1. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 3 Decimals

2. 3-1-2 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Section 3.1 Understanding Decimals

3. 3-1-3 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Identify the Place Value of a Digit in a Decimal Decimals have a whole number side and a decimal side separated by a dot known as a decimal point.

4. 3-1-4 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Identify the Place Value of a Digit in a Decimal The place values to the left of the decimal point are powers of 10 and the place values to the right of the decimal point are fractions whose denominators are powers of 10.

5. 3-1-5 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Identify the place value of the indicated digit. a.17.1473 b.6.9426 c.0.00345 d.234.53 e.123.728432

6. 3-1-6 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy a.17.1473 Identify the place value of the indicated digit. tenths b.6.9426thousandths c.0.00345hundred-thousandths d.234.53hundredths e.123.728432ten-thousandths

7. 3-1-7 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Write a Decimal in Word Form

8. 3-1-8 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Write each decimal in word form. a.0.516 b.0.0385 c.9.43 d.35.718 e.324.1839

9. 3-1-9 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy a.0.516 Write each decimal in word form. five hundred sixteen thousandths b.0.0385three hundred eighty-five ten- thousandths c.9.43nine and forty-three hundredths

10. 3-1-10 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy d.35.718 Write each decimal in word form. thirty-five and seven hundred eighteen thousandths e.324.1839three hundred twenty-four and one thousand eight hundred thirty-nine ten-thousandths

11. 3-1-11 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Write a Decimal in Standard Form In writing decimals in standard notation, we must make sure that the last digit is in the correct place. We do so by inserting zeros as placeholders when necessary.

12. 3-1-12 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Write each decimal in standard form. a.five thousandths b.three hundred fifty-six and forty-one thousandths c.thirty-eight and four hundred ninety-eight ten- thousandths

13. 3-1-13 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy a.five thousandths = Write each decimal in word form. 0.005 b.three hundred fifty-six and forty-one thousandths = 356.041 c.thirty-eight and four hundred ninety-eight ten-thousandths = 38.0498

14. 3-1-14 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Convert a Decimal to a Fraction Rule for Converting a Decimal to a Fraction To convert a decimal to a fraction, write the whole number formed by the digits to the right of the decimal point as the numerator, and write the power of 10 that has as many zeros as place values in the decimal as the denominator.

15. 3-1-15 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Convert each decimal to a fraction or mixed number. Simplify, if possible. a.0.37 b.0.009 c.16.5 d.68.075

16. 3-1-16 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy Convert each decimal to a fraction or mixed number. Simplify, if possible.

17. 3-1-17 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Compare Decimals

18. 3-1-18 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Insert the symbol, or = to form a true statement. a. 7.269 b. 0.053866 7.314 0.0538

19. 3-1-19 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy Insert the symbol, or = to form a true statement. a. 7.2697.314 b. 0.0538660.0538 < >

20. 3-1-20 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Round a Decimal to a Specified Place Value

21. 3-1-21 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Round each decimal to the specified place value. a. 7.269 to the nearest tenth b. 0.053866 to the nearest hundredth c. 0.053866 to the nearest thousandth d. 0.053866 to the nearest ten-thousandth

22. 3-1-22 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy a. 7.269 to the nearest tenth = Round each decimal to the specified place value. 7.3 b. 0.49716 to the nearest hundredth =0.50 c. 0.12345 to the nearest thousandth =0.123 d. 0.00985 to the nearest ten-thousandth =0.0099

23. 3-1-23 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example Apply your knowledge a.You are writing a check for one hundred twenty-seven dollars and eight cents. Write the decimal notation for this. b.You are writing a check for $283.56. Write the word form for this amount.

24. 3-1-24 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Solution Strategy $127.08 a.You are writing a check for one hundred twenty-seven dollars and eight cents. Write the decimal notation for this. b.You are writing a check for $283.56. Write the word form for this. Two hundred eighty-three dollars and fifty-six cents.