Types of Numbers - SAT Math

Card 0 of 32

Question

Express 374 in base six.

Answer

To convert a base ten number to base six, divide the number by six, with the remainder being the digit in the units place; continue, dividing each successive quotient by 6 and putting the remainder in the next position to the left until the final quotient is less than 6.

$374 \div 6 = 62\textrm{ R }\underline{2}$ - the rightmost digit is 2

$62 \div 6 = 10 \textrm{ R }\underline{2}$ - the next digit to the left is 2

$10 \div 6 = \underline{1} \textrm{ R }\underline{4}$ - the next digit to the left is 4, and the digit to the left of that is 1.

$374 = 1422_{\textrm{six}}$

Compare your answer with the correct one above

Question

Express $13241 _{\textrm{five}}$ in base ten.

Answer

Place values in the base five system are powers of five rather than powers of ten. $13241 _{\textrm{five}}$ is equal to

$1 \times 5^{4} + 3 \times 5 ^{3} + 2 \times 5^{2} + 4 \times 5 + 1$

$= 1 \times 625 + 3 \times 125 + 2 \times 25 + 4 \times 5 + 1$

Compare your answer with the correct one above

Question

Which of the following is the smallest prime number:?

Answer

A prime number has only two factor, and itself.

This is not true for or so they are not the answer.

are all prime numbers and is the smallest so it is your answer.

Compare your answer with the correct one above

Question

Which of the following is a rational number?

$\frac{1}{2},\sqrt{5},2i,3.658$

Answer

A rational number is any number that can be expressed as an integer p or a fraction p/q. In the set of number given only $\tiny \frac{1}{2}$ fits into that category.

Compare your answer with the correct one above

Question

Express 73 as a binary (base two) number.

Answer

73 can be uniquely expressed as the sum of distinct powers of two as follows:

$73 = 64 + 8 + 1 = 2^{6} + 2^{3}+ 2^{0}$

Therefore, there is a "1" in the seventh, fourth, and first positions from the right, and a "0" everywhere else. So,

$73 = 1001001_{\textrm{two}}$

Compare your answer with the correct one above

Question

Express $1011101_{\textrm{two}}$ as a base ten number.

Answer

Place values in the base two system are powers of two rather than powers of ten.

$1011101_{\textrm{two}}$ is equal to:

$1\times 2^{6}+0\times 2^{5}+ 1\times 2^{4}+1 \times 2^{3}+ 1 \times 2^{2}+ 0 \times 2^{1} +1$

$= 1\times 64+0\times32+ 1\times 16+1 \times 8+ 1 \times 4+ 0 \times2+1$

Compare your answer with the correct one above

Question

Express 68 as a base two (binary) number.

Answer

68 can be expressed as the sum of distinct powers of two as follows:

$68 = 64 + 4 = 2^{6}+ 2^{2}$

Therefore, there are 1's in the seventh and third place from the right, and 0's everywhere else, so

$68 = 1000100_{\textrm{two}}$

Compare your answer with the correct one above

Question

Which of the following numbers is an imaginary number?

Answer

By definition, an imaginary number is a number with the term "i" in it. For this problem 7i is the only answer with the imaginary part.

Compare your answer with the correct one above

Question

Express 374 in base six.

Answer

To convert a base ten number to base six, divide the number by six, with the remainder being the digit in the units place; continue, dividing each successive quotient by 6 and putting the remainder in the next position to the left until the final quotient is less than 6.

$374 \div 6 = 62\textrm{ R }\underline{2}$ - the rightmost digit is 2

$62 \div 6 = 10 \textrm{ R }\underline{2}$ - the next digit to the left is 2

$10 \div 6 = \underline{1} \textrm{ R }\underline{4}$ - the next digit to the left is 4, and the digit to the left of that is 1.

$374 = 1422_{\textrm{six}}$

Compare your answer with the correct one above

Question

Express $13241 _{\textrm{five}}$ in base ten.

Answer

Place values in the base five system are powers of five rather than powers of ten. $13241 _{\textrm{five}}$ is equal to

$1 \times 5^{4} + 3 \times 5 ^{3} + 2 \times 5^{2} + 4 \times 5 + 1$

$= 1 \times 625 + 3 \times 125 + 2 \times 25 + 4 \times 5 + 1$

Compare your answer with the correct one above

Question

Which of the following is the smallest prime number:?

Answer

A prime number has only two factor, and itself.

This is not true for or so they are not the answer.

are all prime numbers and is the smallest so it is your answer.

Compare your answer with the correct one above

Question

Which of the following is a rational number?

$\frac{1}{2},\sqrt{5},2i,3.658$

Answer

A rational number is any number that can be expressed as an integer p or a fraction p/q. In the set of number given only $\tiny \frac{1}{2}$ fits into that category.

Compare your answer with the correct one above

Question

Express 73 as a binary (base two) number.

