1.
Write the following in decimal form and say what kind of decimal expansion each
has:
36
4
8
100

October 10, 2021

By Bella

1 thought on “1.<br />Write the following in decimal form and say what kind of decimal expansion each<br />has:<br />36<br />4<br />8<br />100<b”

1. Answer:

   Question 1

   Write the following in decimal form and say what kind of decimal expansion each has:

   i) 36100

   ii) 111

   iii) 418

   iv) 313

   v) 211

   vi) 329400

   Answer

   i) 36100 = 0.36. It is a terminating decimal.

   ii) 111= 0.09¯¯¯¯¯. It is a non-terminating repeating decimal expansion.

   iii) 418 = 4.125. It is a terminating decimal.

   iv) 313 = 0.230769¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯. It is a non-terminating repeating decimal expansion.

   v) 211 = 0.18¯¯¯¯¯. It is a non-terminating repeating decimal expansion.

   vi) 329400 = 0.8225. It is a terminating decimal.

   Question 2

   You know that the value of 17 = 0.142857¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯. Can you predict what the decimal expansions of 27, 37, 47, 57, and 67 are, without doing the long division? If so, how?

   Solution

   Question 3

   Express the following in the form pq, where p and q are integers and q ≠ 0:

   i) 0.6¯¯¯

   ii) 0.47¯¯¯

   iii) 0.001¯¯¯¯¯¯¯¯

   Solution

   Question 4

   Express 0.9¯¯¯ in the form pq:

   Solution

   Question 5

   What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 117? Perform the division to check.

   Solution

   Question 6

   Look at several examples of rational numbers in the form pq (q ≠ 0), where p and q are integers with no common factors other than 1 and have terminating decimal expansions. What property must q satisfy?

   Solution

   Question 7

   Write three numbers whose decimal expansions are non-terminating non-recurring.

   Answer

   1. 0.1401400140001400001400000…

   2. 0.080080008000080000080000008…

   3. 0.40400400040000400000…

   Question 8

   Find three different irrational numbers between the rational numbers 57 and 911.

   Answer

   First, let us find the decimal expansions of 57 and 911.

   57=0.714285¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

   911=0.81¯¯¯¯¯

   We have to find irrational numbers between 0.714285¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ and 0.81¯¯¯¯¯

   If we write three numbers that are non-terminating and non-recurring, we will have written three irrational numbers between the two given fractions.

   0.73073007300073…, 0.7890789007890007890000…, and 0.80800800080000… are irrational numbers between the two given fractions.

   Question 9

   Classify the following numbers as rational or irrational:

   i) √23

   ii) √225

   iii) 0.3769

   iv) 7.478478….

   v) 1.101001000100001…

   Answer

   i) √23 = 4.753… It is a non-terminating and non-recurring decimal. It is an irrational number. It cannot be expressed in the form pq where p and q are integers and q ≠ 0.

   ii) √225 = 15. It is a terminating decimal. It is a rational number. It can be expressed in the form pq as 151.

   iii) 0.3769. It is a terminating decimal. It is a rational number. It can be expressed in the form pq as 376910000.

   iv) 7.478478…. It is a non-terminating but recurring decimal. It is a rational number. It can be expressed in the form pq as 7478999 or 7471999.

   v) 1.101001000100001… It is a non-terminating and non-recurring decimal. It is an irrational number. It cannot be expressed in the form pq where p and q are integers and q ≠ 0.

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