Math help!!!?

Question

1.Explain why 0.1 million has to be 100 000

2.a) How many numbers are there between 100 000 and 125 000 where the digits are n order from least to greatest? No digit can be repeated.

b) Which number is the least and which is the greatest?

3. Johann Carl Friedrich Gauss was born on April 30, 1777. He was one of the universal mathematicians; he studied every area of mathematics known at the time. Gauss was a child prodigy. One problem he solved as a child was to add the numbers from 1 to 100.
This may not sound like a big problem (especially with a calculator, which Gauss did not have), but he is said to have done the problem instantly at the age of 7. Try a simpler problem: Add the numbers from 1 to 10. See if you can see a pattern that might have helped Gauss find his sum of the numbers from 1 to 100.

Another question:

Canadians ate 2296.8 million kg of fruit in 2002.
a) About how many tonnes of fruoit is this? Show your work.
b) There are about 30 million Canadians. Did a typical canadian eat closer to 1 tonne, 0.1 tonnes, or 0.01 of fruit? Explain.

Answer 1

The first question has been answered and is pretty trivial. The other two are moch more interesting.

2. Your number must start with 1 since all numbers between 100000 and 125000 do. Since each digit must be greater than the previous one, the next digit is 2 since 130000 is too big. To get the smallest number possible, keep choosing the smallest digit available for each successive place. The smallest number is: 123456

Noe find the other numbers. After 123456 you can start choosing larger numbers in the least significant place to make sure you have the next in the series. The next several are:

123457, 123458, 123459

Now we need to choose larger numbers for the tems place and pick all the possible larger digits for the remaining position:

123467, 123468, 123469
123478, 123479
123489

Thats it for the 1234xx numbers. Move on the 1235 the same way:

123567, 123568, 123569
123578, 123579
123589

Thats it for 1235xx. Now the 1236xx:

123678, 123679
123689

Notice that each set is a little shorter. Do 1237xx:

123789

That's it for 123xxx, on to 124xxx. By now you see the routine:

124567, 124568, 124569
124578, 124579
124589,

124678, 124679
124689

124789

That's all the numbers that meet your criterion, 30 of them rangijng from 123456 to 124789.

3. The formula for adding numbers is pretty easy to derive. Noice that you can go straight to the sum of 1-100. No need to work with 1-10.

1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
........
47 + 54 = 101
48 + 53 = 101
49 + 52 = 101
50 + 51 = 101

So you have 50 sums, each equaling 101. The sum of numbers from 1 to 100 then is 50 * 101 = 5050. In general you have n/2 sums totally n+1 each so the general formula is (n+1)xn/2.

Answer 2

1.
1 million = 1,000,000
0.1 million = 0.1 * 1 000 000 = 100 000

3.
Write the numbers forward then underneath write them backwards.
1 + 2 + 3 + ... + n
n + (n-1) + (n-2) ... + 1
Add the top row to the bottom row one term at a time
(n+1) + (n -1 +2) + (n-2 + 3) ... (n+1)=
(n+1) + (n+1) + (n+1) ... (n+1)

These terms are all the same. The number of terms is the same as the number of terms in 1 + 2 + 3 + ... + n which is n
So you can rewrite that as n(n+1).
Since you added the numbers both forwards and backwards, n(n+1) is double the sum. divide it by 2

the sum will be n(n+1)/2

Answer 3

#1: Because x million MEANS x*1,000,000, and .1*1,000,000 is 100,000.

#2: There are 30 possibilities. In order from least to greatest, they are:
123456
123457
123458
123459
123467
123468
123469
123478
123479
123489
123567
123568
123569
123578
123579
123589
123678
123679
123689
123789
124567
124568
124569
124578
124579
124589
124678
124679
124689
124789

#3: The sum of the first n numbers is n(n+1)/2. The sum of the first 100 numbers is 5050.

Answer 4

1. 0.1 million is one tenth of a million, which is 100,000

2a. 1

2b. 123456 and 123456

3. The numbers from 1 to 10 equal 55. Gauss used the formula (n+1)/2 to find the answer, where n equals the largest of the numbers. Of course one assumes that the sequence starts at 1.

Answer 5

1 75% 2 10% 3 92% 4 2% 5 13% 6 38% 7 80% 8 14% 9 25% 11 70%

Answer 6

1 1000000 is also 10^6, .1 is 10^-1 so either multiply the original numbers or use the law of exponents and add the exponents to get 100000 which is 10^5




3. By listing conseutve in asending and deceding order, their sum of the ajacent pair is the same giving sum n = n(n+1)/2

Answer 7

1. it's because 0.1 is one tenth. so devide one million by 10 and you get 100,000

2. 123456 is both the greatest and least and the only one that works.

3. 1 plus 2 is 3. plus 3 is 6. plus 4 is ten. plus five is 15. plus six is 21. plus 7 is 28. plus 8 is 36. plus nine is 45. plus 10 is 55. there isn't a pattern that i can see.

Answer 8

1 million=1,000,000
0.1 million=0.1*1,000,000=100,000

2.leasr nimber is 123456
greatest123456

3.1+10=11
2+9=11
3+8=11
4+7=11
5+6=11
so 5*11=55

Answer 9

1.0.1 million is 1/10 of 1million so it is 1000000 divided by 10
2a. somit must be wrong the answer if the q is right is 1
2b. if 2a is right it is 100 000
3.?