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Unit 3

Unit 3. Decimal Fractions. DECIMAL FRACTIONS. Written with a decimal point Equivalent to common fractions having denominators which are multiples of 10 The chart below gives the place value for each digit in the number 1.234567. READING DECIMAL FRACTIONS.

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Unit 3

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  1. Unit 3 Decimal Fractions

  2. DECIMAL FRACTIONS • Written with a decimal point • Equivalent to common fractions having denominators which are multiples of 10 • The chart below gives the place value for each digit in the number 1.234567

  3. READING DECIMAL FRACTIONS • To read a decimal, read number as whole number. • Say name of place value of last digit to right. • 0.567 is read “five hundred sixty-seven thousandths” • To read a mixed decimal (a whole number and a decimal fraction), read whole number, read word and at decimal point, and read decimal. • 45.00753 is read “forty-five and seven hundred fifty-three hundred thousandths”

  4. ROUNDING DECIMAL FRACTIONS • Rounding rules: • Determine place value to which number is to be rounded • Look at digit immediately to its right • If digit is less than 5, drop it and all digits to its right • If digit is 5 or more, add 1 to digit in place to which you are rounding. Then drop all digits to its right

  5. ROUNDING EXAMPLES • Round 14.763 to the nearest hundredth • 6 is in the hundredths place value, so look at 3. Since 3 is less than 5, leave 6 alone and drop 3. • Ans: 14.76 • Round 0.0065789 to the nearest ten thousandth • 5 is in the ten thousandths place value, so look at 7. Since 7 is greater than 5, raise 5 to 6 and drop all digits to its right. • Ans: 0.0066

  6. CONVERTING FRACTIONS TO DECIMALS • Fractions can be converted to decimals by dividing the numerator by the denominator • Express 5/8 as a decimal fraction: Ans • Place a decimal point after the 5 and add zeros to the right of the decimal point. • Bring the decimal point straight up in the answer. Divide. 8 20 16 40 40

  7. CONVERTING DECIMALS TO FRACTIONS • To change a decimal to a fraction, use the number as the numerator and the place value of the last digit as the denominator • Change 0.015 to a common fraction: • 0.015 is read as fifteen thousandths

  8. ADDITION AND SUBTRACTION • To add and subtract decimals, arrange numbers so that decimal points are directly under each other. • Add or subtract as with whole numbers • Place decimal point in answer directly under the other decimal points

  9. ADDITION AND SUBTRACTION • Perform the following operations: 13.475 + 6.367 3.537 – 1.476 2.061 Ans 19.842 Ans

  10. MULTIPLICATION • Multiply decimals using same procedures as with whole numbers • Count total number of digits to right of decimal points in both numbers being multiplied • Begin counting from last digit on right in answer and place decimal point same number of places as there are total in both of the numbers being multiplied

  11. MULTIPLICATION Multiply 62.4  1.73: • Since 62.4 has 1 digit to right of decimal and 1.73 has two points to right of decimal, answer should have 3 digits to right of decimal point • 62.4 • 1.73 1 872 43 68 62 4 107 952 = 107.952 Ans

  12. DIVISION • Divide using the same procedure as with whole numbers • Move the decimal point of the divisor as many places as necessary to make it a whole number • Move the decimal point in the dividend the same number of places to the right • Divide and place the decimal point in the answer directly above the decimal point in the dividend

  13. .38Ans 2 5 12 5 12 DIVISION • Divide 2.432 by 6.4: • Move decimal point 1 place to right in 6.4 • Move decimal point 1 place to right in 2.432 • Place decimal point straight up in the answer • Divide

  14. POWERS • Product of two or more equal factors • Appear slightly smaller • Located above and to right of number being multiplied

  15. POWERS • Evaluate each of the following powers: • .43 • (2.5 × 3)2 The power 3 means to multiply .4 by itself 3 times .43 = .4 × .4 × .4 = .064 Ans Parentheses first: 2.5 × .3 = .75 (.75)2 = .75 × .75 = .5625 Ans

  16. ROOTS • A quantity that is taken two or more times as an equal factor of a number • Finding a root is opposite operation of finding a power • Radical symbol () is used to indicate root of a number • Index indicates number of times a root is to be taken as an equal factor to produce the given number • Note: Index 2 for square root is usually omitted

  17. FINDING ROOTS • Determine the following roots: • This means to find the number that can be multiplied by itself to equal 64. Since 8 × 8 = 64, the = 8Ans • This means to find the number that can be multiplied by itself three times to equal 27. Since 3 × 3 × 3 = 27, = 3 Ans • Note: Roots that are not whole numbers can easily be computed using a calculator

  18. ORDER OF OPERATIONS • Order of operations including powers and roots is: • Parentheses • Fraction bar and radical symbol are used as grouping symbols • For parentheses within parentheses, do innermost parentheses first • Powers and Roots • Multiplication and division from left to right • Addition and subtraction from left to right

  19. ORDER OF OPERATIONS • Parentheses and grouping symbols (square root) first: (1.2)2 + 6 ÷ 2 • Powers next: 1.44 + 6  2 • Divide: 1.44 + 3 • Add: 4.44 Ans

  20. PRACTICE PROBLEMS • Write the following numbers as words. a. 0.0027 b. 143.45 c. 1.007368 • Round 10.2364579 to each of the following place values:

  21. PRACTICE PROBLEMS (Cont) • Express each of the following as decimal fractions: 4. Express each of the following as fractions in lowest terms: a. 0.16 b. 0.1204 c. 0.635 5. Perform the indicated operations: a. 0.0027 + 0.249 + 0.47 b. 6.45 + 2.576 c. 3.672 – 1.569 d. 45.3 – 16.97

  22. PRACTICE PROBLEMS (Cont) e. 1.54 × 2.7 f. 25.63 × 3.46 g. 0.12  .4 h. 15.325  2.5 i. 0.33 j. (12.2 × .2)2

  23. Writing Twenty-seven ten thousandths One hundred forty-three and forty-five hundredths One and seven thousand three hundred sixty-eight millionths Rounding 10.2 10.24 10.236 10.2365 10.23646 10.236458 Solutions

  24. Convert to decimal 0.5 0.875 0.9375 Decimal to Fraction a b c Solutions

  25. Order of operations 0.7217 9.026 2.103 28.33 4.158 88.6798 0.03 6.13 0.027 5.9536 4 5.32 3.82 Solutions

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