Rules for Adding & Subtracting Decimals
Decimals are rational numbers that let you express values that are greater than or less than one whole. Values that are greater than one are written to the left of the decimal, while numbers written to the right of the decimal have a value that is less than one. The numbers written to the right of the decimal are in base 10 form: tenths, hundredths, thousandths and so on. Decimals can be found regularly in your daily life, from the prices of groceries at the store to the stock market. The frequency with which you encounter decimals demands the ability to add or subtract them correctly.
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When to Add or Subtract Decimals
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The most common occurrence for adding or subtracting decimals is in dealing with money. Whether you are calculating the amount of your grocery bill or figuring out the amount of money you will have left over after expenditures, accurately adding or subtracting decimals is essential. However, dealing with money is not the only time you need to be able to add or subtract decimals. You also need to be able to accurately add or subtract decimals in the timing of sporting events, such as track and field, to determine the winner.
Line Up the Decimals
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The most important rule to remember when adding or subtracting decimals is to line up the decimals. Lining up the decimals means to place the larger decimal number over the smaller decimal so that they have an equal number of digits to the right and left of the decimal point. For example, in the problem 5.54 plus 3.23, the decimals would be aligned so that the five would be directly over the three, the second five would be directly over the two and the four would be directly over the second three. Lining up the decimals allows you to add following the rules for addition.
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Adding Zeros
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Sometimes when adding or subtracting decimals one of the numbers has more digits than the other, making the lining up of decimals more difficult. For example, .45 plus 3.36. To solve this, add a zero to the left of the decimal, so .45 is rewritten as 0.45. Adding zeros does not change the value of a number, assuming you are placing the zero at the beginning or end of a number, but it does make lining up the decimals easier. For example, 3.36 can be rewritten as 03.360000 without changing the value of the number.
Decimal Placement
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After adding or subtracting the digits in your decimal problem, you must correctly place a decimal point in your answer to accurately name the value of two numbers. For adding and subtracting decimals, simply move the decimal point down so that you have the same number digits to the right and left of the decimal in your answer as you did in your problem. For example, in the problem 6.187 plus 2.220, there are three digits to the right of the decimal point and one digit to the left of the decimal point, that means there should be three digits to the right of the decimal point and one digit to the left in the answer.
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References
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