# 9.6.2: Converting from decimal to non-decimal bases. info About A number N is given below in decimal format. Compute the representation of N in the indicated base. (a) N = 217, binary. (b) N = 99, hex. (c) N = 344, hex. (d) N =136, base 7. (e) N = 542, base 5. (f) N = 727, base 8. (g) N = 171, hex. (h) N = 91, base 3. (i) N = 840, base 9.

g

Step-by-step explanation:

a) A good method to convert a decimal number to binary is dividing it by 2 and using the remainder of the division as the converted number, starting by the most significant bit (the right one). We we can't divide anymore. So we have:

217/2 = 108 + 1

108/2 = 54 + 0

54/2 = 27 + 0

27/2 = 13 + 1

13/2 = 6 + 1

6/2 = 3 + 0

3/2 = 2 +1

2/2 = 1

The binary equivalent to 217 is 11011001

b) To convert a number from decimal to hex we can divide the number by 16, taking out the decimal part and multiplying it by 16 using that as our most significant number while using the result of the original division to continue our conversion. So we have:

99/16 = 6.1875

The decimal part is 0.1875, we multiply it by 16 and obtain 3 as our most significant number. Since we can't divide 6 by 16 we have that as our least significant number then the hexadecimal equivalent is 63.

c) We follow the same steps as in item b:

344/16 = 21.5

The most significant number is 0.5*16 = 8

21/16 = 1.3125

The next number is 0.3125*16 = 5

Since we can't divide it anymore we have our result wich is 158 in hex.

d) To convert from decimal to base 7 we'll use the same method as to hex, but this time dividing and multiplying by 7.

136/7 = 19.428571

The most significant number is 0.428571 * 7 = 3

19/7 = 2.71428571

The next number is 0.71428571*7 = 5

Since we can't divide it anymore we have our result wich is 253.

e) To convert from decimal to a base 5 we'll use the same method as before but dividing and multiplying by 5.

542/5 = 108.4

The most significant number is 0.4*5 = 2

108/5 = 21.6

The next number is 0.6*5 = 3

21/5 = 4.2

The next number is 0.2*5 = 1

Since we can't divide it anymore we have our result that is 4132.

f) To convert from decimal to a base 8 we'll use the same method as before but dividing and multiplying by 8.

727/8 = 90.875

The most significant number is 0.875*8 = 7

90/8 = 11.25

The next number is 0.25*8 = 2

11/8 = 1.375

The next number is 0.375*8 = 3

Since we can't divide anymore we have our result wich is 1327

g) Following the same steps as before:

171/16 = 10.6875

The most significant number is 0.6875*16 = 11

Since we can't divide anymore we have our result wich is 1011

h) Following the same steps as before:

91/3 = 30.333333333

The most significant number is 0.333333*3 = 1

30/3 = 10

The next number is 0

10/3 = 3.3333333333

The next number is 0.333333*3 = 1

3/3 = 1

Since we have the final value remainder as 0 the least significant number is 1

Since we can't divide anymore we have our result that is 10101.

i) Following the same steps as before:

840/9 = 93.333333

The most significant number is 0.33333*9 = 3

93/9 =  10.3333333

The next number is 0.333333*9 = 3

10/9 = 1.11111111

The next number is 0.11111111*9 = 1

Since we cant divide anymore we have our result that is 1133

To convert decimal numbers to non-decimal bases, divide the number by the base, note the remainders, and read the remainders in reverse order to get the converted number. This applies to binary, hexadecimal, and other bases like base 7 or base 5. The process continues until the quotient is zero.

### Explanation:

The process of converting numbers from decimal to non-decimal bases involves division for integer parts and multiplication for fractional parts, using the target base until the dividends are zero or an acceptable level of fractional precision is reached. For whole numbers, divide the number by the new base, note the remainder, and continue dividing the quotient until it equals zero. The remainders noted, read in reverse order (from last to first), give the resulting non-decimal number.

To convert 217 to binary, you would start by dividing 217 by 2, the base for binary numbers, and noting the remainders. This division continues until the quotient is zero. Read the remainders backwards to get the binary representation.

