Please help me with this math...???????

Question

this is pre-algebra and im in 10th grade and I canot pass this class I need help please explain how you get the answer to these.

(I Used the "^" sign in front of the exponent)

1.Write 4.73 x 10^7 in standard notation
(would the answer be 4,730,000,000)


2.A family won a $500 million lottery. Their winnings in scientific notation are $_____.


3.Is 125 a prime or composite number? If composite, list all of its factors.


4. Reduce 6 16/24 to lowest terms.


5.Simplify and reduce: 4 10/32 + 7 2/32

thank u rosypink and other that have helped I apperciate it alot!
=)

Answer 1

Question 1: 4.73 x 10^7 in standard notation

Answer: Since the exponent is 7, move the decimal point over 7 places to get 47,300,000.

Question 2: $500 million in scientific notation

Answer: 5,000,000 = $ 5.0 x 10^6

Question 3: 125 - composite or prime?
Well, a prime number is one that can only be divided by 1 and itself...but it can be divided by 5 and 25, so it's not prime - it's composite.

Question 4: 6 16/24

Answer: the fraction 16/24 can be reduced...because both the 16 and 24 can be divided by 8 to get 2/3. So ur answer is 6 2/3 or 20/3.

Question 5: simplify 4 10/32 + 7 2/32

Answer: the 10/32 can be reduced to 5/16 by dividing both the numerator and denomenator by 2. Also, the 2/32 can be reduced to 1/16 by dividing both the numerator and denomenator by 2...this will give you 4 5/16 and 7 1/16. The mixed fraction 4 5/16 can be converted to 69/16. And the mixed fraction 7 1/16 can be converted to 113/16. Then just add these fractions together like this:

69/16 + 113/16
= (69 + 113)/16
= 182/16
= 11.375 (in decimal form) OR 91/8 (in fractional form)

The answers are in their simplest form.

Answer 2

By the numbers:

1. You're making the classical mistake of thinking that the power of ten, the 7 in 10^7, is how many zeroes you add. Sometimes, but not always.

10^7 means to multiply the number by ten SEVEN TIMES. Now, take 4.73 and multiply by ten ONCE. You'll get 47.3. Then multiply by ten again, and you'll get 473. So, you see that the decimal point moves to the right each time you multiply by ten. In your answer the decimal point moved from behind the four to behind the last zero -- NINE times. So that is wrong.

Your method works if you start with a natural number (1,2,3,etc.) and multiply by a power of ten. Each time the decimal place moves to the right, you add a zero -- but 4.73 isn't a natural number.

2. You first have to write 500 million in standard notation. Remember that the first comma you'll add is the thousands comma, and the second the millions, so it's 500,000,000. Now, write the proper mantissa (the number before the *10^whatever -- it has to be a number from one UP TO ten, but not ten itself!). In this case, that would be 5. Now, figure out how many times you'd have to move the decimal to the right to make 500,000,000. That's how many POWERS of ten you'll need.

3. Prime means the only way to make the number (using natural numbers) by multiplication is 1 times itself. For example, the only way to make 7 is 1 times 7, so seven is PRIME. Composite means that there are OTHER WAYS to make the number; so 6 is composite because though 6 is 1 times 6, it's also 2 times 3.

Now, 125 is interesting because it ends in a five, and every number that ends in 5 is made by doing 5 times SOMETHING. 15 = 5 * 3, 25 = 5 * 5, 35 = 5 * 7, etc. so we can guess that 125 can be made by 5 * SOMETHING, so it's composite.

But what are ALL its factors? This is where it helps to know how to divide and how to find the square root. First, estimate on the high side the square root of 125 -- I'd try 12, because 12 * 12 is 144, so you're safe there. Then, starting at 1 and going up to 12, divide 144 by each of them. When you get no remainder, like when you divide 144 by 1 and get 144, or 144 by 2 and get 72, list both the number you divided by (the divisor) and the number you got (the quotient). So, 1,144, 2 and 72 are all FACTORS of 144. Keep going all the way up to 12. Note: Don't bother dividing by 5, however, because 144 doesn't end in 5 -- did you remember that??

4. For 6 and 16/24, leave the 6 alone -- it's whole and complete. Focus on the 16/24 and look for the greatest shared factor of 16 and 24. If you've learned the prime factorization method, 16 = 2 x 2 x 2 x 2, and 24 = 2 x 2 x 2 x 3, and you can see that they BOTH have 2 x 2 x 2, or 8, in common. That means you can leave out the 2 x 2 x 2, and just write what's left: the 16 becomes 2, and the 24 becomes 3, and your fraction reduces to 2/3.

