that the rounding digit is 9, so if we add 1 to it, it becomes 10. This will effect
the digit to its the left. In other words, if the 9 needs to change to 10, then the 7 will change to an 8.
2.8000  2.8000 But remember, if we have zeros at the very end of a number, after the decimal
point, we do not need them.
So, 2.7963  2.8
You Try It 8: Round the number 945.9721 to the nearest tenth.
5
2015 Worrel
Math 40
Prealgebra
Section 5.1 – Introduction to Decimals
Example 9: Round the number 113.246 to the nearest tenth.
Solution:
113.246
rounding digit
testing digit
Since the testing digit, 4, is less than 5, the rounding digit will stay the same and we will turn all
digits to the right into zeros. 113.246  113.200 But remember, if we have zeros at the very end of a
number, after the decimal point, we do not need them.
So, 113.246  113.2
You Try It 9: Round the number 65.1234 to the nearest thousandth.
Note:
Zeros at the end of a number, after the decimal point, can be added or deleted
without changing the value of the number.
Ex) 314.5  314.50  314.500  314.5000 
Ex) 7.8000  7.800  7.80  7.8 
Comparing POSITIVE Decimal Numbers
1. Add trailing zeros so that both numbers have the same number of decimal places.
2. Compare the digits in each place, moving left to right.
3. As soon as you find two digits in the same place value that are different, compare those
digits. The number with the larger number in that place value, is the larger number.
Example 10: Compare 4.25 and 4.227.
Solution: Add one zero to the end of 4.25, so that both numbers have the same number of decimal places.
4.250
4.227
Same digits
Same digits
Different digits
Since 5 (from the top number) is larger than 2 (from the bottom number), the top number is larger.
Hence, 4.25  4.227 .
You Try It 10: Compare 8.34 and 8.348.
6
2015 Worrel
Math 40
Prealgebra
Section 5.1 – Introduction to Decimals
Comparing NEGATIVE Decimal Numbers
1. Add trailing zeros so that both numbers have the same number of decimal places.
2. Compare the digits in each place, moving left to right.
3. As soon as you find two digits in the same place value that are different, compare those
digits. The number with the larger number in that place value, is the smaller number.
Notice this is the opposite of what we did with positive decimal numbers.
Note: The larger the negative number is the smaller its value becomes.
Ex) 240  5 , 240 is less than 5 because it is a larger negative.
Example 11: Compare 9.57813 and 9.57 .
Solution: Add one zero to the end of 9.57 , so that both numbers have the same number of decimal places.
 9.57813
 9.57000
Same digits
Same digits
Same digits
Different digits
Since 8 (from the top number) is larger than 0 (from the bottom number) and these are negative
numbers, the top number is smaller.
Hence, 9.57813  9.576 .
You Try It 11: Compare 7.861 and 7.8 .
7
2015 Worrel