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How to Round Decimals
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The digit immediately to the right of the decimal point is the
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Hi, I'm Zoya Popova for About.com, and today I'm going to show you how to round decimals.Let's start with the basics.In the decimal system, we know the value of each digit from the position that it takes. So, in the number 143,269, 6 is not merely a 6—it actually stands for 60. In any whole number, we have, from right to left, the ones place; the tens place; the hundreds place; the thousands place; the ten-thousands place; the hundred-thousands place, and so on. The same holds true for decimals, which have digits after the decimal point. The digit immediately to the right of the decimal point is the tenths place; followed by hundredths place; followed by thousandths place; followed by ten-thousandths place; and so on. Keep this terminology in mind when you are asked to round decimals.So let's do an example using the number Pi, which has an infinite number of digits after the decimal point: 3.14159265... Let's round it to three decimal places. First, locate the rounding digit three positions after the decimal point – 1. Next, take a look at the digit immediately following the rounding digit. For us, that digit is 5. The rule is, if the the rounding digit is followed by a digit 5 or greater, the rounding digit must be increased by one. So we replace the rounding digit 1 by 2, and Pi rounded to three decimal places ends up being 3.142. Now let's say we want to round Pi to the hundredth place. This is where you should remember the terminology: the hundredth place is the second decimal place. For us, this place is occupied by 4.Next, let's take a look at the digit following our rounding digit. That digit is 1, and the rule is, if the following digit is 4 or smaller, then the rounding digit should remain unchanged. So Pi rounded to the hundredth place is 3.14.Finally, let's take a trickier example. Round 78.5695 to the nearest thousandth. First, let's find the thousandth place: it's the third position to the right of the decimal point. We look at the digit following it, which is 5, and when it's 5 or greater, we want to increase our rounding digit by 1. 9 must turn into 10, which means that the preceding digit, 6, must also be increased by 1. 69 becomes 70. The rest of the numbers remain the same, and we cut off everything after our rounding digit. The answer is 78.570. You may be tempted to write it down as 78.57, but that would be a mistake because the zero at the end shows that our rounding has an accuracy to the nearest thousandth. And this is it for rounding decimals.
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