Decimals

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Decimals
Chapter Five
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Introduction to Decimals
Section 5.1
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Like fractional notation, decimal notation is
used to denote a part of a whole. Numbers written
in decimal notation are called decimal numbers,
or simply decimals. The decimal 16.734 has three
parts.
16.743
Whole- number part
Decimal part
Decimal point
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The position of each digit in a number determines
its place value.
hundred-thousandths
thousandths
hundreds
tens
tenths
hundredths
ten-thousandths
ones
1 6 7 3 4
Place Value
100
10
1
decimal point
5
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16.734
The digit 3 is in the hundredths place, so its
value is 3 hundredths or .
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Writing (or Reading) a Decimal in Words

• Step 1. Write the whole-number part in words.
• Step 2. Write and for the decimal point.
• Step 3. Write the decimal part in words as
  though it were a whole number, followed by the
  place value of the last digit.

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Writing a Decimal in Words

• Write the decimal 143.056 in words.

143.056
one hundred forty-three
and
fifty-six thousandths
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A decimal written in words can be written in
standard form by reversing the procedure.
Writing Decimals in Standard Form
Write one hundred six and five hundredths in
standard form.
one hundred six and five hundredths
5 must be in the hundredths place
106
.
05
10
Helpful Hint

• When writing a decimal from words to decimal
  notation, make sure the last digit is in the
  correct place by inserting 0s after the decimal
  point if necessary.
• For example,
• three and fifty-four thousandths is 3.054

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Writing Decimals as Fractions
Once you master writing and reading decimals
correctly, then you write a decimal as a fraction
using the fractions associated with the words you
use when you read it.
0.9 is read nine
tenths and written as a fraction as

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twenty-one hundredths and written as a fraction
as
0.21 is read as
0.011 is read as eleven thousandths and written
as a fraction as
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2 zeros
3 decimal places
3 zeros
2 decimal places
Notice that the number of decimal places in a
decimal number is the same as the number of zeros
in the denominator of the equivalent fraction. We
can use this fact to write decimals as fractions.
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Comparing Decimals
One way to compare decimals is to compare their
graphs on a number line. Recall that for any two
numbers on a number line, the number to the left
is smaller and the number to the right is larger.
To compare 0.3 and 0.7 look at their graphs.
0
1
0.3
0.7
0.3 lt 0.7 or 0.7 gt 0.3
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Comparing decimals by comparing their graphs on a
number line can be time consuming, so we compare
the size of decimals by comparing digits in
corresponding places.
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Comparing Two Positive Decimals
Compare digits in the same places from left to
right. When two digits are not equal, the number
with the larger digit is the larger decimal. If
necessary, insert 0s after the last digit to the
right of the decimal point to continue
comparing. Compare hundredths place digits

35.638
35.657
3
5
lt
35.638
35.657
lt
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Helpful Hint
For any decimal, writing 0s after the last digit
to the right of the decimal point does not change
the value of the number.
8.5 8.50 8.500, and so on When a whole
number is written as a decimal, the decimal point
is placed to the right of the ones digit. 15
15.0 15.00, and so on
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Rounding Decimals
We round the decimal part of a decimal number in
nearly the same way as we round whole numbers.
The only difference is that we drop digits to the
right of the rounding place, instead of replacing
these digits by 0s. For example,
63.782 rounded to the nearest hundredth is
63.78
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Rounding Decimals To a Place Value to the Right
of the Decimal Point

• Step 1. Locate the digit to the right of the
  given place value.
• Step 2. If this digit is 5 or greater, add 1 to
  the digit in the given place value and drop all
  digits to the right. If this digit is less than
  5, drop all digits to the right of the given
  place.

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Rounding Decimals to a Place Value

• Round 326.4386 to the nearest tenth.

Locate the digit to the right of the tenths place.
326.4386
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 326.4
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