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All questions of Scientific Notation for EmSAT Achieve Exam
What is the result when 5,678,732 is rounded to the nearest thousand and then put in scientific notation? - a)5.679 × 10−6
- b)5.678 × 106
- c)5.679 × 103
- d)5.679 × 106
Correct answer is option 'D'. Can you explain this answer?
What is the result when 5,678,732 is rounded to the nearest thousand and then put in scientific notation?
a)
5.679 × 10−6
b)
5.678 × 106
c)
5.679 × 103
d)
5.679 × 106
|
Orion Classes answered |
First, when we round to the nearest thousand we get 5, 679, 000 since we round up when the next digit is greater than 5.
Then, to put it in scientific notation, we arrange the digits so that a decimal point creates a number between 1 and 10. We get 5.679.
Then, we want the exponent of the 10 to be the number of times the decimal needs to move to the right. This is 6 times.
Thus, we get our answer.5.679 × 106
Convert from decimal to scientific notation:0.0000034- a)3.4 × 10−5
- b)3.4 × 106
- c)3.4 × 10−4
- d)3.4 × 10−6
Correct answer is option 'D'. Can you explain this answer?
Convert from decimal to scientific notation:
0.0000034
a)
3.4 × 10−5
b)
3.4 × 106
c)
3.4 × 10−4
d)
3.4 × 10−6
|
Thomas Montgomery answered |
Conversion to Scientific Notation
Given Decimal Number: 0.0000034
Step 1: Move the decimal point to the right until there is only one non-zero digit to the left of the decimal point.
Step 2: Count the number of places you moved the decimal point. If you moved it to the right, the exponent of 10 in the scientific notation will be negative.
Step 3: Write the number in scientific notation by multiplying the non-zero digit by 10 raised to the power of the number of places you moved the decimal point.
Calculation:
0.0000034 = 3.4 × 10^(-6)
Therefore, the decimal number 0.0000034 in scientific notation is 3.4 × 10^(-6).
What is the number 350,000,000 in scientific notation?- a)3.5 x 108
- b)3.5 x 106
- c)3.5 x 109
- d)3.5 x 105
Correct answer is option 'A'. Can you explain this answer?
What is the number 350,000,000 in scientific notation?
a)
3.5 x 108
b)
3.5 x 106
c)
3.5 x 109
d)
3.5 x 105
|
|
Orion Classes answered |
350,000,000 = 3.5 x 108 (exponent is equal to the number of decimal points shifted)
Given the equation 2xy + 4x² - y = 2x, if x = 2, what does y equal?- a)-4
- b)4
- c)2
- d)0
Correct answer is option 'A'. Can you explain this answer?
Given the equation 2xy + 4x² - y = 2x, if x = 2, what does y equal?
a)
-4
b)
4
c)
2
d)
0
|
|
Orion Classes answered |
We plug in the value given for x and solve for y.
2xy + 4x² - y = 2x
2(2)y + 4(2)² - y = 2(2)
4y + 4(4) - y = 4
4y - y + 16 = 4
3y = -12
y = -4
Convert from scientific to decimal notation:2.3 × 104- a)2300
- b)230,000
- c)23,000
- d)0.0023
Correct answer is option 'C'. Can you explain this answer?
Convert from scientific to decimal notation:
2.3 × 104
a)
2300
b)
230,000
c)
23,000
d)
0.0023
|
|
Orion Classes answered |
In this case the exponent is positive hence you have to move the decimal point 4 places to the right from where it is in the problem giving us 23,000
2 × 100 + 3 × 102 + 4 × 104 = ?- a)40,302
- b)40,320
- c)400,032
- d)4,032
Correct answer is option 'A'. Can you explain this answer?
2 × 100 + 3 × 102 + 4 × 104 = ?
a)
40,302
b)
40,320
c)
400,032
d)
4,032
|
|
Orion Classes answered |
2 × 100 + 3 × 102 + 4 × 104 =
2 + 300 + 40,000 = 40,302
Give this number in scientific notation:125,000,000- a) 12.5 × 1010
- b)1.25 × 108
- c)12.5 × 108
- d)1.25 × 109
Correct answer is option 'B'. Can you explain this answer?
Give this number in scientific notation:
125,000,000
a)
12.5 × 1010
b)
1.25 × 108
c)
12.5 × 108
d)
1.25 × 109
|
|
Orion Classes answered |
There are six zeros and two more number places, for a total of eight, so 125,000,000 is equivalent to 1.25 × 108.
What is the sum of the solutions of the equation x2-2x-8=0?- a)-2
- b)2
- c)6
- d)-10
Correct answer is option 'B'. Can you explain this answer?
What is the sum of the solutions of the equation x2-2x-8=0?
a)
-2
b)
2
c)
6
d)
-10
|
|
Orion Classes answered |
The equation factors to (x-4)(x+2)=0, indicating that the roots are x=-2,4. The sum of these two roots is 2.
How do you express 657,800 in scientific notation?- a)65.78 × 106
- b)6.578 × 103
- c)6.578 × 104
- d)65.78 × 104
Correct answer is option 'D'. Can you explain this answer?
How do you express 657,800 in scientific notation?
a)
65.78 × 106
b)
6.578 × 103
c)
6.578 × 104
d)
65.78 × 104
|
|
Orion Classes answered |
657800 = 6.578 × 105
OR
657800 = 65.78 × 104
Exponent on 10 is the number of decimal points over the number has shifted.
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