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Chapter 7

Chapter 7. Decimals, Ratio, Proportion and Percent. 7.1 Decimals. Decimals are used to represent fractions in our base ten place-value notation. 1000. 100. 10. 1. 1/10. 1/100. 1/1000. 3. 4. 5. 7. 9. 6. 8. thousands. hundreds. tens. ones. tenths. hundredths. thousandths.

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Chapter 7

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  1. Chapter 7 Decimals, Ratio, Proportion and Percent

  2. 7.1 Decimals Decimals are used to represent fractions in our base ten place-value notation. 1000 100 10 1 1/10 1/100 1/1000 3 4 5 7 9 6 8 thousands hundreds tens ones tenths hundredths thousandths

  3. Write 3457.968 in expanded form: Write 978.314 in expanded form:

  4. Theorem: Let be a fraction in simplest form. Then has a terminating decimal representation if and only if b contains only 2’s and/or 5’s in its prime factorization.

  5. Ordering Decimals Terminating decimals can be compared using a hundreds square, using a number line, by comparing them in their fraction form, or by comparing place values one at a time from left to right just as we compare whole numbers.

  6. Multiplying or Dividing by Powers of 10 Theorem:Let n be any decimal number and m represent any nonzero whole number. Multiplying a number n by 10^m is equivalent to forming a new number by moving the decimal point of n to the rightm places. Dividing a number n by 10^m is equivalent to forming a new number by moving the decimal point of n to the leftm places.

  7. 7.2 Operations with Decimals Addition and Subtraction requires the numbers to be aligned at the decimal point, add or subtract the numbers as if they were whole numbers, and insert a decimal point directly below the numbers being added or subtracted.

  8. Multiplication of Decimals Perform multiplication as if the decimal point were not there. Insert a decimal point in the answer as follows: The number of digits to the right of the decimal point in the answer is the sum of the number of digits to the right of the decimal points in the numbers being multiplied.

  9. Division of Decimals Multiply both the divisor and dividend by the power of ten necessary to result in the divisor being a whole number.

  10. Repeating Decimals Theorem: Let be a fraction in simplest form. Then has a repeating decimal representation that does not terminate if and only if b has a prime factor other than 2 or 5.

  11. 7.3 Ratios and Proportion Definition:A ratio is an ordered pair of numbers, written a:b, with b not equal to 0. Definition: Equality of Ratios if and only if

  12. Proportions Definition: A proportion is a statement that two given ratios are equal.

  13. Rates Ratios involving different units are called rates. Examples: miles per hour, miles per gallon, cents per ounce, dollars per pound, etc.

  14. Example 7.21: Adams School orders 3 cartons of chocolate milk for every 7 students. If there are 581 students in the school, how many cartons of chocolate milk should be ordered? n = # cartons to be ordered Step 1: Define your variable. Step 2: Set up a proportion. Step 3: Cross multiply and solve. The school needs to order 249 cartons of chocolate milk.

  15. Example 7.24: In a scale drawing, 0.5 centimeter represents 35 miles. How many miles will 4 centimeters represent? n = # of miles Step 1: Define your variable. Step 2: Set up a proportion. Step 3: Cross multiply and solve. Four centimeters represents 280 miles.

  16. 7.4 Percent Percents “Percent” means “per hundred” Fractions Repeating Decimals

  17. Conversions

  18. Solving Percent Problems Grid Approach

  19. Example 7.29a: A car was purchased for $13000 with a 20% down payment. How much was the down payment? Shade 20 out of the 100 squares (20%) 100 squares = $13000, so 1 square = $130. 20 squares represent the down payment of $2600. 20 X $130 = $2600

  20. Solving Percent Problems Ex 7.30a: Proportion Approach Since percents can be written as ratios, percent problems can be solved using proportions. The down payment was $2600.

  21. Solving Percent Problems Equation Approach

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