# Thread: rules on rounding off numbers ...

1. Good post? |

## rules on rounding off numbers ...

In the number 1.4ab5, a and b represent single positive digits. If x = 1.4ab5, what is the value of 10 – x?

(1) If x is rounded to the nearest hundredth, then 10 – x = 8.56.
(2) If x is rounded to the nearest thousandth, then 10 – x = 8.564.

SPOILER: OA: B. This tells us that x rounded to the nearest thousandth must be 1.436. This means, that a, the hundredths digit, is equal to 3. As forb, the thousandths digit, we know that it is followed by a 5 (the ten-thousandths digit); therefore, if x is rounded to the nearest thousandth, b must rounded UP. Since b is rounded UP to 6, then we know that b must be equal to 5 ..... this is the official explanation,however, Iam not sure if we can say that b was rounded up. The original number could be 1.4355 OR 1.4365.

The rounding off rule that I am using is this ....

In rounding off numbers, if the first figure dropped is 5, and all the figures following the five are zero or if there are no figures after the 5, then the last figure kept should be unchanged if that last figure is even.

In rounding off numbers, if the first figure dropped is 5, and all the figures following the five are zero or if there are no figures after the 5, then the last figure kept should be increased by 1 if that last figure is odd.

2. Good post? |
The rounding-off rule is following-

Add 1 to the last digit retained if the first digit dropped is greater than or equal to 5.
No change to the last digit retained if the first digit dropped is less than 5.
Now coming to the question, from B u know that 10-8.564=1.436 and x is given as 1.4ab5. this means that if u want to drop-off 5 then u have to increase B by 1. when B is 6 after rounding off then it must have been 5 before rounding-off.
i hope it is clear now.

3. Good post? |
I found this for you. Hope it is clear now.

When rounding whole numbers there are 2 rules to remember:

I will use the term rounding digit - which means: When asked to round to the closest tens - your rounding digit is the second number to the left (ten's place) when working with whole numbers. When asked to round to the nearest hundred - the third place from the left is the rounding digit (hundreds place).
Rule 1. Determine what your rounding digit is and look to the right side of it. If the digit is 0,1,2,3 or 4 do not change the rounding digit. All digits that are on the right hand side of the requested rounding digit will become 0
Rule 2. Determine what your rounding digit is and look to the right of it. If the digit is 5,6,7, 8 or 9, your rounding digit rounds up by one number. All digits that are on the right hand side of the requested rounding digit will become 0

Rounding with decimals: When rounding numbers involving decimals, there are 2 rules to remember:
Rule 1. Determine what your rounding digit is and look to the right side of it. If that digit is 4,3, 2 or 1, simply drop all digits to the right of it.
[b[Rule 2.</B> Determine what your rounding digit is and look to the right side of it. If that digit is 5, 6, 7, 8 or 9 add one to the rounding digit and drop all digits to the right of it.
Rule 3: Some teachers prefer this method:
This rule provides more accuracy and is sometimes referred to as the 'Banker's Rule'. When the first digit dropped is 5 and there are no digits following or the digits following are zeros, make the preceding digit even (i.e. round off to the nearest even digit). E.g., 2.315 and 2.325 are both 2.32 when rounded off to the nearest hundredth. Note: The rationale for the third rule is that approximately half of the time the number will be rounded up and the other half of the time it will be rounded down.
An example:
765.3682 becomes:
1000 when asked to round to the nearest thousand (1000)
800 when asked to round to the nearest hundred (100)
770 when asked to round to the nearest ten (10)
765 when asked to round to the nearest one (1)
765.4 when asked to round to the nearest tenth (10th)
765.37 when asked to round to the nearest hundredth (100th.) 765.368 when asked to round to the nearest thousandth (1000th)

4. Good post? |
excellent explanation hangptt !!

though I am familiar with the banker's rule for rounding off. I haven't come across it in any of the GMAT books .... so is this rule only used by statisticians or we can use it in GMAT as well ?

I have come across questions for which the solution will be different depending on if we use the banker's rule. I will post it if I can find it now.

for eg: a number like 0.225 rounded to the nearest hundredth would be 0.23 using the standard rules but will be 0.22 using the banker's rule.

5. Good post? |
statement 1: If x is rounded to the nearest hundredth, then 10 – x = 8.56.
=>x=1.44 => a'=a=4 if b<4 else a=3 if b>4
not sufficient

statement 2: If x is rounded to the nearest thousandth, then 10 – x = 8.564.
=>x=1.436 => b=5 and a=3 => x=1.4355
10-x = 8.5645
sufficient

Good work hangptt

6. Good post? |
Great explanation Hangptt

7. Good post? |
10.0000
-1.4ab5
=8.564(5) - this is the result wanted
from statement (2) it is clear that b=5 and a=3
ans is B