Help with some homework.
13. What is 3.56 x 10^-5 in standard form?
14. Which of the following appears to be an irrational number?
15. Which number is equivalent to 0.454545?
16. Riding the bus, Roger uses 1/3 of his money for bus fare. What is the fraction of his money expressed as a decimal?
17. Josh has 5/8 of a foot of plywood. To finish building the deck, he needs five times that amount. How many feet of plywood does Josh need?
18. -1/6 + (-3/7)=
19. 11/12 + (-2 /3)=
20. 10 5/18 - 8 5/6
21. 1/4 x -1/2
I'm super desperate, I have until midnight.
#13: move the decimal place 5 to the left, filling in zeroes as needed
#14: ???
#15: when you have a group of repeating digits, place them over an equal number of nines. Thus
0.454545... = 45/99 = 5/11
Of course, you may have to adjust if there are leading non-repeating digits.
0.004545 = 0.01 * 0.454545 = 1/100 * 5/11 = 5/1100 = 1/220
0.23454545 = 0.23 + 0.00454545 = 23/100 + 1/220 = 129/550
#16: just do the division ... 1/3 = 0.3333...
#17: 5 * 5/8 = 25/8 = 3 1/8
#18: -1/6 + (-3/7) = -1/6 - 3/7 = -7/42 - 18/42 = -25/42
#19: 11/12 + (-2 /3) = 11/12 - 8/12 = 3/12 = 1/4
#20: 10 5/18 - 8 5/6 = 9 23/18 - 8 15/18 = 1 8/18 = 1 4/9
#21: 1/4 x -1/2 = -(1/4)(1/2) = -1/8
when multiplying fractions, multiply the tops and bottom, then simplify.
2/3 * 3/8 = 6/24 = 1/4
when dividing, multiply by the reciprocal of the divisor.
2/3 ÷ 3/8 = 2/3 * 8/3 = 16/9
If any of this is still unclear, you have some studying to do, yeah?
Thank you so much. I really appreciate this.
If you’re expecting someone to hand you the answers, you’ve come to the wrong website. But if you actually want help, a math tutor might give up part of New Year’s Eve. No guarantees, though.
I understand, I'm just trying to get this done so I dont fail this semester and get kicked out of school. Sorry.
Here’s something you can do now. Go to https://www.mathsisfun.com/ and click on Numbers. Then go into the Fractions menu, and you should find explanations and examples for some of your questions.
You’re welcome.
There’s an Algebra section there, too, which you might find helpful.
I'll be happy to help you with your homework. Let's go through each question step by step:
13. What is 3.56 x 10^-5 in standard form?
To convert a number from scientific notation to standard form, you move the decimal point to the right or left depending on the sign of the exponent. In this case, the exponent is -5, so we need to move the decimal point 5 places to the left. Starting with 3.56, we move the decimal point to get 0.0000356. Therefore, 3.56 x 10^-5 in standard form is 0.0000356.
14. Which of the following appears to be an irrational number?
To determine if a number is irrational, check if it can be expressed as a fraction or a repeating decimal. Without the provided options, I cannot specifically identify an irrational number for you. However, common examples of irrational numbers include pi (π) and the square root of 2 (√2).
15. Which number is equivalent to 0.454545?
To determine the equivalent number, notice that the decimal part is repeating. To convert this repeating decimal to a fraction, let x be the original number. Multiply both sides of the equation x = 0.454545... by 100 to eliminate the repeating part. You get 100x = 45.454545...
Now, subtract the initial equation x = 0.454545... from both sides of the equation 100x = 45.454545.... The repeating part will cancel out, so you have 100x - x = 45.454545... - 0.454545.... Simplify this to 99x = 45.
Finally, divide both sides of the equation by 99 to solve for x. You get x = 45/99. Simplifying this fraction, you get x = 5/11. Therefore, the number equivalent to 0.454545 is 5/11.
16. Riding the bus, Roger uses 1/3 of his money for bus fare. What is the fraction of his money expressed as a decimal?
To express a fraction as a decimal, divide the numerator by the denominator. In this case, Roger uses 1/3 of his money. Dividing 1 by 3 gives us 0.33333... as the decimal representation for 1/3.
17. Josh has 5/8 of a foot of plywood. To finish building the deck, he needs five times that amount. How many feet of plywood does Josh need?
To find out how much plywood Josh needs, multiply the given amount (5/8 of a foot) by 5.
(5/8) * 5 = (5 * 5) / 8 = 25/8.
Since we are talking about feet of plywood, we cannot have a fraction in the answer. To convert 25/8 into a mixed number, divide the numerator by the denominator. You get 3, with a remainder of 1. So Josh needs 3 and 1/8 feet of plywood.
18. -1/6 + (-3/7) =
To add or subtract fractions, you need to have a common denominator. The common denominator for 6 and 7 is 42. Multiply each fraction by the appropriate factor:
(-1/6) * (7/7) + (-3/7) * (6/6) =
-7/42 + (-18/42) =
After combining the numerators, you get -25/42 as the final answer.
19. 11/12 + (-2/3) =
Again, find a common denominator, which in this case is 12. Multiply each fraction accordingly:
(11/12) + (-2/3) * (4/4) =
11/12 + (-8/12) =
After combining the numerators, you get 3/12. Simplify by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 3:
3/12 ÷ 3/12 = 1/4.
Therefore, 11/12 + (-2/3) equals 1/4.
20. 10 5/18 - 8 5/6 =
To subtract mixed numbers, convert them into improper fractions.
10 5/18 can be written as (10*18 + 5)/18 = 185/18
8 5/6 can be written as (8*6 + 5)/6 = 53/6
Now that we have the mixed numbers as improper fractions, we can subtract them:
185/18 - 53/6 =
To have a common denominator, we multiply the first fraction by 6 and the second fraction by 18:
(185/18) * (6/6) - (53/6) * (3/3) =
1110/108 - 159/18 =
Now, find a common denominator of 108:
(1110 - 159*6)/108 =
(1110 - 954)/108 =
156/108.
This fraction can be simplified by dividing the numerator and denominator by their GCD, which is 12:
(156/12)/(108/12) =
13/9.
Therefore, 10 5/18 - 8 5/6 equals 13/9.
21. 1/4 x -1/2 =
To multiply fractions, multiply the numerators together and the denominators together:
(1 * -1)/(4 * 2) =
-1/8.
Therefore, 1/4 x -1/2 equals -1/8.
I hope this helps! Let me know if you have any further questions.