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Quizzes > High School Quizzes > Mathematics

Scientific Notation Practice Quiz

Improve numeric fluency with quick practice tests

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting a scientific notation quiz for high school students.

Easy
What is scientific notation?
A method of writing very large or very small numbers using powers of 10
A type of notation used solely in scientific laboratories
A method to round numbers to the nearest whole number
A representation of numbers using Roman numerals
Scientific notation is a standardized way to express large or small numbers as a product of a coefficient and a power of 10. This form simplifies calculations and comparisons between numbers.
Convert the standard number 4500 into scientific notation.
4.5 x 10^3
45 x 10^2
0.45 x 10^4
450 x 10^1
4500 can be written as 4.5 x 10^3 because moving the decimal point three places to the left gives the coefficient 4.5 while the exponent 3 represents the factor of 1000. This is the standard procedure for converting to scientific notation.
Which of the following correctly expresses 0.0056 in scientific notation?
5.6 x 10^-3
0.56 x 10^-2
5.6 x 10^-2
0.56 x 10^-3
In standard scientific notation, the coefficient must be between 1 and 10. Converting 0.0056 requires moving the decimal point three places to the right, which correctly gives 5.6 x 10^-3, while the other options either use an improper coefficient or incorrect exponent.
What does the exponent in scientific notation represent?
The number of times to multiply 10 by itself
The number of digits in the original number
A multiplier for the coefficient
The position of the decimal point in the coefficient
The exponent indicates how many times the base 10 is multiplied by itself. This number determines the scale of the number in scientific notation.
Convert the scientific notation 3.2 x 10^2 into standard form.
320
32
0.32
3200
Multiplying 3.2 by 10^2 means multiplying by 100, resulting in 320. Converting from scientific notation to standard form involves shifting the decimal point to the right by the exponent's value.
Medium
Multiply the numbers (2 x 10^3) and (3 x 10^4) and express the answer in scientific notation.
6 x 10^7
5 x 10^7
6 x 10^6
2 x 10^7
When multiplying numbers in scientific notation, you multiply the coefficients and add the exponents. Here, 2 multiplied by 3 equals 6, and 10^3 multiplied by 10^4 gives 10^(3+4) or 10^7.
Divide (8 x 10^5) by (4 x 10^2) and express the result in scientific notation.
2 x 10^3
2 x 10^7
4 x 10^3
2 x 10^2
Dividing the coefficients 8 by 4 gives 2, and subtracting the exponents (5 - 2) gives 10^3. This application of the rules for division in scientific notation yields 2 x 10^3.
Express the number 0.00032 in scientific notation.
3.2 x 10^-4
32 x 10^-6
3.2 x 10^-3
0.32 x 10^-3
To convert 0.00032 into scientific notation, move the decimal four places to the right, resulting in 3.2, and indicate this shift with an exponent of -4. This standardizes the number with a coefficient between 1 and 10.
What is the standard form of the scientific notation 7.5 x 10^3?
7500
75
0.75
750
Multiplying 7.5 by 10^3 (or 1000) gives 7500. The exponent tells you how far to move the decimal point to convert from scientific notation to standard form.
Simplify the expression (4.0 x 10^-2) × (2.5 x 10^3) in scientific notation.
1.0 x 10^2
1.0 x 10^1
10.0 x 10^2
1.0 x 10^3
Multiplying 4.0 by 2.5 gives 10.0, and adding the exponents -2 and 3 results in 10^1. Since the coefficient 10.0 is not between 1 and 10, it is adjusted to 1.0 x 10^2, which is the proper scientific notation.
Which of the following is an incorrect scientific notation form for a number?
0.9 x 10^5
9.0 x 10^4
5.5 x 10^-3
2.3 x 10^2
In proper scientific notation, the coefficient must be between 1 and 10. Since 0.9 is less than 1, the expression 0.9 x 10^5 does not conform to the standard format.
If a number in scientific notation is written as 3.45 x 10^n equals 3450, what is the value of n?
3
2
4
5
Dividing 3450 by 3.45 yields 1000, which is 10^3. Therefore, the exponent n must be equal to 3.
Convert 9.87 x 10^-4 to standard notation.
0.000987
0.00987
0.0987
9870
To convert 9.87 x 10^-4 into standard notation, move the decimal point four places to the left. This results in 0.000987, which is the correct standard form.
Which operation is performed on the exponents when multiplying two numbers in scientific notation?
Add the exponents
Subtract the exponents
Multiply the exponents
Divide the exponents
When multiplying numbers in scientific notation, the exponents are added together according to the laws of exponents. This simplifies the multiplication of large or small numbers.
How many times should the decimal be moved to convert 5.2 x 10^2 into standard notation?
2 times to the right
2 times to the left
Depends on the coefficient
No movement is needed
An exponent of 2 indicates that the decimal point should be moved two places to the right. This converts 5.2 x 10^2 into the standard number 520.
Hard
Simplify and express in correct scientific notation: (6.0 x 10^7) ÷ (2.0 x 10^3).
3.0 x 10^4
3.0 x 10^3
3.0 x 10^5
0.3 x 10^5
Dividing the coefficients 6.0 by 2.0 gives 3.0, and subtracting the exponents (7 - 3) yields 10^4. Therefore, the simplified result is 3.0 x 10^4.
Calculate the product of (2.5 x 10^-3) and (4.0 x 10^5) and express the answer in standard scientific notation.
1.0 x 10^3
10.0 x 10^2
1.0 x 10^2
1.5 x 10^3
Multiplying 2.5 by 4.0 gives 10.0, and adding the exponents (-3 + 5) results in 10^2. Since the coefficient 10.0 is not between 1 and 10, it must be adjusted to 1.0 x 10^3, which is the proper scientific notation.
A calculator displays the result of an operation as 0.00027. Which of the following is the correct scientific notation?
2.7 x 10^-4
27 x 10^-5
2.7 x 10^-3
0.27 x 10^-3
Moving the decimal four places to the right in 0.00027 gives 2.7, which then requires a factor of 10^-4 to scale back to the original number. This makes 2.7 x 10^-4 the proper scientific notation.
Solve the following: Express the sum of (3.5 x 10^4) and (4.5 x 10^4) in scientific notation.
8.0 x 10^4
8.0 x 10^5
7.0 x 10^4
8.0 x 10^3
Since both numbers have the same exponent, their coefficients can be added directly: 3.5 plus 4.5 equals 8.0. The final sum is then expressed as 8.0 x 10^4 in scientific notation.
Determine which expression correctly rewrites the number 12300000 in scientific notation.
1.23 x 10^7
12.3 x 10^6
123 x 10^5
1.23 x 10^6
To write 12300000 in scientific notation, the decimal must be moved seven places to the left, resulting in 1.23, and the exponent is 7. This yields the standard form 1.23 x 10^7, while the other options either use an improper coefficient or an incorrect exponent.
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Study Outcomes

