Algebra I All-in-One For Dummies. Mary Jane Sterling

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integer. The target number is the 3. Because the next digit, the 6, is greater than 5, you round the 3 up to 4 and eliminate the rest of the digits. You can replace them with 0 or, in this case, just keep the number 4. So, in rounded form, or .

      What if you’re asked to round 1234.567 to the nearest hundred? The target number is the 2. The next digit down is 3, which is smaller than 5, so you leave the 2 as is and replace the 3 and the rest of the smaller digits with 0s. or .

      Note: When the digit below the target digit is exactly 5, and nothing else, you round up.

      The greatest integer function acts a bit differently than rounding. It’s similar in that the greatest integer function eliminates unwanted fractions or decimals, but the greatest integer function only goes in one direction: down. Or, if you already have an integer, the greatest integer leaves the number alone.

      

Q. Which is larger: 5.7 rounded to the nearest integer or [5.7]?

      A. Rounding 5.7 to the nearest integer, you home in on the 7, which will be eliminated. Because 7 is larger than 5, you round up: or . Using the greatest integer function, . So, rounding gives you the larger value.

      Q. Compare rounded to the nearest integer and .

      A. Rounding to the nearest integer, you drop off the , because its decimal value is about 0.333, or less than half; so, rounds to 13. Applying the greatest integer function, . So the values are the same.

      35 Round 146.95 to the nearest integer.

36

Practice Question Answers and Explanations

      1 5. First do the subtraction in the parentheses. Then multiply the result by 3. Finally, add 14.

      2 77. Work inside the brackets first. Perform the two operations in the parentheses. Then perform the multiplications on the two results. Add the products. Then multiply that result by 4. Finally, subtract 11.

      3 180. Multiplying by the 5 outside the braces will come last. First, do the subtraction in the parentheses. Then add inside the brackets. Multiply that result by 8, and then subtract 4. Finally, multiply by 5.

      4 Your last step will be to divide the result in the numerator by the result in the denominator. In the numerator, first do the subtraction in the parentheses, multiply that result by 3, and then subtract that product from 19. Finally, find the square root of the difference. In the denominator, do the subtraction in the parentheses, multiply the result by 4, subtract that product from 8, and then multiply the difference by 6. Finally, subtract 1 from the product. Then you can do the division indicated by the fraction line.

      5 –56. Working inside the absolute value bars, first do the subtraction in the parentheses, multiply the difference by 3, and then subtract the product from 6. Find the absolute value of the result before multiplying by 5. Then subtract the product from 4.

6 8. Work on the numerator and denominator separately — leaving the division for the last step. In the numerator, do the subtraction in the first parentheses and do the multiplication in the last term. Multiply the remainder by 5. Then subtract the second term from the first. In the denominator, do the subtraction under the first radical. Then look at the radical-within-the-radical and do the addition. Evaluate the two radical values you’ve formed. Next, find the difference under the remaining radical and evaluate it. Perform the subtraction in the denominator — and, finally, divide.

      If you’re ready to test your skills a bit more, take the following chapter quiz that incorporates all the chapter topics.

      7 . Multiply each term in the parentheses by 4.

      8 . Multiply each term in the parentheses by –3.

      9 . This problem involves operations with fractions. You will see more on fractions in Chapter 4.

      10 –5.

      11 .

      12 .

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