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Ch 1 Test Results
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2. Chapter 2
Decimals

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Objectives
Reading and writing decimal numbers
Determining the value of decimal fractions
Adding, subtracting, multiplying, and dividing decimals
Changing a decimal to a fraction
Changing a fraction to a decimal
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Decimal Numbers
Writing & reading decimal numbers
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What are the components of a decimal number?
A decimal number consists of an integer (whole number), a decimal point, and a decimal fraction. Whole numbers are written to the left of the decimal point, and decimal fractions are written to the right of the decimal point.
How do you read a decimal number?
First, read the whole number, then read the decimal as “and,” and then read the decimal fraction. Example: Twenty-three and four hundred five thousandths.

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Decimal
The word "Decimal" really means "based on 10" (From Latin decima: a tenth part).
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Decimal Fractions
Which decimal fraction (0.75, 0.235, 0.008) has the greatest value?
Which decimal number (1.5, 1.007, 0.95, 0.432) has the least value?
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Which decimal fraction (0.75, 0.235, 0.008) 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.
Which decimal number (1.5, 1.007, 0.95, 0.432) 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.

7. Adding and Subtracting Decimals
Examples:
Add:
Subtract: – 0.51
In this class we will keep it simple, use your calculator
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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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Multiplying Decimals
Examples:
Multiply: × 2.1
Multiply: × 0.51
Use your calculator, we will not practice multiplication skills
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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

9. Multiplying a Decimal by 10 or a Power of 10
Move decimal point to right when multiplying.
Example:
0.458 × 10,000
4580
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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.

10. Multiplying a Number by 0.1 or a Multiple of 0.1
Move decimal point to left when multiplying.
Example:
43.58 × 0.01 =
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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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Dividing Decimals
Examples:
Divide: ÷ 2.1
Divide: 0.87 ÷ 0.517
Use your calculator
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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).

12. Dividing a Decimal by 10 or a Multiple of 10
Move decimal point to left when dividing.
Example:
2.56 ÷ 100 = 0.026
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When dividing a decimal number by a power of 10, move the decimal point to the left by the same number of spaces as the number of zeros in the divisor (power of 10).
Divide: 2.56 ÷ 100
The answer is

13. Dividing a Number by 0.1 or a Multiple of 0.1
Move decimal point to right when dividing.
Example:
2.56 ÷ = 2560
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When dividing a decimal number by a multiple of 0.1, move the decimal point to the right by the same number of spaces as 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.

14. Converting a Decimal Fraction to a Proper Fraction
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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The numerator simply consists of the digits to the right of the decimal point.
The denominator is a power of 10 with the same number of zeros as the number of digits to the right of the decimal point.

15. Converting a Decimal Fraction to a Proper Fraction (cont’d)
Example: Reduce to
Example: Reduce to 7 20
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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.)

16. Converting a Proper Fraction to a Decimal Fraction
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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17. Converting a Proper Fraction to a Decimal Fraction
Examples:
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Convert: 1/3
In most cases, unless instructed otherwise, it is acceptable to round decimal numbers to two decimal places (the nearest hundredth). The answer, rounded to the nearest hundredth, is 0.33.
Convert: 9/11
The answer, rounded to the nearest hundredth, is 0.82.

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Homework/classwork
Itty bitty dot song
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Bell Work 8/28
Which number has the least value?
0.2, 0.25, 0.025, 0.02
2.8, 2.82, 2.082, 2.822
Which number has the greatest value?
0.04, 0.45, 0.8, 0.86
1.202, 1.22, 1.2, 1.222
Change the decimal fraction to a proper fraction
0.005
0.6
Change the proper fraction to a decimal fraction
1/125
1/400
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