Overview
Decimals and percent are used in many different types of mathematical calculations and applications. They require attention to detail to use correctly.
Adding and Subtracting Decimals
In order to add and subtract numbers that contain decimal points, the numbers must be aligned so that the place values are the same. Then they can be added or subtracted as if they were whole numbers. Suppose 3.4 + 90.030 + 5.14 were to be added. In order to line up the numbers around the decimal point, 3.4 could also be written as 3.400, and 5.14 could be written as 5.140. Then 3.400 + 90.030 + 5.140 are all lined up, and equal 98.570. Subtraction is similar. 34.07 -1.569 could be rewritten as 34.070 to line up the decimal points, and then subtract 1.569 to equal 32.501.
Figure 1: Line up decimal points for addition and subtraction.
Multiplying and Dividing Decimals
When multiplying numbers containing decimal points, factors can be multiplied as if they were whole numbers. Then, the number of decimal places in the answer is determined by the number of decimal places to the right in both factors. Suppose that 2.99 is multiplied by 4.8. The answer, 14.352, has three decimal places to the right, two from the factor 2.99 and one from the factor 4.8. Division is the reverse process, with an additional step. Suppose that 12.6 is divided by 2.24. In order to make 2.24 a whole number, both the numerator and the denominator must be multiplied by 100. Therefore, the new ratio is (12.6 ∙ 100)/(2.24 ∙ 100) = 1260/224 = 5.63. Multiplying the numerator and the denominator by 100/100 is the same thing as multiplying by 1, the identity element for multiplication.
Rounding Decimals
When rounding decimals, the place value is always specified. Suppose 36.266 is to be rounded to the nearest hundredth. If the digit to the right of the hundredth place, the thousandth place, is more than 5, then the number in the hundredth place will be rounded up to the next number, or 36.27. Suppose the number 36.313 is to be rounded to the nearest hundredth. The digit 3 in the thousandth place is less than 5. The number remains as 36.31, and the digit in the thousandth place drops off, or the number is truncated.
Percent
The word percent means “per hundred”. Suppose that the decimal is 0.7. For the percent, the decimal is moved two spaces to the right, or multiplied by 100. If necessary, zeroes are added, so that .7 is 70%. Similarly, .35 is 35%, and 0.012 is 1.2 %.
Figure 3: For decimal to percent, move the decimal two spaces to the right.
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