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3. Operations with Decimal Numbers

Multiplying decimals

You went to the grocery store today to buy a couple of things 1 liter of milk, 24 eggs, a pound of tomatoes, 2 lbs of potatoes and 3 2 liters of Coca Cola. You checked the price tag for each item and you found out that 1 liter of whole fat milk costs C$3.11, 12 large eggs costs$4.28, 2 lbs of tomatoes costs $4.02, 2 lbs of potatoes costs C$ 2.57 and a 2 liter of Coca Cola costs C\$ 2.38. To come up with the total amount of money you need to pay, you will need to apply the different operations with the set of decimal numbers given above.

In this chapter, we will learn about the proper skills that will help you solve the problem above. This chapter has four parts. In the first chapter we will learn how to add and subtract decimal numbers. The rule is simple as you only need to align the given numbers according to the location of the decimal point. Then, depending on the instructions, we will need to round off the resulting number to the nearest tenth. Rounding off numbers is mostly used to simplify the results.

For the second part of this chapter, we will look at how to multiply decimals. In this operation, we will simply multiply the decimal numbers like a regular whole number by ignoring the decimal point. We will only put the decimal point in place after we get the product. By counting the combined number of decimal places of the two numbers we have multiplied we will determine where to put the decimal point.

Following this discussion is the third part of the chapter where we will study how to divide decimals numbers. If the divisor is is not a whole number, we will move the decimal point to the right until the number becomes a whole number. The dividend's decimal point should also be moved accordingly. After the adjustments are made, we can proceed as usual. The quotient's decimal point should be placed directly above that of the dividend. In some cases, we may encounter repeating numbers in the quotient like 1/3 which will give us the repeating decimal 0.3333….

Finally, in the last part of this chapter, we will discuss the Order of operations ­ PEMDAS, which stands for P Parentheses first, E Exponents (ie Powers and Square Roots), MD Multiplication or Division (left­-to-­right) and AS Addition or Subtraction (left­-to-­right).

Multiplying decimals

Previously, we learned how to add and subtract decimal numbers. In this section, we will learn how to multiply decimal numbers. As learned in previous section, when adding and subtracting decimal numbers, the decimal points must be lined up. In contrast, when multiplying decimal numbers, it is not important that the decimal points be lined up. Instead, it is important to line up the digits in the lowest place values of both numbers. In order to figure out where to place the decimal point in the answer, we must count how many digits total, between the two numbers being multiplied together, are behind the decimal points.