ACC. Module #1 Unit 1.2

1. DemingEarly College High SchoolUnit 1.0 Arithmetic 1.2 Decimal Operations

2. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.1 Recognition of Decimals The decimal system is a way of writing out numbers that uses ten different numerals: 0,1,2,3,4,5,6,7,8, and 9. This is called the “base ten” or “base 10” system. Other bases are also used. For example, computers work with a base of 2. This means they only use the numerals 0 and 1.The decimal place denotes how far to the right of a decimal point a numeral is. The first digit to the right of the decimal point is in the tenths place. The next is the hundredths. The third is the thousandths.

3. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.1 Recognition of Decimals Example: 693.142 has a 6 in the hundreds place, a 9 in the tens place, a 3 in the units place, a 1 in the tenths place, a 4 in the hundredths place, and a 2 in the thousandths place, etc.

4. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.1 Recognition of Decimals The decimal point is a period or dot used the separate the ones or units place from the tenths place when writing out a number as a decimal.A decimal number is a number written out with a decimal point instead of a fraction, for example, 1.25 instead of . Depending on the situation, it can sometimes be easier to work with fractions and sometimes easier to work with decimals.A decimal is terminating if it stops at some point. It is called repeating if it never stops, but repeats a pattern over and over again. It is important to note that every rational number can be written as a terminating decimal or as a repeating decimal.

5. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.1 Recognition of Decimals In the number 591.534 5 What number is in the hundreds place? Ones (or units) What is the name of the place where the 1 is?

6. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.1 Recognition of Decimals In the number 591.534 What number is in the hundredths place? 3 What is the name of the place where the 9 is? hundreds

7. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.2 Addition With Decimals To add decimal numbers, each number in the columns need to be lined up by the decimal point. For each number to be added, the zeros to the right of the last number need to be filled in so that each of the numbers has the same number of places to the right of the decimal point. Here is an example of 2.45 + 1.3 + 8.891 written in column form: 2.450 1.300+ 8.891 Zeros have been added in the columns so that each number has the same number of places to the right of the decimal point.

8. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.2 Addition With Decimals Added together, the correct answer is 12.641: 2.450 1.300+ 8.89112.641 Zeros have been added in the columns so that each number has the same number of places to the right of the decimal point.

9. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.2 Addition With Decimals Add the following decimal numbers together: 47.3 + 0.77 + 1.123

10. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.2 Addition With Decimals Add the following decimal numbers together: 47.3 + 0.77 + 1.123 47.300 0.770 + 1.123 49.193 Zeros have been added in the columns so that each number has the same number of places to the right of the decimal point.

11. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.2 Addition With Decimals Add the following decimal numbers together: 471.4 + 5.066 + 13

12. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.2 Addition With Decimals Add the following decimal numbers together: 471.4 + 5.066 + 13 471.400 5.066 + 13.000 489.466 Zeros have been added in the columns so that each number has the same number of places to the right of the decimal point.

13. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.3 Subtraction With Decimals Subtracting decimal numbers is the same procedure as adding decimal numbers (except you can only subtract one number from another number). Here is 7.89 – 4.235 written in column form: 7.890 - 4.235 3.655

14. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.3 Subtraction With Decimals Subtract the following decimal numbers: 47.301 – 7.1

15. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.3 Subtraction With Decimals Subtract the following decimal numbers: 47.301 – 7.1 47.301 - 7.100 40.201 Zeros have been added in the columns so that each number has the same number of places to the right of the decimal point.

16. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.3 Subtraction With Decimals Subtract the following decimal numbers: 341.1 – 15.333

17. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.3 Subtraction With Decimals Subtract the following decimal numbers: 341.1 – 15.333 341.100 - 15.333 325.767 Zeros have been added in the columns so that each number has the same number of places to the right of the decimal point.

18. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.4 Multiplication With Decimals Decimals can be multiplied as if there were no decimal points in the problem. For example, 0.5 * 1.25 can be written and multiplied as 5 * 125, which equals 625.The final answer will have to have the same number of decimal points as the total number of decimal places in the problem. The first number has one decimal place, and the second number has two decimal places. Therefore, the final answer will contain three decimal places: 0.5 * 1.25 = 0.625

19. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.4 Multiplication With Decimals Multiply the following decimal numbers: 4.5 * 5.1

20. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.4 Multiplication With Decimals Multiply the following decimal numbers: 4.5 * 5.1 4.5 * 5.1 = 45 * 51 = 2295 A total of 2 decimal places in the problem gives: 22.95

21. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.4 Multiplication With Decimals Multiply the following decimal numbers: 500 *0.04

22. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.4 Multiplication With Decimals Multiply the following decimal numbers: 500 *0.04 500 * 4 = 2000 A total of 2 decimal places in the problem gives: 20.00

23. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.5 Division With Decimals Dividing a decimal by a whole number entails using long division first by ignoring the decimal point. Then, the decimal point is moved the number of places given in the problem. For example, 6.8 / 4 can be rewritten as 68 / 4, which is 17. There is one non-zero integer to the right of the decimal point, so the final solution would have one decimal place to the right of the solution. In this case, 1.7

24. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.5 Division With Decimals Dividing a decimal by another decimal requires changing the divisor to a whole number by moving its decimal point. The decimal place of the dividend should be moved by the same number of places as the divisor. Then the problem is the same as diving a decimal by a whole number.

25. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.5 Division With Decimals For example, has a divisor with one decimal point in the denominator. The expression can be rewritten as by moving each number one place to the right to eliminate the decimal in the denominator. The long division can be completed as with a result of 52. Since there is one non-zero integer to the right of the decimal point in the original problem, the final solution is 5.2

26. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.5 Division With Decimals In another example, has a divisor with two decimal points in the denominator. The expression can be rewritten as by moving each number two decimal places to the right to eliminate the decimal in the divisor. The long division can be completed with a result of 50.

27. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.5 Division With Decimals Divide the following decimal numbers: Divide the following decimal numbers:

28. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.5 Division With Decimals Divide the following decimal numbers: Divide the following decimal numbers:

29. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.5 Division With Decimals Divide the following decimal numbers: (1) 21.6 4 (2) 308.72 8 (3) 9.0 0.4

30. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.5 Division With Decimals Divide the following decimal numbers: (1) 21.6 4 (1) 5.4 (2) 308.72 8 (2) 38.59 (3) 9.0 0.4 (3) 22.5

31. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.5 Division With Decimals (1) Joe’s Taffy Shop made 51.2 pounds of taffy in 5 days. How much taffy, on average, did the shop make per day? Word problems involving decimals

32. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.5 Division With Decimals (1) Joe’s Taffy Shop made 51.2 pounds of taffy in 5 days. How much taffy, on average, did the shop make per day? Word problems involving decimals Average =

33. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.5 Division With Decimals Word problems involving decimals (2) 8 people will equally split 0.6 acres of land. How much land will each get?

34. Unit 1.0 Arithmetic 1.2 Decimal Operations 1.2.5 Division With Decimals Word problems involving decimals (2) 8 people will equally split 0.6 acres of land. How much land will each get? Land per person =

35. (3) Steve bikes 5.7 miles each school day. In total, how far will he bike in 2 two school days? Word problems involving decimals Distance = rate * time

36. (3) Steve bikes 5.7 miles each school day. In total, how far will he bike in 2 two school days? Word problems involving decimals Distance = rate * time = 5.7 miles * 2 days = day 11.4 miles