1.
Compare the decimal forms of
How are they alike, and how are they different?
(Use 2/5 and 4/9 to type your answers.)
2.
How are the values of -4^{3 }and 4^{-3} alike and how do they differ?
3.
Write your answer in scientific notation.
example: 10^{8 }= 10^8
(5.4 x 10^{8}) (3.2 x 10^{6}) =
4.
The diameter of the Sun is 1.4 x 10^{9} meters long.
The diameter of the Moon is 3.5 x 10^{6} meters long.
About how many times more significant is the Sun's diameter than the Moon's diameter.
Write your answer in scientific notation.
example: 10^{8} = 10^8
5.
What are the two square roots of 400?
6.
What fraction equals a repeating decimal?
Correct Answer
B. 1/3
Explanation
A repeating decimal is a decimal number that has a repeating pattern of digits after the decimal point. To find the fraction equivalent of a repeating decimal, we can set up an equation. Let x be the repeating decimal. Multiply both sides of the equation by a power of 10 that eliminates the repeating part. Subtracting the original equation from the new equation, we can eliminate the repeating part and solve for x. In this case, the repeating decimal is 0.3333..., which can be expressed as 1/3. Therefore, the correct answer is 1/3.
7.
Which is the best name for numbers that describe distances on a map?
Correct Answer
D. Rational numbers
Explanation
Rational numbers are the best name for numbers that describe distances on a map because rational numbers include both positive and negative integers as well as fractions. Distances on a map can be represented by whole numbers (such as 1, 2, 3), positive integers (such as 5, 10, 15), negative integers (such as -5, -10, -15), and fractions (such as 1/2, 3/4, 2/3), all of which are included in the set of rational numbers.
8.
Write the following mixed number as a decimal:
Correct Answer
12.25
Explanation
The given mixed number, 12.25, is already in decimal form. There is no need to convert it further.
9.
Which equivalent expression is equal to 7/9?
Correct Answer
B. 0.777777...
Explanation
The repeating decimal 0.777777... is equal to 7/9, because the digit 7 repeats infinitely. To convert the repeating decimal to a fraction, let x = 0.777777... Then, multiplying both sides by 10, we get 10x = 7. Subtracting x from both sides, we get 9x = 7. Dividing both sides by 9, we find x = 7/9. Therefore, the expression 0.777777... is equal to 7/9.
10.
Find an integer between
Correct Answer
-2, -1, 0, 1
Explanation
The given question asks to find an integer between -2, -1, 0, and 1. However, the answer provided includes all the given integers -2, -1, 0, and 1. Therefore, the answer does not provide an integer between the given numbers.
11.
What two whole numbers would be in between?
Correct Answer
C. 11 and 12
Explanation
The given question asks for two whole numbers that would be in between 5 and 6. Looking at the options, we can see that the numbers 11 and 12 are the only ones that fit this criteria. Therefore, the correct answer is 11 and 12.
12.
A small square garden has an area of 25 square yards. How long is each side of the garden?
Correct Answer
C. 5 yards
Explanation
The area of a square is calculated by multiplying the length of one side by itself. In this case, the area is given as 25 square yards. To find the length of each side, we need to find the square root of the area. The square root of 25 is 5, so each side of the garden is 5 yards long.
13.
What is an estimate of ?
Correct Answer
C. 3.9
Explanation
An estimate is an approximate calculation or judgement of a value. Among the given options, 3.9 is the closest estimate to the unknown value being asked for.
14.
What is the value of 3^{-5 }?
Correct Answer
D. 1 / 243
Explanation
The value of 3-5 is equal to 1/243. This can be determined by subtracting 5 from 3, which gives us -2, and then raising 10 to the power of -2, resulting in 1/100. Simplifying further, we can express 1/100 as 1 / (10^2), which is equivalent to 1/243.
15.
Which of the following is true:
Correct Answer
A. Only I
16.
Which number is between 3.1415 and ?
Correct Answer
C. 3.5
Explanation
The number that is between 3.1415 and 3.5 is 3.5 itself.
17.
Estimate the square root of 150 to the nearest tenth.
Correct Answer
12.2
Explanation
To estimate the square root of 150 to the nearest tenth, we can use the fact that the square root of 121 is 11 and the square root of 169 is 13. Since 150 is closer to 169 than 121, we can estimate the square root to be closer to 13 than 11. Therefore, the estimated square root of 150 to the nearest tenth is 12.2.
18.
The population of a South American country is about 17,400,000. Which expression shows his number in scientific notation?
Correct Answer
B. 1.74 x 10^{7}
Explanation
The expression 1.74 x 107 represents the population of the South American country in scientific notation. In scientific notation, a number is written as the product of a decimal number between 1 and 10 and a power of 10. In this case, 1.74 is the decimal number between 1 and 10, and 107 is the power of 10. Therefore, 1.74 x 107 is the correct expression for the population in scientific notation.
19.
What is the answer in scientific notation?
(3.3 x 10^{7}) + (7.7 x 10^{8})
Correct Answer
B. 8.03 x 10^{8}
Explanation
The given expression is a sum of two numbers in scientific notation. To add them, we need to make sure that the exponents are the same. In this case, we can rewrite (3.3 x 107) as (0.33 x 108) to match the exponent of (7.7 x 108). Adding these two numbers gives us (0.33 + 7.7) x 108 = 8.03 x 108. Therefore, the correct answer is 8.03 x 108.
20.
One type of insect is 0.0052 meters long. What is this length in scientific notation?
Correct Answer
A. 5.2 x 10^{-3}
Explanation
The length of the insect is given as 0.0052 meters. In scientific notation, we express this number as a decimal between 1 and 10 multiplied by a power of 10. To convert 0.0052 to scientific notation, we move the decimal point 3 places to the right, resulting in 5.2. Since we moved the decimal point to the right, the power of 10 is negative, indicating that the number is less than 1. Therefore, the correct scientific notation for the length of the insect is 5.2 x 10-3.
21.
The sun is 1.4 x 10^{9}^{ }meters in diameter. What is the diameter of the sun in standard notation? DO NOT put commas in to receive full credit.
Correct Answer
1400000000
Explanation
The diameter of the sun is given as 1.4 x 10^9 meters. In standard notation, this can be written as 1400000000.
22.
The diameter of a blood cell is 8.4 x 10^{-6}
What is the diameter of a blood cell in standard notation?
Correct Answer
0.0000084
Explanation
The diameter of a blood cell is given as 8.4 x 10^-6. In standard notation, this can be expressed as 0.0000084. This is because when we have a number in scientific notation, we move the decimal point to the left or right to convert it into standard notation. In this case, we move the decimal point 6 places to the left, resulting in 0.0000084.