1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 3.5 Decimal Numbers and Fractions

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Change decimal numbers to fractions. o Change fractions to decimal numbers. o Operate with both fractions and decimal numbers.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Changing Decimal Numbers to Fractions To Change from Decimal Numbers to Fractions A terminating decimal number can be written in fraction form by writing a fraction with the following: 1.a numerator that consists of the whole number formed by all the digits of the decimal number, and 2.a denominator that is the power of ten that names the position of the rightmost digit.

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Changing Decimal Numbers to Fractions hundredths

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Changing Decimal Numbers to Fractions hundredths

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Changing Decimal Numbers to Fractions thousandths

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Changing Decimal Numbers to Fractions thousandths

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Changing Decimal Numbers to Fractions tenths or, as a mixed number, tenths

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Changing Fractions to Decimal Numbers

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 7: Changing Fractions to Decimal Numbers

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 8: Changing Fractions to Decimal Number Continuing to divide will give a remainder of 4 each time. The 3 will repeat without end.

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 8: Changing Fractions to Decimal Number (Cont.) We write where the three dots (called an ellipsis) mean “and so on” or to continue the pattern without stopping. Or, if we agree to round, we can write (to the nearest thousandth).

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 9: Changing Fractions to Decimal Number The remainder will repeat in sequence 1,3,2,6,4,5,1, and so on. Therefore, the digits in the quotient will also repeat in sequence. The six digits will repeat in the same pattern without end. We write

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Operating with Both Fractions and Decimal Numbers Notes In some cases changing fractions to decimal form may involve rounding the decimal form of a number and settling for an approximate answer. To have a more accurate answer, we may need to change the decimals to fraction form and then perform the operations.

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 10: Operating with Both Fractions and Decimal Numbers Find the sum in decimal form. Solution

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 11: Operating with Both Fractions and Decimal Numbers Determine whether is larger than 0.18 by changing to decimal form and then comparing the two numbers. Find the difference.

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 11: Operating with Both Fractions and Decimal Numbers (cont.) Solution Divide first.

18. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Thus is larger than 0.18 and their difference is 0.0075. Example 11: Operating with Both Fractions and Decimal Numbers (cont.) Now subtract.

19. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Convert the following to fraction form. 1.0.475 2. 2.9 3. 0.003 4. 1.17 Convert the following to decimal form. Write repeating decimals using bar notation. 5.6. 7. 8. 9. Find the sum in decimal form.

20. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1.2. 3. 4.5. 0.81256. 0.05 7.8. 9. 15.21