Introduction to decimals
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Introduction to Decimals. 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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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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1 a part of a whole. Numbers written in decimal notation are called

1

1

10

1000

100,000

1

1

100

10,000

The position of each digit in a number determines its place value.

hundred-thousandths

hundreds

tens

tenths

hundredths

thousandths

ten-thousandths

ones

1 6 7 3 4

Place Value

100

10

1

decimal point


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Notice that the value of each place is a part of a whole. Numbers written in decimal notation are called

of the value of the place to its left.

1

10


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3 a part of a whole. Numbers written in decimal notation are called

100

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 a part of a whole. Numbers written in decimal notation are called

  • 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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A decimal written in words can be written in standard form by reversing the procedure.

Writing Decimals in Standard Form


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thousandths place by reversing the procedure.

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 by reversing the procedure.

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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21 by reversing the procedure.

100

11

1000

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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37 by reversing the procedure.

29

=

0

.

37

=

0

.

029

100

1000

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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3 by reversing the procedure.

7

10

10

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

0.3

0.7

1

0.3 < 0.7 or 0.7 > 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 line can be time consuming, so we compare the size of decimals by comparing digits in corresponding places.

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

<

35.638

<

35.657


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Helpful Hint line can be time consuming, so we compare the size of decimals by comparing digits in corresponding places.

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 line can be time consuming, so we compare the size of decimals by comparing digits in corresponding places.

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.