1. What is 0.48 written as a simplified fraction?
A. 100/48
B. 24/50
C. 12/25 >> My answer
D. 48/100
2. Ms. Kim's class is having a pizza party. If there are 21 students and 6 pizzas cut into 8 slices, what answer choice represents the fraction of one pizza that each student receives?
A. 1/8
B. 2/7
C. 7/8
D. 21/48
3. What makes the statement true? 6-^3 =?
A. -18
B. -1/216
C. 1/216
D. -216
4. Based upon a 2020 census data, the total population of India is 1,380,004,385 people. Approximately what is this population in scientific notation.
A. 1.4 x 10^9
B. 1.4 x 10^8
C. 14 x 10^8
D. 1.4 x 10^-9
5. What is the solution to (3x10^7) x (7 x 10^5), written in scientific notation?
A. 21 x 10^12
B. 2.1 x 10^12
C. 21 x 10^35
D. 2.1 x 10^13
1.
Correct
0.48 = 48 / 100 = 4 • 12 / 4 • 25 = 12 / 25
2.
None of the answers are correct.
6 pizzas cut into 8 slices = 6 • 8 = 48 slices
48 / 21 = 3 • 16 / 3 • 7 = 16 / 7
3.
6-^3 = 1 / 6^3 =
6-^3 = 1 / 6^3 = 1 / 216
4.
1,380,004,385 = 1.380004385 • 10^9
approx. 1.4 • 10^9
5.
3 • 10^7 • 7 • 10^5 =
3 • 7 • 10 ^7 • 10 ^ 5 = 21 • 10^{ 7+ 5 ) =
21 • 10 ^12 = 2.1 • 10 • 10^12 =
2.1 • 10^1 • 10^12 = 2.1 • 10 ^( 1 + 12 ) =
2.1 • 10^13
1. To write 0.48 as a simplified fraction, we need to express it as a fraction with a numerator and denominator that have no common factors. To do this, we can multiply both the numerator and denominator by 100 to remove the decimal point:
0.48 * 100 = 48
Therefore, 0.48 is equivalent to the fraction 48/100. However, this fraction can be simplified further by dividing both the numerator and denominator by their greatest common factor, which is 4:
48 ÷ 4 = 12
100 ÷ 4 = 25
So, the simplified fraction for 0.48 is 12/25. Therefore, the correct answer is option C.
2. To find the fraction of one pizza that each student receives, we need to divide the total number of pizza slices by the number of students.
First, we need to find the total number of pizza slices:
6 pizzas * 8 slices = 48 slices
Now, we divide the total number of slices by the number of students:
48 slices ÷ 21 students
This can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 3:
48 ÷ 3 = 16
21 ÷ 3 = 7
So, each student receives 16/7 of a pizza slice. Therefore, the correct answer is option B.
3. The expression 6-^3 means 6 raised to the power of -3. To evaluate this expression, we need to understand that any number raised to the power of -n is equal to 1 divided by the number raised to the power of n.
So, 6-^3 = 1 / (6^3)
= 1 / (6 * 6 * 6)
= 1 / 216
Therefore, the correct answer is option C.
4. To write the population of India (1,380,004,385) in scientific notation, we need to move the decimal point to the right so that there is only one non-zero digit to the left of the decimal point. Count the number of places you move the decimal point, and write it as a power of 10.
Starting with 1,380,004,385, we can simplify it by moving the decimal point 9 places to the left:
1,380,004,385 = 1.380004385 * 10^9
Therefore, the population of India can be written approximately as 1.4 x 10^9. Therefore, the correct answer is option A.
5. To multiply numbers written in scientific notation, we first multiply their coefficients and then add their exponents.
(3x10^7) x (7 x 10^5)
= (3 x 7) x (10^7 x 10^5)
= 21 x 10^(7+5)
= 21 x 10^12
Therefore, the solution is 21 x 10^12. Therefore, the correct answer is option A.