What is the decimal expansion of 7/10?

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What is the decimal expansion of 7/10?

Use part 4 three grammar corretly work all. proper and decimal

3/4 = 75/100 = 0.75

0.75 is a terminated decimal (does not continue forever)

0.75 is a rational number (it is a decimal)

1/3 = 33.33.../100

0.333333 is a continuing decimal, and so it is a repeating decimal

1/3 is a repeating number

1. Some numbers, such as [tex]\frac{1}{10}[/tex], have a decimal expansion that terminates.

2. All real numbers have a decimal expansion.

5. Some numbers, such as [tex]\frac{1}{18}[/tex], have a decimal expansion that repeats but does not terminate.

Step-by-step explanation:

According to the options, we have,

1. Some numbers, such as [tex]\frac{1}{10}[/tex], have a decimal expansion that terminates.

It is correct as the decimal expansion of [tex]\frac{1}{10}[/tex]is 0.1, which terminates.

2. All real numbers have a decimal expansion.

This is also correct as both rational and irrational numbers can be written in decimal form.

3. Some numbers, such as [tex]\sqrt{13}[/tex] do not have a decimal expansion

This is not correct as [tex]\sqrt{13}=3.605551275[/tex] i.e. it has a decimal expansion.

4. Only some real numbers have a decimal expansion.

It is not correct as 2 is correct.

5. Some numbers, such as [tex]\frac{1}{18}[/tex], have a decimal expansion that repeats but does not terminate.

It is correct as [tex]\frac{1}{18}=0.0555555..[/tex], which is non-terminating decimal expansion.

So, the correct options are,

1. Some numbers, such as [tex]\frac{1}{10}[/tex], have a decimal expansion that terminates.

2. All real numbers have a decimal expansion.

5. Some numbers, such as [tex]\frac{1}{18}[/tex], have a decimal expansion that repeats but does not terminate.

Yes, All Real Nos. have Decimal Expansion.

Correct Options are :

Option A : Some nos. , sucha as [tex]\frac{1}{10}[/tex]. have a decimal expansion that terminates.

Option B : All Real Nos. have a decimal expansion.

Option E : Some nos. , such as [tex]\frac{1}{18}[/tex], have a decimal expansion that repeats but does not terminate.

Step-by-step explanation:

Real Number consist of Rational Numbers and Irrational Numbers.

Rational Nos. have 2 type of Decimal Expansion which are terminating and non terminating but repeating.

[tex]\frac{4}{2}=2.0\:,\;\frac{1}{10}=0.1\:,\:\frac{1}{4}=0.25[/tex] are some example of terminating decial expansion.

[tex]\frac{1}{3}=0.333333...\:=\;0.\overline{3}\:,\:\frac{1}{18}=0.0555555...\:=\:0.0\overline{5}[/tex] are some examples of non terinating but repeating decimal expansions.

Irrational Nos. have non terminating non repeating decimal expansions.

[tex]\sqrt{2},\sqrt{3}, so\:on\:, 0.1011001110001111000...\:, \:\pi[/tex] are some examples of non terminating non repeating decimal expansions.

Therefore, ALL Real Nos. have Decimal Expansion.

Correct Options are :

Option A : Some nos. , sucha as [tex]\frac{1}{10}[/tex]. have a decimal expansion that terminates.

Option B : All Real Nos. have a decimal expansion.

Option E : Some nos. , such as [tex]\frac{1}{18}[/tex], have a decimal expansion that repeats but does not terminate.

please find the answer in the explanation

Step-by-step explanation:

1.) All integers are rational numbers.

The statement is false because 1/2 is a rational number but not an integer

2.) Which of the following must describe an irrational number?

- A number with a repeating or terminating decimal expansion.

3.) Which axiom is used to prove that the product of two rational numbers is rational?

Integers are closed under division

4.) Without calculating, how do you know the product 2/21 x 3/31 is rational?

