1. Chapter 2
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Decimals

2. Lesson 2.1 Reading, Determining the Value of, Adding, Subtracting, and Multiplying a Decimal
1. Reading and writing decimal numbers
2. Determining the value of decimal fractions
3. Adding, subtracting, multiplying, and dividing decimals
4. Multiplying and dividing decimals by 10 or a power of 10
5. Multiplying and dividing decimals by 0.1 or a multiple of 0.1
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3. Decimal Numbers For example: 23.405 Writing decimal numbers
Reading decimal numbers
For example:
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4. Decimal Fractions
Place decimal numbers in a vertical column with aligned decimal points.
For example: 7.45
0.206
34.2
Of 0.75, 0.235, and 0.008, which decimal fraction has the greatest value?
Of 1.5, 1.007, 0.95, and 0.432, which decimal fraction has the least value?
Of 0.75, 0.235, and 0.008, which decimal fraction has the greatest value?
Compare the numbers to the right of the decimal point for all fractions. In this case, 0.75 has the greatest value because 7 is larger than 2 and 0.
Of 1.5, 1.007, 0.95, and 0.432, which decimal fraction has the least value?
Start by comparing the whole numbers to the left of the decimal point. Then compare the numbers to the right of the decimal point. In this case, has the least (smallest) value.  
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5. Adding and Subtracting Decimals (1 of 2)
Place decimal numbers in a vertical column with aligned decimal points.
Add zeros to complete the columns as needed.
Add or subtract each column as indicated.
Place the decimal point in the sum or difference.
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6. Adding and Subtracting Decimals (2 of 2)
For examples:
Add:
Subtract: − 0.51
Add:
Add these numbers. Remember to place the decimal point for the sum directly below the decimal points in the column. The sum is
Subtract: − 0.51
Subtract 0.51 from Remember to place the decimal point for the sum directly below the decimal points in the column. The difference is
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7. Multiplying Decimals (1 of 2)
Place the decimal number with the fewer digits underneath the other number.
Multiply the decimal numbers as if the decimals were not present.
Count the number of digits to the right of the decimal point for each decimal number being multiplied.
Place the decimal point in the final number.
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8. Multiplying Decimals (2 of 2)
For examples:
Multiply: × 2.1
Multiply: × 0.51
Multiply: × 2.1
The number of digits to the right of the decimal point is 3, and the answer is Note: It is possible to check your answer by estimating what you expect to get using whole numbers. If you round up to 14 and 2.1 down to 2, then you can multiply 14 and 2 to get 28. Therefore, the final answer seems reasonable.
Multiply: × 0.51
The number of digits to the right of the decimal point is 5, and the answer is
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9. Multiplying a Decimal by 10 or a Power of 10
Move the decimal point to the right when multiplying.
For example: × 10,000
When multiplying a decimal number by a power of 10, move the decimal point to the right by the same number of spaces as the number of zeros in the multiplier (power of 10).
Multiply: × 10,000
The answer is 4580.
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10. Multiplying a Number by 0.1 or a Multiple of 0.1
Move the decimal point to the left when multiplying.
For example: × 0.01
When multiplying a decimal number by a multiple of 0.1, move the decimal point to the left by the same number of spaces as there are numbers to the right of the decimal point in the multiplier (multiple of 0.1).
Multiply: × 0.01
The answer is
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11. Lesson 2.2 Rounding, Dividing, and Converting a Decimal
1. Adding, subtracting, multiplying, and dividing decimals 2. Rounding decimal fractions to an indicated place value 3. Multiplying and dividing decimals by 10 or a power of Multiplying and dividing decimals by 0.1 or a multiple of Converting a decimal fraction to a proper fraction 6. Converting a proper fraction to a decimal fraction
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12. Rounding a Decimal Fraction (1 of 2)
Find the number to the right of the place value desired.
If the number is 5, 6, 7, 8, or 9, add 1 to the number in the place value desired.
If the number is 0, 1, 2, 3, or 4, drop numbers to the right.
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13. Rounding a Decimal Fraction (2 of 2)
For examples:
Round to the nearest tenth.
Round to the nearest hundredth.
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14. Dividing Decimals (1 of 3)
Place a caret (^) to the right of the last number in the divisor.
Count the number of digits between the decimal point and the decimal in the divisor.
Place a caret (^) in the dividend.
The technique here is to divide whole numbers rather than decimal numbers. So, first you need to determine which decimal number has more digits to the right of the decimal point. Then place a caret to the right of each decimal number, but the caret should be the same number of spaces to the right of the decimal place for each decimal number.
It might be necessary to add zeros to the right of the decimal numbers when placing the caret the correct number of spaces to the right of the decimal point.
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15. Dividing Decimals (2 of 3)
Place a decimal point on the quotient line directly above the caret (^).
Divide, extending the decimal fraction three places to the right of the decimal point.
Zeros may be added to extend the decimal fraction dividend.
Round the quotient to the nearest hundredth.
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16. Dividing Decimals (3 of 3)
For examples:
Divide: ÷ 2.1
Divide: ÷ 0.517
Divide: ÷ 2.1
In this example, would become 13.75^, and 2.1 would become 2.10^ (note that a 0 had to be added to 2.1). The answer, rounded to the nearest hundredth, is 6.55 (rounding up from 6.547).
Divide: 0.87 ÷ 0.517
In this example, would become 0.517^, and 0.87 would become 0.870^ (note that a 0 had to be added to 0.87). The answer, rounded to the nearest hundredth, is 1.68 (rounding down from 1.682).
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17. Dividing a Decimal by 10 or a Multiple of 10
Move the decimal point to the left when dividing.
For example:
Divide: 2.56 ÷ 100
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18. Dividing a Number by 0.1 or a Multiple of 0.1
Move the decimal point to the right when dividing.
For example:
Divide: 2.56 ÷ 0.001
When dividing a decimal number by a multiple of 0.1, move the decimal point to the right by the same number of spaces because there are numbers to the right of the decimal point in the divisor (multiple of 0.1).
Divide: 2.56 ÷ 0.001
The answer is 2560.
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19. Converting a Decimal Fraction to a Proper Fraction (1 of 2)
Remove the decimal point and the zero to the left of it.
Determine the numerator.
Determine the denominator.
Reduce to lowest terms.
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20. Converting a Decimal Fraction to a Proper Fraction (2 of 2)
For example:
Convert: 0.35
Convert: 0.35
In this case, the numerator is 35, and the denominator is 100. That makes the final answer 35/100. (This proper fraction can be reduced to 7/20.)
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21. Converting a Proper Fraction to a Decimal Fraction (1 of 2)
Divide the numerator by the denominator.
Extend the decimal fraction to the desired number of places.
Be sure to place a zero to the left of the decimal point.
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22. Converting a Proper Fraction to a Decimal Fraction (2 of 2)
For examples:
Convert: 1 3
Convert: 9 11
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