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DecimalsDecimals
Chapter FiveChapter Five
Introduction to DecimalsIntroduction to Decimals
Section 5.1
Whole- number part
Decimal point
Decimal part
16.743
Like fractional notation, decimal notation Like fractional notation, decimal notation is used to denote a part of a whole. is used to denote a part of a whole. Numbers written in decimal notation are Numbers written in decimal notation are called called decimal numbersdecimal numbers, or simply , or simply decimalsdecimals. The decimal 16.734 has three . The decimal 16.734 has three parts.parts.
3
The position The position of each digit of each digit in a number in a number determines its determines its place value.place value.
1 6 7 3 4 o
nes
tho
usa
nd
ths
hu
nd
red
s
ten
s
ten
ths
hu
nd
red
ths
ten
-th
ou
san
dth
s
hu
nd
red
-th
ou
san
dth
s
Place Value
decimal point
100 10 11
1001
10,000
110
1100,000
11000
4
Notice that the value of each place is Notice that the value of each place is
of the value of the place to its left.of the value of the place to its left.
110
5Martin-Gay, Prealgebra, 5ed
16.73416.734
The digit 3 is in the hundredths place, soThe digit 3 is in the hundredths place, so
its value is 3 hundredths or .its value is 3 hundredths or .3
100
6Martin-Gay, Prealgebra, 5ed
Writing (or Reading) a Decimal Writing (or Reading) a Decimal in Wordsin Words
Step 1. Write the whole-number part in words.Step 1. Write the whole-number part in words.Step 2. Write “and” for the decimal point.Step 2. Write “and” for the decimal point.Step 3. Write the decimal part in words as Step 3. Write the decimal part in words as
though it were a whole number, though it were a whole number, followed by the place value of the last followed by the place value of the last digit.digit.
7Martin-Gay, Prealgebra, 5ed
Writing a Decimal in WordsWriting a Decimal in Words
Write the decimal 143.056 in words.Write the decimal 143.056 in words.
143.056
one hundred forty-three and fifty-six thousandths
whole-number part decimal part
8Martin-Gay, Prealgebra, 5ed
A decimal written in words can be written A decimal written in words can be written in standard form by reversing the in standard form by reversing the procedure.procedure.
Writing Decimals in Writing Decimals in Standard FormStandard Form
Write one hundred six and five hundredths in Write one hundred six and five hundredths in standard form.standard form.
one hundred six and five hundredths
106 . 05
decimal partwhole-number part decimal
5 must be in thehundredths place
5 must be in thehundredths place
9
Helpful Hint
When writing a decimal from words to When writing a decimal from words to decimal notation, make sure the last decimal notation, make sure the last digit is in the correct place by inserting digit is in the correct place by inserting 0s after the decimal point if necessary.0s after the decimal point if necessary.
For example, For example,
three and fifty-four thousandths is 3.054 three and fifty-four thousandths is 3.054
thousandths place
10Martin-Gay, Prealgebra, 5ed
Once you master writing and reading Once you master writing and reading decimals correctly, then you write a decimals correctly, then you write a decimal as a fraction using the fractions decimal as a fraction using the fractions associated with the words you use when associated with the words you use when you read it.you read it.
0.90.9
is read “nine tenths” and written as a is read “nine tenths” and written as a fraction asfraction as
9
10
Writing Decimals as FractionsWriting Decimals as Fractions
11Martin-Gay, Prealgebra, 5ed
twenty-one hundredthstwenty-one hundredths
and written as a fraction asand written as a fraction as
2121
100100
0.011 is read as 0.011 is read as
eleven thousandthseleven thousandths
and written as a fraction asand written as a fraction as
1111
10001000
0.21 is read as0.21 is read as
12Martin-Gay, Prealgebra, 5ed
Notice that the number of decimal places Notice that the number of decimal places in a decimal number is the same as the in a decimal number is the same as the number of zeros in the denominator of the number of zeros in the denominator of the equivalent fraction. We can use this fact equivalent fraction. We can use this fact to write decimals as fractions.to write decimals as fractions.
