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### Rounding to One Digit Accuracy

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Date: 04/16/98 at 21:33:06
From: Lori
Subject: Rounding to 1-digit accuracy

Hello,

I can't figure out how do round to 1-digit accuracy. I received a
paper and I only got a few right. I had to guess, and one of the
problems was 3.82___________. I put 4 and I got it right. On all the
other ones, like 14.98__________, I put 15.0 and that was wrong.

examples so I can see it too! Thank you so much.

LORI
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Date: 04/21/98 at 14:11:09
From: Doctor Derrel
Subject: Re: Rounding to 1-digit accuracy

Hi Lori,

I'll try to help. I'm going to tell you how to do rounding and show
you some examples; then I'll try to explain why you would want to
do it.

When you round, only look at the digit to the right of the one that
you are going to round. If that digit is

1) less than 5, round down
2) 5 or greater, round up

(Why does 5 always round up? Well, if the digit to the right of the
one we are rounding is 0,1,2,3, or 4, we have five numbers that round
down; then 5,6,7,8, or 9 are the five numbers that round up.)

Don't look more than one digit to the right of the one you are
rounding to. For example, if you are given the number 564,982 and
asked to round to two-digit accuracy, think of the number as 564,XXX
where the "X" can be any digit. This is because the two digits that
you will care about after rounding are "56" and the "4" tells you
whether you have to round up or round down. In this case, you round
down (the "6" stays a "6"), then all of the other digits besides the
560,000.

Maybe you are confused that 560,000 has six digits, but we are talking
about two-digit accuracy. The key word here is "accuracy." You have to
know how big the number is; that is, is it in the hundreds? Thousands?
Billions? Or on the other side of the decimal, in the ten-thousandths?
Millionths? Trillionths? Otherwise you would end up with 56 as your
answer, and you know that 56 is nowhere near 564,982!

Examples of rounding to one-digit accuracy (--> means "rounds to"):

3.82    --> 4
4.233   --> 4
3.5     --> 4 (The 5 rounds up)
4.5     --> 5
4.599   --> 5 (Only look at the digit to the right of the one you
are rounding to - ignore the two 9's. It's the 5
thatrounds up.)
3.6837  -->   4
10.962  -->  10 (Look only at the 0; ignore the .962)
14.98   -->  10 (Look only at the 4; ignore the 98)
153.68  --> 200

Did you notice that the "10," "10," and "200" are rounded to one-digit
accuracy even though they have more than one total digits?

Try this one on your own: Round 428,379.62 to 1-digit accuracy and
signature so that you won't be tempted to peek!) :-)

What if you write 4.0, 10.0, 10.0, or 200.0 for the last four numbers
above? Well, those would be wrong because adding the digit to the
right of the decimal point shows that you know something about what
goes in the tenths place. In this case, you said it is zero tenths.
Instead of one-digit accuracy, you would now have two digits for 4.0,
three digits for 10.0, and a whopping four digits for 200.0 . Your
15.0 was wrong for the 14.98 because you had three-digit accuracy.

Okay, I can see you scratching your head - how is it that putting in
a decimal point and a zero in the tenths place, the way we did for the
numbers in the previous paragraph, suddenly means we have more
accuracy? The key here is the decimal point. By putting in a zero to
the right of the decimal point, we said, "I know that the value in
the tenths place is zero." And if we know the value in the tenths
place, we know the values (and the accuracy) for all of the others.

Now, let's try two-digit accuracy:

Rounding to two-digit accuracy:

3.82    --> 3.8
4.233   --> 4.2
3.5     --> 3.5 (It already has two digits.)
10.487  --> 10  (Look at the 4; ignore the 87.)

On the last one, we got "10," which is two-digit accuracy. But above,
we also got "10" when we were rounding to one-digit accuracy. How do
we know whether 10 is two-digit or one-digit accuracy? Well, we don't
know just by looking at the number. You have to have some more
information, like how many digits it was rounded to. (You will learn
later that we do have a way of knowing how many digits of accuracy we
have, but you need to know about something called "scientific
notation.")

I hope this helped you with the rules of rounding when working only
with numbers. I also suggest that you look up the term "significant
digits" in a math dictionary (your teacher or library should have one)
because it will go into more detail about rounding.

However, rounding is something you do because it makes sense for the
problem you are working on. When working on problems, you have to
think about when to round, and sometimes you don't follow the rules.

For example, if you are going on a school trip, each bus holds 50
students, and you have 110 students going, would you say: "Well, 110
divided by 50 is 2.2. Since we can only take whole buses, the rule
says we round to one digit. Looks like we take only two buses." You
would have 10 disappointed students if you followed that line of
reasoning!

In short, when doing tests where you are given numbers to round, just
it makes sense to round, and how you are going to round.

I did not give examples about rounding negative numbers and decimal
numbers between 0 and 1. The rules for these really make sense if you
think about why you are rounding. However, if you would like some
examples of those, please write again. If you still have questions,

-Doctor Derrel,  The Math Forum
Check out our web site! http://mathforum.org/dr.math/

428,379.62 to one-digit accuracy is 400,000 -- can you explain why?

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