1. UNIT 2
Decimal Fractions

2. Key Terms Continuing number Decimal Decimal fraction Decimal place
Decimal system
Multiplier

3. Understanding Decimal Fractions

4. Reading Decimals (continues) Decimal Read as 0.1 One tenth 0.01
One hundredth
0.001
One thousandth
0.0001
One ten-thousandth
One hundred-thousandth
One millionth
(continues)

5. Reading Decimals
When reading a whole number and a decimal fraction, the decimal point is read as “and” or “point”
Example: 1.5 = One and five tenths
It is a good practice to place a zero (0) before the decimal point when using decimal fractions
Example: 0.75
(continues)

6. Reading Decimals Note place value of decimal point
Example: 0.67
Read number to right of decimal point
Example: sixty-seven
Use the name that applies to the decimal place of last number
Example: sixty-seven one hundredths

7. Power of 10 Process of multiplying tens together
Number of tens determines the power
All decimals are fractions with denominator of 10 or power of 10

8. Common to Decimal Fractions
Divide denominator into numerator
Place decimal point after numerator
Place decimal point in quotient directly over decimal point in numerator
Place 0 after decimal point in numerator
Divide, placing 0 before decimal point in quotient

9. Check Your Work
Always double-check the accuracy of your work by multiplying the quotient by the denominator (divisor)
This should give you the same number as your numerator (dividend)

10. Decimal to Common Fractions
Read decimal fraction aloud
Numerator is number to right of decimal
Denominator is number of decimal places, expressed by power of 10
Reduce to lowest terms

11. Adding Decimals Arrange numbers in column Line up decimal points
Add numbers as you would whole numbers
Place decimal point directly under decimal points in problem

12. Reminder!
When adding or subtracting decimals, you may use a zero (0) after the last digit to help you form even columns
Example: = _____
0.125
0.265

13. Subtracting Decimals Arrange numbers in column Line up decimal points
Subtract numbers as you would whole numbers
Place decimal point directly under decimal points in problem

14. Multiplying Decimals Multiply as you would whole numbers
Count total number of decimal places in multiplier and number to be multiplied
Starting on right of product, count number of decimal places from previous step
Always count places from right to left

15. Multiplying by Power of 10
Move decimal one place to the right for each zero in the multiplier
Example: 0.5 x 10 = 5.0
Example: 0.5 x 100 = 50.0
Example: 0.5 x 1,000 = 500.0

16. Dividing Decimals by Whole Numbers
Place decimal point in quotient directly over decimal point in dividend
Divide dividend by divisor
Double-check accuracy by multiplying quotient by divisor (answer equals dividend)

17. When the Divisor Is Larger Than the Dividend
Place decimal point in quotient on answer line above decimal point in dividend
Place zero (0) before decimal point
(continues)

18. When the Divisor Is Larger Than the Dividend
If whole number will not go into first number, place a zero (0) immediately after decimal point
Continue placing zeros until you are able to divide the numbers

19. Dividing Whole Numbers by Decimals
Place decimal point at the end of the whole number of the dividend
Place a zero after the decimal point
Move the decimal point to the end of the divisor
(continues)

20. Dividing Whole Numbers by Decimals
Move the decimal point the same number of places to the right in the dividend that you moved it in the divisor
Divide as usual

21. Dividing Decimals by Decimals
Make divisor a whole number by moving the decimal point to the right
Move the decimal point the same number of spaces in the dividend that you did in the divisor
(continues)

22. Dividing Decimals by Decimals
Place a decimal point on the answer line above the new decimal point in the dividend
Place a zero before the marked-off decimal point
Divide as usual

23. Percentage Percent: “per hundred” Whole numbers are expressed as 100%
% = denominator of 100
Percent indicates parts of a whole
To express percents as fractions, remove the percent sign and write as numerator of fraction with denominator of 100
Example: 75% = 75/100
(continues)

24. Percentage If percent is mixed number, numerator is divided by 100
Example: 1.5% = 150/100
To express fractions as percents, multiply by 100 and add the percent sign
Example: 3/4 = 75%

25. Quantity of Percents Express percent as a decimal or fraction
Multiply whole number by decimal or fraction
Example: How much is 10% of 80?
10% = 0.10 = 10/100 or 1/10
80 x 0.10 = 8.0
80 x 1/10 = 8