0 3737
100.
2 decimal places
2 zeros
0 02929
1000.
3 decimal places
3 zeros
13
Comparing DecimalsComparing Decimals
One way to compare decimals is to compare their One way to compare decimals is to compare their graphs on a number line. Recall that for any two graphs on a number line. Recall that for any two numbers on a number line, the number to the left numbers on a number line, the number to the left is smaller and the number to the right is larger. To is smaller and the number to the right is larger. To compare 0.3 and 0.7 look at their graphs.compare 0.3 and 0.7 look at their graphs.
0 10.3
3
10
7
10
0.70.3 < 0.7 or
0.7 > 0.314
Martin-Gay, Prealgebra, 5ed
Comparing decimals by comparing their Comparing decimals by comparing their graphs on a number line can be time graphs on a number line can be time consuming, so we compare the size of consuming, so we compare the size of decimals by comparing digits in decimals by comparing digits in corresponding places.corresponding places.
15Martin-Gay, Prealgebra, 5ed
Comparing Two Positive Comparing Two Positive DecimalsDecimals
Compare digits in the same places from left to Compare digits in the same places from left to right. When two digits are not equal, the number right. When two digits are not equal, the number with the larger digit is the larger decimal. If with the larger digit is the larger decimal. If necessary, insert 0s after the last digit to the necessary, insert 0s after the last digit to the right of the decimal point to continue comparing.right of the decimal point to continue comparing.
Compare hundredths place digits Compare hundredths place digits
3 5<35.638 35.657<
35.638 35.657
16Martin-Gay, Prealgebra, 5ed
Helpful Hint
For any decimal, writing 0s after the last For any decimal, writing 0s after the last digit to the right of the decimal point does digit to the right of the decimal point does not change the value of the number. not change the value of the number.
8.5 8.5 == 8.50 8.50 == 8.500, and so on 8.500, and so on
When a whole number is written as a When a whole number is written as a decimal, the decimal point is placed to the decimal, the decimal point is placed to the right of the ones digit.right of the ones digit.
15 15 == 15.0 15.0 == 15.00, and so on 15.00, and so on 17Martin-Gay, Prealgebra, 5ed
We We round the decimal partround the decimal part of a decimal of a decimal number in nearly the same way as we number in nearly the same way as we round whole numbers. The only difference round whole numbers. The only difference is that we drop digits to the right of the is that we drop digits to the right of the rounding place, instead of replacing these rounding place, instead of replacing these digits by 0s. For example,digits by 0s. For example,
Rounding DecimalsRounding Decimals
63.782 rounded to the nearest hundredth is63.782 rounded to the nearest hundredth is
63.7863.7818
Martin-Gay, Prealgebra, 5ed
Rounding Decimals To a Place Value to Rounding Decimals To a Place Value to the Right of the Decimal Pointthe Right of the Decimal Point
Step 1. Locate the digit to the right of the Step 1. Locate the digit to the right of the given place value.given place value.
Step 2. If this digit is 5 or greater, add 1 to Step 2. If this digit is 5 or greater, add 1 to the digit in the given place value and the digit in the given place value and drop all digits to the right. If this drop all digits to the right. If this digit is less than 5, drop all digits to digit is less than 5, drop all digits to the right of the given place.the right of the given place.
19Martin-Gay, Prealgebra, 5ed
Rounding Decimals to a Place ValueRounding Decimals to a Place Value
Round 326.4386 to the nearest tenth.Round 326.4386 to the nearest tenth.Locate the digit to the right of the tenths place.
326.4386
tenths place
digit to the right
Since the digit to the right is less than 5, drop it and all digits to its right.
326.4386 rounded to the nearest tenths is 326.420Martin-Gay, Prealgebra, 5ed