Rounding DecimalsDate: 10/19/98 at 21:56:18 From: Pam Martin Subject: Rounding decimals I am trying to teach my daughter how to round decimals. It has been a long time since I have done it. Could you please explain how to round them in a simple way that I can make her understand? Thank you, Pam Martin Date: 10/20/98 at 13:13:42 From: Doctor Peterson Subject: Re: Rounding decimals Hi, Pam. Let's see if I can help. The first thing to know about rounding decimals is that it works exactly like rounding whole numbers. To round to the nearest tenth, you do the same thing you do to round to the nearest ten, except that you are working with a different digit in the number. I can use the same picture to explain both: | | X-------->| +----+----+----+----+----+----+----+----+----+----+ 140 141 142 143 144 145 146 147 148 149 150 This shows that 148 is between 140 and 150, and is closer to 150 because it's bigger than 145. The next picture shows that 1.48 is between 1.40 and 1.50, and is closer to 1.50 because it is bigger than 1.45: | | X-------->| +----+----+----+----+----+----+----+----+----+----+ 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.50 To round to the nearest ten, you drop all digits to the right of the tens place, replacing them with zero, so that you are left with a multiple of 10. Then you check to see whether your original number is actually nearer to the next multiple of 10, by checking whether the next digit (the leftmost one you dropped) was 5 or more: 148 rounded to nearest 10: |\ | \ replace 8 with 0 V \ 140 8 is greater than 5, so add 10: | | V 150 What all this means is that 148 is between 140 and 150, but is closer to 150 so we round it to that. Now, to round to the nearest tenth, you do the same thing, but using the tenths digit rather than the tens: 1.48 rounded to nearest 0.1: |\ | \ replace 8 with 0 V \ 1.40 8 is greater than 5, so add 0.1: | | V 1.50 Again, this means that 1.48 is between 1.4 and 1.5, but is closer to 1.5. If the number had been 1.45, exactly between the two, you would still round up to 1.5. If it were 1.43, you would have rounded down, leaving it at 1.40, because 3 is less than 5. The only real difference is that when you put zeroes to the right of a decimal, you can ignore them completely because they don't affect the number. So you can write the answer as 1.5 rather than 1.50. Here's another answer in our Dr. Math archives that talks about rounding decimals: http://mathforum.org/library/drmath/view/58938.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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