# Lesson: Introduction to Decimals

## Comment on Introduction to Decimals

### The 3rd problem linked below

The 3rd problem linked below the video has no explanation of the answer. Would you mind explaining how A & D are the answers?:

Maurice entered a number into his calculator and erroneously divided the number by 0.03 instead of 0.0003, resulting in an incorrect result. Which of the following is a single operation that Maurice could perform on his calculator to correct the error?

Indicate all such operations.

A. Multiply the incorrect product by 100
B. Divide the incorrect product by 100
C. Multiply the incorrect product by 0.01
D. Divide the incorrect product by 0.01 ### You're referring to this

You're referring to this question: http://greprepclub.com/forum/qotd-2-maurice-entered-a-number-into-his-ca...

### for the decimals is it always

for the decimals is it always the case that the first digit represents tenths, 2nd digit hundredths, and so on after the decimal??? ### Yes, it's always the case.

Yes, it's always the case.

### How to round off to the

How to round off to the nearest 0.05.
for example if we have a decimal 0.16, how to round to nearest 0.05?
In ETS guide 2nd edition (page number 298 question number 16), they have asked to round to nearest 0.05 ### You will never be tested on

So, here we must consider increments of 0.05, as in 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, etc

Since 0.16 lies between 0.15 and 0.2, we must determine which value 0.16 is closer to.

Since 0.16 is closer to 0.15, we can say that 0.16, rounded to the nearest 0.05 is 0.15

### Suppose if number is 0.18,

Suppose if number is 0.18, which is in between 0.15 and 0.20. on this case we can round of 0.18 to 0.20, right?
Like wise 0.17 to 0.15

Am I correct? ### Yes, that's correct.

Yes, that's correct.

0.18 is closer to 0.20 than it is to 0.15, so if we're rounding to the nearest 0.05, then we'd round it to 0.20

The same goes for rounding 0.17 to 0.15

### Hi BRENT,

Hi BRENT,
can you give an example video or any online source for an example of one of this type of nearest 0.05 sum? it would be helpful. ### The only example I've seen of

The only example I've seen of this kind of rounding can be found in ETS's Official Guide to the GRE - 2nd edition (page 298, question 16b).

The same question can be found in ETS's Official Guide to the GRE - 3rd edition (page 322, question 16b).

### Hi, in the ETS's official

Hi, in the ETS's official guide 3rd edition p. 232, problem 1 the question (g) is
(20/5)^2-(-2+6)^3 but the answer on the next page says 1,024. Can you please explain? thanks ### You're absolutely right.

You're absolutely right.

(20/5)^2-(-2+6)^3 = (4)^2-(4)^3
= 16 - 64
= -48

The answer of 1024 would be correct IF the question involved multiplication and not subtraction.

That is, (20/5)^2 x (-2+6)^3 = (4)^2 x (4)^3
= 16 x 64
= 1024

### thank you for clarifying!

thank you for clarifying!

### Can't we just use the

Can't we just use the calculator given on GRE instead of having to learn these manual techniques of multiplying and dividing decimals? ### Great question!

Great question!
The GRE's onscreen calculator is pretty clunky (and may even function differently from your personal calculator), so if you plan to use it on test day, be sure you know how it works. See this video: https://www.greenlighttestprep.com/module/general-gre-info-and-strategie...

Also note that the GRE can test your knowledge of the manual techniques by adding a few variables.
For example, if x and y represent single digits and (3.x)(1.2y) = 4.25, what can we conclude (if anything) about x and y?

As you can see, this kind of question reduces the effectiveness of the onscreen calculator, and relies more on your understanding of how we multiply decimals.

Cheers,
Brent

### Thanks for clarifying.

Thanks for clarifying.

### In the first practice

In the first practice question, the solution says that K could be 0,1 and 2. If it will be 2,(1.325) it will be 1.33 and in the problem it says that is less than 1.33 not less and not equal.
I don't know if I am missing something else which should include k=2 I believe that you are ROUNDING 1.325 to the nearest hundredth to get 1.33
However, the question makes no mention of "rounding."
Given this, we can see that 1.325 is less than 1.33

Does that help?

Cheers,
Brent

### Is long division necessary

Is long division necessary for the GRE? (I've never understood it.)  