Ignoring ZerosDate: 09/03/98 at 17:41:22 From: Cole Krivoski Subject: Math - Decimals Here's the problem. I just want to know what to do. You have 0.76 and 0.760 and you have to find out which number is greater or less, or if they are equal. My teacher says they are equal. The thing I do not understand is the number 0.760. Is point 760 thousandths right or wrong? So shouldn't 0.760 be greater? Or does the zero not count? Date: 09/04/98 at 13:05:14 From: Doctor Peterson Subject: Re: Math - Decimals Hi, Cole. This is an important question! Basically the answer is, as you suggested, that the zero doesn't count; but it's important to understand why that particular zero can be ignored, but others can't. There are several ways to explain the meaning of a decimal. One is to treat it as one big fraction, so that: 76 760 0.76 = --- and 0.760 = ---- 100 1000 Now look closely, and you'll see that you can simplify 760/1000 by dividing the numerator and denominator by 10 to get 76/100. Does that look familiar? I've just shown that these numbers are equal. Another way to look at decimals is by place value, just as you did for whole numbers. Then we can say that 1 1 1 0.760 = 7 * -- + 6 * --- + 0 * ---- 10 100 1000 Now do you see that the zero doesn't add anything to the number? That's why it can be ignored. It's actually the same reason you can ignore the zero in 076, which just means no hundreds, just as this zero means no thousandths. Now what about zeroes that aren't at the end? Look at the meaning of 0.706: 1 1 1 0.706 = 7 * -- + 0 * --- + 6 * ---- 10 100 1000 That's not the same as 0.76, because now the 0 does something: it changes the meaning of the 6 from 6 hundredths (in 0.76) to 6 thousandths (in 0.706). So the rule is: when there is a zero at the left side of a number (to the left of the decimal point), or at the right side of a number (to the right of the decimal point), you can ignore it. If a zero is between two non-zero digits, or between a digit and the decimal point, you have to pay attention to it. I hope that helps. - Doctor Peterson, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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