For conversion to hexadecimal, which is base 16, you divide the number by 16, note the remainders, continue with the quotient, and read the remainders in reverse order to get the hexadecimal equivalent. Alphabetic characters are used for remainders of 10-15, representing 'A' to 'F'.

When converting to other bases like base 7 or base 5, you follow a similar division method but use the base you're converting to. For example, in base 7, you divide by 7 and use the remainders to construct the new base representation. Always read the remainders in reverse to obtain the correct number in the new base.

In cases like base 8 or base 9, the same principles apply. Dividing the number by 8 or 9, respectively, and noting the remainders until you reach a quotient of zero will give you the representation in the new base.

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## Related Questions

72 is 45% of what number

72 is 45% of 160.I hope this helps :D

The mean SAT score in mathematics, M, is 600. The standard deviation of these scores is 48. A special preparation course claims that its graduates will score higher, on average, than the mean score 600. A random sample of 70 students completed the course, and their mean SAT score in mathematics was 613. a) At the 0.05 level of significance, can we conclude that the preparation course does what it claims? Assume that the standard deviation of the scores of course graduates is also 48.

Step-by-step explanation:

The mean SAT score is , we are going to call it \mu since it's the "true" mean

The standard deviation (we are going to call it ) is

Next they draw a random sample of n=70 students, and they got a mean score (denoted by ) of

The test then boils down to the question if the score of 613 obtained by the students in the sample is statistically bigger that the "true" mean of 600.

- So the Null Hypothesis

- The alternative would be then the opposite

The test statistic for this type of test takes the form

and this test statistic follows a normal distribution. This last part is quite important because it will tell us where to look for the critical value. The problem ask for a 0.05 significance level. Looking at the normal distribution table, the critical value that leaves .05% in the upper tail is 1.645.

With this we can then replace the values in the test statistic and compare it to the critical value of 1.645.

### since 2.266>1.645 we  can reject the null hypothesis.

The null hypothesis is that the SAT score is not significantly different for the course graduates.

Alternate hypothesis: there is a significant difference between the SAT score achieved by the course graduates as compared to the non-graduates.

Apply the t-test. The Test Statistic value comes out to be t = 1.738 and the p-value = 0.0844

Since the p-value is larger than 0.05, the evidence is weak and we fail to reject eh null hypothesis.

Hope that answers the question, have a great day!

The sum of two integers is 44. The difference of the two integers is 8.What is the smaller integer?

18

Step-by-step explanation:

44/2=22

the difference between the two numbers= 8

8/2=4

(22-4) + (22+4) = 18+26 = 44

the smaller number = 18

The smaller integer is 18.

Step-by-step explanation:

x is the larger integer, and y is the smaller integer.

x + y = 44

x - y = 8

For x - y = 8, add y to both sides and get x = 8 + y.

Change x in x + y = 44 for 8 + y.

8 + y + y = 44

8 + 2y = 44

2y = 36

y = 18

A small jar of peanut butter sells for 0.08 per ounce. A large jar of peanut butter sells for $1.20 per pound. Which is the better buy and by how much (in cents per pound)? ### Answers Answer: a small jar of penuts buteer sells for 0.08 per ounce A large jar of penut buttter sells for$1.20 per pound

Greg used 1 inch tiles to help make a ruler what mistake did he make

Answer: he didn't make a mistake?

Step-by-step explanation:

Please help!!! Will mark brainliest!!!!!!!! Dan wants to determine the probability that the republican on the ballot will be elected mayor of his town. He surveys a random sample of 25 people in the town who are registered to vote. Based on this data, the republican on the ballot has a 36% probability of being elected. Dan now wants to gauge the variation in predictions, to determine how accurate this probability may be. Which if the following would be the best method for him to do this?A) Ask the same 25 people he originally surveyed to make sure they are convinced of their choices

B) Survey several more random samples of 25 people each from people in the town who are registered to vote

C) Survey serveral more random samples of 25 people each from the Republican voters in town

D) Survey a random sample of 25 people who are registered to vote in another town