5. Add like terms. The 4 10/32 means "Four ones and 10 thirty-seconds" and the 7 2/32 means "Seven ones and 2 thirty-seconds". Add the ones together (four and seven), and the thirty-seconds together (10 and 2) to get 11 and 12/32.

Use the prime factorization method for the fraction 12/32: 12 = 2 x 2 x 3, and 32 = 2 x 2 x 2 x 2 x 2, and see that they both share the 2 x 2, so leave that out and write the 12 as 3 and the 32 as 2 x 2 x 2, or 8. (You're really factoring out 2 x 2 -- or four -- but that's a concept that is REALLY hard for many students to get, and I still haven't figured out why!!).

Good luck passing your class. I feel for you!!

Answer 3

1. No - that is not the correct answer. If the exponent is positive (as in this case) you move the decimal point that many places to the right. So, we want to move the decimal place 7 places to the right, giving us:

4 7 3 _ _ _ _ _.

Fill in these places with a 0:

47300000

So your final answer is 47,300,000.

(If you have a negative exponent, you would move it that many places to the left.)

2. $500 million = 500,000,000.

We want the decimal place directly after the 5 to give us

5 x 10^(?) = 500,000,000.

To figure out the exponent, how many places do you need to move the decimal point to bring it after the 5? (Just count!) 8 places. So,

5 x 10^8 = 500,000,000

3.A composite number is a number than can be divided by at least one other number besides 1 and itself. Well, 25 goes into 125 5 times, so both 25 and 5 are factors of 125, thus it is composite.

List of factors: 1,5,25,125.

4. We can leave 6 - it is a whole number and cannot be reduced any further. Look at 16/24 - what number is a factor of both the numerator and the denominator? You might try 2, 4 or 8 - all would work, except if you choose 2 or 4, you will have to reduce it again. So, use 8. 16/24 = (16/8)/(24/8) = 2/3. So, reduced to lowest terms, it equals 6 2/3.

5. Whole numbers are just whole numbers, so these can immediately be added: 4 + 7 = 11. This gives us:

11 + (10/32 +2/32)

Since the denominators are already the same, we can simply add the numerators to get:

11 + (12/32).

Now we need to reduce our fraction to lowest terms. 4 goes into both 12 and 32, so divide both top and bottom by 4 to get:

11 + (3/8).

There is no number that goes into both 3 and 8 (besides 1), so we are done, and the final answer is 11 3/8.

Answer 4

1) To convert to standard notation, count 7 places past the decimal place. The answer would be 47,300,000.

2) To convert to scientific notation, find the number between 1 and 9 in the number you want to convert. In 500,000,000, that number is 5. The decimal place goes after 5. Then cout the number of places after the decimal place. There are 8, so 500,000,000 converts to 5 x 10^8

Another example: Convert 869,700 to scientific notation. The number between 1 and 9 is 8.697. Count all the places after the decimal place. There are 5, so the answer is 8.697 x 10^5

3) Any number that ends in 5 or 0 is divisible by 5. Therefore, 125 is a composite number. A prime number is only divisible by 1 and itself. Memorize the divisibility rules.

4) 6 and 16/24 is equal to (6*24 + 16)/24 or 160/24. This reduces to 20/3 or 6 and 2/3.

5) 4 and 10/32 + 7 and 2/32 =
(4*32 + 10)/32 + (7*32 + 2)/32 =
138/32 + 226/32 =
(138 + 226)/32 =
244/32 =
61/8 or 7 and 5/8

Answer 5

1.Write 4.73 x 10^7 in standard notation
Write 4.73 and string a bunch of 0' behind it
4.730000000000
Move the decimal point 7 places to the right.
4.7300000.00000
Erase the original decimal point and the 0's behind the new decimal point.
47300000.
Put in your commas
47,300,000.