Answer

73 can be uniquely expressed as the sum of distinct powers of two as follows:

$73 = 64 + 8 + 1 = 2^{6} + 2^{3}+ 2^{0}$

Therefore, there is a "1" in the seventh, fourth, and first positions from the right, and a "0" everywhere else. So,

$73 = 1001001_{\textrm{two}}$

Compare your answer with the correct one above

Question

Express $1011101_{\textrm{two}}$ as a base ten number.

Answer

Place values in the base two system are powers of two rather than powers of ten.

$1011101_{\textrm{two}}$ is equal to:

$1\times 2^{6}+0\times 2^{5}+ 1\times 2^{4}+1 \times 2^{3}+ 1 \times 2^{2}+ 0 \times 2^{1} +1$

$= 1\times 64+0\times32+ 1\times 16+1 \times 8+ 1 \times 4+ 0 \times2+1$

Compare your answer with the correct one above

Question

Express 68 as a base two (binary) number.

Answer

68 can be expressed as the sum of distinct powers of two as follows:

$68 = 64 + 4 = 2^{6}+ 2^{2}$

Therefore, there are 1's in the seventh and third place from the right, and 0's everywhere else, so

$68 = 1000100_{\textrm{two}}$

Compare your answer with the correct one above

Question

Which of the following numbers is an imaginary number?

Answer

By definition, an imaginary number is a number with the term "i" in it. For this problem 7i is the only answer with the imaginary part.

Compare your answer with the correct one above

Question

Express 374 in base six.

Answer

To convert a base ten number to base six, divide the number by six, with the remainder being the digit in the units place; continue, dividing each successive quotient by 6 and putting the remainder in the next position to the left until the final quotient is less than 6.

$374 \div 6 = 62\textrm{ R }\underline{2}$ - the rightmost digit is 2

$62 \div 6 = 10 \textrm{ R }\underline{2}$ - the next digit to the left is 2

$10 \div 6 = \underline{1} \textrm{ R }\underline{4}$ - the next digit to the left is 4, and the digit to the left of that is 1.

$374 = 1422_{\textrm{six}}$

Compare your answer with the correct one above

Question

Express $13241 _{\textrm{five}}$ in base ten.

Answer

Place values in the base five system are powers of five rather than powers of ten. $13241 _{\textrm{five}}$ is equal to

$1 \times 5^{4} + 3 \times 5 ^{3} + 2 \times 5^{2} + 4 \times 5 + 1$

$= 1 \times 625 + 3 \times 125 + 2 \times 25 + 4 \times 5 + 1$

Compare your answer with the correct one above

Question

Which of the following is the smallest prime number:?

Answer

A prime number has only two factor, and itself.

This is not true for or so they are not the answer.

are all prime numbers and is the smallest so it is your answer.

Compare your answer with the correct one above

Question

Which of the following is a rational number?

$\frac{1}{2},\sqrt{5},2i,3.658$

Answer

A rational number is any number that can be expressed as an integer p or a fraction p/q. In the set of number given only $\tiny \frac{1}{2}$ fits into that category.

Compare your answer with the correct one above

Tap the card to reveal the answer

Types of Numbers - SAT Math

Express 374 in base six.

Express in base ten.

Place values in the base five system are powers of five rather than powers of ten. is equal to

Which of the following is the smallest prime number:?

A prime number has only two factor, and itself. This is not true for or so they are not the answer. are all prime numbers and is the smallest so it is your answer.

Which of the following is a rational number?

A rational number is any number that can be expressed as an integer p or a fraction p/q. In the set of number given only fits into that category.

Express 73 as a binary (base two) number.

73 can be uniquely expressed as the sum of distinct powers of two as follows: Therefore, there is a "1" in the seventh, fourth, and first positions from the right, and a "0" everywhere else. So,

Express as a base ten number.

Place values in the base two system are powers of two rather than powers of ten. is equal to:

Express 68 as a base two (binary) number.

68 can be expressed as the sum of distinct powers of two as follows: Therefore, there are 1's in the seventh and third place from the right, and 0's everywhere else, so

Which of the following numbers is an imaginary number?

By definition, an imaginary number is a number with the term "i" in it. For this problem 7i is the only answer with the imaginary part.

Express 374 in base six.

Express in base ten.

Place values in the base five system are powers of five rather than powers of ten. is equal to

Which of the following is the smallest prime number:?

A prime number has only two factor, and itself. This is not true for or so they are not the answer. are all prime numbers and is the smallest so it is your answer.

Which of the following is a rational number?

A rational number is any number that can be expressed as an integer p or a fraction p/q. In the set of number given only fits into that category.

Express 73 as a binary (base two) number.

73 can be uniquely expressed as the sum of distinct powers of two as follows: Therefore, there is a "1" in the seventh, fourth, and first positions from the right, and a "0" everywhere else. So,

Express as a base ten number.

Place values in the base two system are powers of two rather than powers of ten. is equal to:

Express 68 as a base two (binary) number.

68 can be expressed as the sum of distinct powers of two as follows: Therefore, there are 1's in the seventh and third place from the right, and 0's everywhere else, so

Which of the following numbers is an imaginary number?