When multiplying fractions, the product of two fractions is rational so long as both fractions are less than 1.

5.) What rational number, when multiplied by an irrational number, has a product that is a rational number? 1/10

1. (1010 0110)₂ = (166)₁₀

2. (145)₁₀ = (1001 0001)₂

3. (101 000 111 100)₂ = (5074)₈

4. (1111 1100 0011 0110)₂ = (FC36)₁₆

1. Convert the 8-binary binary expansion (1010 0110)₂ to a decimal expansion.

In order to solve this problem we have to use the expansion:

n = aₓbˣ + aₓ₋₁bˣ⁻¹ + ... + a₁b¹ + a₀

where b = 2, x = 8 - 1 = 7 due is a 8-binary

(1010 0110)₂ = 1 x 2⁷ + 0 x 2⁶ + 1 x 2⁵ + 0 x 2⁴ + 0 x 2³ + 1 x 2² + 1 x 2¹ + 0 x 2⁰

(1010 0110)₂ = 128 + 0 + 32 + 0 + 0 + 4 + 2 + 0

(1010 0110)₂ = (166)₁₀

2. Convert the following decimal expansion (145)₁₀ to an 8-bit binary expansion.

To solve this problem we have to use the divide by 2 process.

Since we are dividing by 2, when the dividend is an even number, the remainder will be 0, and when the dividend is an odd number the binary residual will be 1.

145 > 1 Less significant bit

145/2 = 72 > 0

72/ 2 = 36 > 0

36/2 = 18 > 0

18/2 = 9 > 1

9/2 = 4 > 0

4/2 = 2 > 0

2/2 = 1 > 1 Most significant bit

Then we order from the most significant bit to the less significant bit (from the bottom to the top) to obtain the 8-binary number:

(145)₁₀ = (1001 0001)₂

3. Convert the following hexadecimal expansion (A3C)₁₆ to an octal expansion.

To convert a hexadecimal expansion to an octal expansion we have to convert from hexadecimal to binary and then to octal using the table hexadecimal to binary and binary to octal.

Converting from hexadecimal to binary:

(A3C)₁₆

A = 1010, 3 = 0011 and C = 1100

(A3C)₁₆ = (1010 0011 1100)₂

Converting from binary to octal:

To convert binary to octal we have to order the binary expansion into group of 3-bits and use the table to convert binary to octal.

(1010 0011 1100)₂ = (101 000 111 100)₂

101 = 5, 000 = 0, 111 = 7 and 100 = 4

(101 000 111 100)₂ = (5074)₈

4. Convert the following binary expansion (1111 1100 0011 0110)₂ to a hexadecimal expansion.

To solve this exercise we have to use the binary to hexadecimal table.

(1111 1100 0011 0110)₂

1111 = F, 1100 = C, 0011 = 3 and 0110 = 6

(1111 1100 0011 0110)₂ = (FC36)₁₆

0.7 is the decimal expansion okok

Step-by-step explanation:

a number with a non repeating and non terminating decimal expansion.

Step-by-step explanation:

Irrational numbers are numbers which cannot be expressed as fractions, they are real numbers which cannot be expressed as rational numbers such as the square root of natural numbers other than perfect squares.

Irrational numbers are non repeating, non terminating decimal numbers with no group of the digits repeated. Therefore the decimal expansion does not terminate but continues without repetition example is π.

D.

Step-by-step explanation:

A irrational number can be defined as those numbers which are real but can NOT be expressed in simple fractions. The term 'irrational' means 'a number which can not be expressed in ratio of two integers', 'no ratio.'

When a irrational number is expressed in decimal, the numbers keep on expanding without repeating andd without terminating, which means it keeps on expanding infinitely.

For example, π (pi) is an irrational number. When it is expressed in decimals it keeps on expanding non-repeatedly and unendingly.

Another example of an irrational number is √2.

Thus the correct statement that defines irrational number is option D.