Types of Numbers

SAT Subject Test in Math I · Learn by Concept

Help Questions

SAT Subject Test in Math I › Types of Numbers

1 - 4

Express 374 in base six.

$1422_{\textrm{six}}$

CORRECT

$1522_{\textrm{six}}$

$1502_{\textrm{six}}$

$1402_{\textrm{six}}$

Explanation

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.

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

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

CORRECT

Explanation

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

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

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

Which of the following is a rational number?

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

$\frac{1}{2}$

CORRECT

$\sqrt{5}$

None

Explanation

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.