Unit 3 Exponents and Scientific Notation Review Which number is Irrational?
Question 1
Which number is Irrational?
a. 5/9
b. 0.123123123....
c. square root 9
Selected:d. 0.2535455565....
Question 2
To find which number is one thousand times larger than 2.3 x 10^2, you would do the following steps.
a. Change 1,000 to Scientific notation and then subtract from (2.3 x 10^6)
b. Change 1,000 to Scientific notation and then multiply by (2.3 x 10^6)
c. Change 1,000 to Scientific notation and then add to (2.3 x 10^2)
Selected:d. Change 1,000 to Scientific notation and then divide by (2.3 x 10^6)
Question 3
Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction. 0.171717.... = what fraction?
subtract (x = 0.171717....)
100x = 17.1717....
x = 0.171717
x = 17/99
99x = 17
Question 4
The first step in simplifying the expression: (1.8 x 10^5) - (2.6 x 10^3)
a. Addition and subtraction do not require any changes, so you would just subtract (2.6 - 1.8) and (10^(5-3))
b. Addition and subtraction do not require any changes, so you would just subtract (1.8 - 2.6) and (10^(5-3))
c. Addition and subtraction requires the terms to be "like terms" with the same power of the base 10, so you would need to change the second number to (2600 x 10^5).
d. Addition and subtraction requires the terms to be "like terms" with the same power of the base 10, so you would need to change the second number to (0.026 x 10^5).
HUH ????
Question 2
To find which number is one thousand times larger than 2.3 x 10^2, you would do the following steps.
a. Change 1,000 to Scientific notation and then subtract from (2.3 x 10^6)
b. Change 1,000 to Scientific notation and then multiply by (2.3 x 10^6)
c. Change 1,000 to Scientific notation and then add to (2.3 x 10^2)
Selected:d. Change 1,000 to Scientific notation and then divide by (2.3 x 10^6)
1000 = 10^3
(2.2*10^2 ) * 10^3 = 2.2 * 10^5
Question 1: To determine which number is irrational, we need to understand the definition of an irrational number. An irrational number is a number that cannot be expressed as a fraction or a ratio of two integers. Let's analyze the given options:
a. 5/9: This number is a fraction, so it is a rational number.
b. 0.123123123....: This decimal represents a repeating decimal, which can be expressed as a fraction. Therefore, it is a rational number.
c. √9: The square root of 9 is 3, which is a rational number.
d. 0.2535455565....: This decimal does not repeat or terminate, indicating that it cannot be expressed as a fraction. Hence, it is an irrational number.
Therefore, the correct answer is d. 0.2535455565....
Question 2: To find a number that is one thousand times larger than 2.3 x 10^2, we need to multiply 2.3 x 10^2 by one thousand. Let's break down the steps:
a. Change 1,000 to scientific notation: 1,000 = 1 x 10^3
Then, multiply: (2.3 x 10^2) * (1 x 10^3) = 2.3 x 10^5
Therefore, the correct answer is b. Change 1,000 to scientific notation and then multiply by (2.3 x 10^6).
Question 3: Let's follow the given steps in order to change the repeating decimal to a fraction:
Step 1: Subtract (x = 0.171717....)
Step 2: Multiply by 100: 100x = 17.1717....
Step 3: Subtract the original equation from Step 2: (100x - x) = (17.1717... - 0.171717....)
Step 4: Simplify both sides:
99x = 17
Step 5: Solve for x by dividing both sides by 99:
x = 17/99
Therefore, the fraction equivalent of the repeating decimal 0.171717.... is 17/99.
Question 4: The first step to simplify the expression (1.8 x 10^5) - (2.6 x 10^3) is to make sure both terms have the same power of the base 10. Let's analyze the given options:
a. Addition and subtraction do not require any changes, so you would just subtract (2.6 - 1.8) and (10^(5-3)): This option implies that the subtraction can be performed without changing the terms, but that is incorrect. The terms need to have the same power of the base 10.
b. Addition and subtraction do not require any changes, so you would just subtract (1.8 - 2.6) and (10^(5-3)): This option is similar to option a, which is incorrect for the same reasons.
c. Addition and subtraction require the terms to be "like terms" with the same power of the base 10, so you would need to change the second number to (2600 x 10^5): This option correctly identifies that the terms need to have the same power of the base 10.
d. Addition and subtraction require the terms to be "like terms" with the same power of the base 10, so you would need to change the second number to (0.026 x 10^5): This option suggests changing the second term to a decimal, which is incorrect.
Therefore, the correct answer is c. Addition and subtraction require the terms to be "like terms" with the same power of the base 10, so you would need to change the second number to (2600 x 10^5).
Question 1: The correct answer is b. 0.123123123.... This is an irrational number because it is a non-repeating decimal.
Question 2: The correct answer is b. Change 1,000 to Scientific notation and then multiply by (2.3 x 10^6). To find a number one thousand times larger than 2.3 x 10^2, you would multiply 2.3 x 10^2 by 1,000.
Question 3: The correct steps in order for changing the repeating decimal 0.171717.... to a fraction are:
1. Subtract (x = 0.171717....)
2. Multiply both sides by 100 to eliminate the repeating decimal: 100x = 17.1717.... or 100x = 17 with the repeating part removed.
3. Subtract x = 0.171717 from the equation above: 100x - x = 17 - 0.171717 or 99x = 17.
4. Simplify the equation: x = 17/99.
Question 4: The correct answer is a. Addition and subtraction do not require any changes, so you would just subtract (2.6 - 1.8) and (10^(5-3)). To simplify the expression (1.8 x 10^5) - (2.6 x 10^3), you subtract the coefficients (1.8 - 2.6) and subtract the exponents (10^(5-3)).