By definition, an imaginary number is a number with the term "i" in it. For this problem 7i is the only answer with the imaginary part.

Express 374 in base six.

Express in base ten.

Place values in the base five system are powers of five rather than powers of ten. is equal to

Which of the following is the smallest prime number:?

A prime number has only two factor, and itself. This is not true for or so they are not the answer. are all prime numbers and is the smallest so it is your answer.

Which of the following is a rational number?

A rational number is any number that can be expressed as an integer p or a fraction p/q. In the set of number given only fits into that category.

Express $13241 _{\textrm{five}}$ in base ten.

Place values in the base five system are powers of five rather than powers of ten. $13241 _{\textrm{five}}$ is equal to

$1 \times 5^{4} + 3 \times 5 ^{3} + 2 \times 5^{2} + 4 \times 5 + 1$

$= 1 \times 625 + 3 \times 125 + 2 \times 25 + 4 \times 5 + 1$

A prime number has only two factor, and itself.

This is not true for or so they are not the answer.

are all prime numbers and is the smallest so it is your answer.

Which of the following is a rational number?

$\frac{1}{2},\sqrt{5},2i,3.658$

A rational number is any number that can be expressed as an integer p or a fraction p/q. In the set of number given only $\tiny \frac{1}{2}$ fits into that category.

73 can be uniquely expressed as the sum of distinct powers of two as follows:

$73 = 64 + 8 + 1 = 2^{6} + 2^{3}+ 2^{0}$

Therefore, there is a "1" in the seventh, fourth, and first positions from the right, and a "0" everywhere else. So,

$73 = 1001001_{\textrm{two}}$

Express $1011101_{\textrm{two}}$ as a base ten number.

Place values in the base two system are powers of two rather than powers of ten.

$1011101_{\textrm{two}}$ is equal to:

$1\times 2^{6}+0\times 2^{5}+ 1\times 2^{4}+1 \times 2^{3}+ 1 \times 2^{2}+ 0 \times 2^{1} +1$

$= 1\times 64+0\times32+ 1\times 16+1 \times 8+ 1 \times 4+ 0 \times2+1$

68 can be expressed as the sum of distinct powers of two as follows:

$68 = 64 + 4 = 2^{6}+ 2^{2}$

Therefore, there are 1's in the seventh and third place from the right, and 0's everywhere else, so

$68 = 1000100_{\textrm{two}}$

Express $13241 _{\textrm{five}}$ in base ten.

Place values in the base five system are powers of five rather than powers of ten. $13241 _{\textrm{five}}$ is equal to

$1 \times 5^{4} + 3 \times 5 ^{3} + 2 \times 5^{2} + 4 \times 5 + 1$

$= 1 \times 625 + 3 \times 125 + 2 \times 25 + 4 \times 5 + 1$

A prime number has only two factor, and itself.

This is not true for or so they are not the answer.

are all prime numbers and is the smallest so it is your answer.

Which of the following is a rational number?

$\frac{1}{2},\sqrt{5},2i,3.658$

A rational number is any number that can be expressed as an integer p or a fraction p/q. In the set of number given only $\tiny \frac{1}{2}$ fits into that category.

73 can be uniquely expressed as the sum of distinct powers of two as follows:

$73 = 64 + 8 + 1 = 2^{6} + 2^{3}+ 2^{0}$

Therefore, there is a "1" in the seventh, fourth, and first positions from the right, and a "0" everywhere else. So,

$73 = 1001001_{\textrm{two}}$

Express $1011101_{\textrm{two}}$ as a base ten number.

Place values in the base two system are powers of two rather than powers of ten.

$1011101_{\textrm{two}}$ is equal to:

$1\times 2^{6}+0\times 2^{5}+ 1\times 2^{4}+1 \times 2^{3}+ 1 \times 2^{2}+ 0 \times 2^{1} +1$

$= 1\times 64+0\times32+ 1\times 16+1 \times 8+ 1 \times 4+ 0 \times2+1$

68 can be expressed as the sum of distinct powers of two as follows:

$68 = 64 + 4 = 2^{6}+ 2^{2}$

Therefore, there are 1's in the seventh and third place from the right, and 0's everywhere else, so

$68 = 1000100_{\textrm{two}}$

Express $13241 _{\textrm{five}}$ in base ten.

Place values in the base five system are powers of five rather than powers of ten. $13241 _{\textrm{five}}$ is equal to

$1 \times 5^{4} + 3 \times 5 ^{3} + 2 \times 5^{2} + 4 \times 5 + 1$

$= 1 \times 625 + 3 \times 125 + 2 \times 25 + 4 \times 5 + 1$

A prime number has only two factor, and itself.

This is not true for or so they are not the answer.

are all prime numbers and is the smallest so it is your answer.

Which of the following is a rational number?

$\frac{1}{2},\sqrt{5},2i,3.658$

A rational number is any number that can be expressed as an integer p or a fraction p/q. In the set of number given only $\tiny \frac{1}{2}$ fits into that category.