Chapter 4. Decimals. Introduction to Decimals. 4.1. Decimal Notation and Writing Decimals in Words.
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Chapter 4
Decimals
Introduction to Decimals
4.1
Decimal Notation and Writing Decimals in Words
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. Place names and place values for the decimal parts are also shown.
Writing and Reading Decimals in Words
decimal part
whole number part
Write the decimal 143.056 in words.
143.056
one hundred forty-three
and
fifty-six thousandths
Examples
Writing Decimals in Standard Form
whole-number part
decimal
decimal part
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
Examples
Writing Decimals as Fractions
Examples
1 decimal place
1 zero
3 decimal places
3 zeros
1 decimal place
1 zero
3 decimal places
3 zeros
Examples
37
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.
3
7
10
10
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
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.
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
5
<
3
35.638
<
35.657
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
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
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.
tenths place
digit to the right
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
Example
Round 0.5942 to the nearest thousandth.
Step 1: Locate the digit to the right of the given place value.
0.5942
2 is to the right of the thousandth place value.
Step 2: Since the digit to the right is less than 5, we delete it and all digits to its right.
Thus 0.5942 rounded to the nearest thousandth is 0.594
Example
Round $0.067 to the nearest cent.
Step 1: Locate the digit to the right of the given place value.
$0.067
7 is to the right of the hundredths place value
Step 2: Since the digit to the right is more than 5, we round up.
Thus $0.067 rounds to $0.07.
Example
An aquarium costs $245.69. Round the price to the nearest dollar.
The nearest dollar means the ones place. Locate the digit to the right of the ones place.
$245.69
6 is to the right of the ones place value
Thus $245.69 rounds to $246.00.