Number Theory

If the value of c is between 0.00082 and 0.0026, which of the following could be c? 0.000095 0.00063 0.0048 0.001

0.0011

Order these least to greatest: (1/4)^3 , 3^-4 , 4^3

3^-4 , (¼)^3 , 4^3

Rounding smaller numbers

ending in 0-4= round down ending in 5-9 = round up EX: 34---30, 36---> 40

Irrational Numbers

rounded decimals not repeate No fractions written with symbols EX: PI=3.14, √2=1.41

place value

the 7 in 5,237 is in the ones place the 7 in 7, 852 is in the thousands place the 7 in 82.047 is in the thousandths place

Rational numbers

written in fraction and decimal not rounded repeated patterns Ex; 0.25, 0.72727272, 4 1/2

What is the difference between -5^2 and (-5)^2?

-5^2 = -(5 × 5) = -25 because the negative sign is not inside the parentheses. (-5)2 = (-5 × -5) = 25 because the negative sign is inside the parentheses.

4, 2, 6, 8, 9, 1, 3 She instructs her students to write down the smallest number possible with the 8 in the thousands place and the 1 in the tens place

2,348,619

Fractional Exponents

25 ^ 1/2 ----> √25= 5 64 ^ 1/3-----> 3√64=4

Negative Exponents

2^-4 = 1/2 X 1/2 x 1/2 X 1/2= 1/16 (1/4)^-3= 4 x 4x 4 x 4 = 64 (-5)^-2= -1/5 x -1/5 = 1/25

Positive Exponents

2^4= 2 x 2 X 2 x2= 16 (1/4)^3 = 1/4 x 1/4 x 1/4 = 1/64 (-5)^2 = -5 x -5= 25

If the number 180 is written as the product of its prime factors in the form a²b²c, what is the numerical value of a + b + c, where c = 5 and a and b do not equal 1?

2²)(3²)(5) = 180 and a + b + c is 2 + 3 +5 = 10.

What is the value of the "3" in the number 17,436,825?

30,000

Which of the following expressions is equivalent to the number 328?

32 tens and 8 ones

Scientific Notation

4, 200,000-------> 4.2 X 10^6 0.000426---------> .4.26 X 10^-4 *Left= positive *Right= Negative

What is the digit in the hundreds place in the product of 63 × 31?

63 × 31 = 1953. The digit that occupies the hundreds place is 9.

In the number 22,672,131, what is the value of the digit 7?

70,000

Shep has the numbers 1 through 8 to arrange in the largest possible number with each numeral only being used once. The 8 must be in the ten-thousands place. What number did he create?

76,584,321

What is the value of the "8" in the number 17,436,825?

800

What value does 8 represent in the number 2.86 x 10^4?

8000 2.86 x 10^4 equals 28600 when expanded correctly.

If the number 888 is written as a product of its prime factors in the form a3bc, what is the numerical value of a + b + c?

888 is 2 x 3 x37 answer: 2 + 3 + 37 = 42.

greatest common factor

The largest factor that two or more numbers have in common. EX: GCF of 12 and 15---> 3 Ex: GCF 12 and 16-----> 4

least common multiple

The smallest multiple (other than zero) that two or more numbers have in common. Ex: LCM of 6 and 8?----> 24 Ex: LCM of 27 and 345 --------> 3 x3x3x5x23= 3105 27= 3 x 3 x3 345= 3 x 5 x23 LCM: 3105

Rounding Larger Numbers

ending in 0-49----> round down ending in 49-99----> round up EX: 1,487---> 1,490 57, 672---> 58,000