2.A family won a $500 million lottery
a million is 1 followed by 6 0's, or 10^6 so you have 500 x 10^6
Move your decimal point 2 places more to the left and add 2 to the exponent
5.00 x 10^8

3.Is 125 a prime or composite number?
The number ends in 5, so it is divisible by 5
125 = 5*25
25 = 5*5
125 = 5*5*5

4. Reduce 6 16/24 to lowest terms.
Both 16 and 24 are divisible by 8
6 16/24 = 6 (2*8)/(3*8) = 6 (2/3)(8/8) = 6 2/3

5.Simplify and reduce: 4 10/32 + 7 2/32
4 10/32 + 7 2/32 = 11 12/32 = 11 (3*4)/(8*4) =
11 (3/4)(8/8) = 11 3/4

Answer 6

FROM SCIENTIFIC TO STANDARD: Anytime you have scientific notation, picture moving the decimal point over. A positive exponent means you move to the right (makes number bigger). A negative exponent means you move to the left (makes number smaller).

FROM STANDARD TO SCIENTIFIC: Basically the opposite. Move the decimal point over until you get a number between 1 and 10. If you moved to the left, the exponent is positive. If you moved to the right, the exponent ought to be negative.

1) Take 4.73 and move the decimal to the right seven spaces (filling in zeroes where necessary) 47300000. Add commas if you wish: 47,300,000.

2) $500 million is $500,000,000. We see that moving the decimal point over eight times to the left gives a number between 1-10. So, move it eight times and show that you did so by multiplying by 10^(-8).
ANSWER: 5.0 x 10^(-8)

3) The number is composite. A prime number means that number divided by any other number (except one and itself) will not give another whole number. A composite number means that you can multiply a string of whole numbers (factors) to get to that number.

This one, you kind of just have to look at. The fact that it ends in "5" should be a dead giveaway, that it has five as a factor. 125/5 = 25 or in other words 5 * 25 = 125. So the only factors are 5 and 25 (and of course, itself and one).

In case you're wondering, the prime factorization is 5*5*5 = 5^3.

4. The denominator of the improper fraction (unsimplified) remains the same. The numerator is (whole number) x (denominator) + (old numerator), so 6*24 + 16 = 160. The improper fraction is 160/24, which reduces (if you divide numerator and denominator by 8) to 20/3. Converting back to the mixed number is 6 2/3.

5. Convert both to improper fractions, using the method in the previous problem.
138/32 + 226/32 = 362/32
The simplified improper fraction (divide numerator and denominator by four) is 91/8.
The corresponding mixed number is 11 3/8.

Answer 7

1. 10 ^ 7 equals 10000000 multiply by 4.73 and the answer is what you found.

2. Scientific notation would be how question one was asked, so determine how much x is when 100 million is 10 ^ x and then the answer would be 5.0 times 10 ^ x. 1,000,000 is one million, count the zeros and you have x.

3. Prime means you can only divide the number by itself and one. As you should already know, any number that ends with five or zero is divisible by five, so start by dividing 5 into 125 (call the result y). Now determine if 'y' is prime (which it is not) and try dividing y by 5 again. I belive you have found that the factors of 125 are 5 and 1.

4. The 6 is already reduced, so you are focusing on the fractions. Determine what numbers can be multipled to equal 16 and what can be multiplied to equal 24. See what is the largest common factor and then divide that into both the 16 and 24 and place them in the fraction accordingly. For instance both numbers are divisible by 2, 4, and 8. If you only divide by the 2 your fraction would be 8/12.

5. Add the whole numbers first. Then add the numerators of the fraction. Determine if the total of the numerators has any common factors with the denominators and divide accordingly. 10 + 2 = 12. 12 has 1,2,3,4,and 6 as factors and 32 has 1,2,3,4, and 8 as factors. I'll leave the division to you.

Answer 8

1. 47,300,000 (move decimal right 7 times...if it was negative move it left 7 times)

2. 5x10^2

3. composite: 1, 125, 5, 25 (anything ending in 5 is composite b/c it can be divided by 5)

4. 20/3 ( "denominator" x "the whole number" then + "numerator"..............24x6 then + 16........when you get that number that equals the new numerator over the old denominator 24, after that you get 160/24 then reduce it)

5. if you follow my #4 directions you get 91/8, if you want a mixed fraction answer: 11 3/8 ( you just add the whole numbers first then add the fractions, if the fractions are different find a common denominator then add them)

Answer 9

1) 47,300,000, because you move the decimal a total of seven times.

2) 500,000,000 = 5x10^8

3) 125 is a composite number because 1,5,25,125 are it's factors.

4) Uhh, I'm going to assume those are mixed fractions.

138/32 + 226/32 = 364/32 = 182/16 = 91/8

Check my work.

Answer 10

1. 47300000
2. 5x10^8
3. composite 1,5, 25, 125
4. 6 2/3
5. 11 3/8