O-Level Additional Math

[PuffyCakes]

My DD says: So does that mean that rational nos. are whole nos.?

[ChewingPencilLine]

Rational numbers can be whole numbers but are not necessarily whole numbers.

For example, 2/3 = 0.66666666 is a rational number but it is not a whole number.

In fact, most of the time, rational numbers are NOT whole numbers. But they can be whole numbers.

[KiausuLormee]

Can someone help in this question:

There are some $2 notes, $10 notes and $50 notes in Mr Singh’s wallet . The number of $50 notes is 1 more than twice the number of $2 notes. The number of $10 notes is 1 less than the number of $2 notes. Let x, y and z be the numbers of $2, $10 and $50 notes respectively.
(a) Express y and z in terms of x.
(b) Express the total amount of money in terms of x.
If there are 4 $2 notes, find the total amount of money.

[PuffyCakes]

Okay…Thx so much.

If this qn comes out, will the teacher accept both ans.?
Sry for being too inquisitive:(

[ChewingPencilLine]

I would not take that as 2 separate answers. That is actually the full complete solution with a detailed explanation.


If the question is ARE (ALL) RATIONAL NUMBERS WHOLE NUMBERS. TRUE OR FALSE? I would go with FALSE.

Hope this helps!

[PuffyCakes]

Oooo...Thx so much:D

:salute:
:thankyou:

[archie2]

can someone help me again with this similar questions

Q1a>> what is the last digit of 7^128?
Q1b>> what is the last two digit of 7^128?
Q1c>> what is the last four digit of 7^128?
thank you

[archie2]

pinkapple:

archie2:

can someone help to solve this.

Q1> What is the unit digit in (243^10)(163^9)(633^8)?

answer: 7 :imcool:

http://www.facebook.com/photo.php?fbid=500572910002062&set=a.500572863335400.1073741830.466376010088419&type=1&relevant_count=1

thanks for the explaination
however when the power is high, the value has lots of zero at the back, say, does your method works for 3^50?

[pinkapple]

archie2:

pinkapple:

[quote=\"archie2\"]can someone help to solve this.

Q1> What is the unit digit in (243^10)(163^9)(633^8)?

answer: 7 :imcool:

http://www.facebook.com/photo.php?fbid=500572910002062&set=a.500572863335400.1073741830.466376010088419&type=1&relevant_count=1

thanks for the explaination
however when the power is high, the value has lots of zero at the back, say, does your method works for 3^50?[/quote]yes. look at Method 2. it's using number pattern 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1,...
so for powers which are multiples of 3, the digit unit will be 7, while powers of multiples of 4 will be 1. anything else, u just work forward of backwards.

for 3^50, the nearest power to multiple of 3 or 4 is 48 (a multiple of 4)
so 3^48 = ...1
3^49 = ...3
3^50 = ...9

[pinkapple]

archie2:

can someone help me again with this similar questions

Q1a>> what is the last digit of 7^128?
Q1b>> what is the last two digit of 7^128?
Q1c>> what is the last four digit of 7^128?
thank you

last digit of 7^128 is 1
last two digit of 7^128 is 01
last four digit of 7^128 is 6401