  1. Understand the concept and purpose of scientific notation.
  2. Apply techniques to convert numbers between standard and scientific notation.
  3. Analyze large and small numbers to determine their appropriate scientific representation.
  4. Solve problems that require the manipulation and comparison of numbers in scientific notation.
  5. Evaluate responses for accuracy and logical consistency in using scientific notation.
  6. Demonstrate exam readiness through dynamic, practice-based problem solving.

Scientific Notation Practice Cheat Sheet

  1. Structure of Scientific Notation - Scientific notation slashes giant and minuscule numbers into neat a×10n packages. You pick a decimal between 1 and 10, attach a power of ten, and voilà - 4,500,000 magically becomes 4.5×106. SparkNotes: Scientific Notation Guide
  2. Converting Between Forms - Shift that decimal left to boost the exponent or right to shrink it, and you'll nail any conversion. For example, 0.00056 transforms into 5.6×10−4 by moving the point four places right. MathBits Notebook: Converting Practice
  3. Addition & Subtraction Tricks - To add or subtract, first match exponents by adjusting coefficients, then combine like terms. For instance, convert 4.5×102 to 0.45×103 before adding to 3.2×103, giving (3.2+0.45)×103=3.65×103. SparkNotes: Adding & Subtracting
  4. Multiplication & Division Rules - Multiply or divide coefficients normally and then add or subtract their exponents. For example, (2×103)×(3×104) becomes 6×107 by adding 3 + 4. SparkNotes: Multiplying & Dividing
  5. Real‑World Applications - Blast off into space calculations or zoom into microscopic worlds using scientific notation to handle extreme scales. It turns mind‑boggling distances and tiny measurements into friendly, work‑able numbers. Carleton College: Practice Problems
  6. Significant Figures Guide - Match your result's significant figures to the least precise measurement you started with. This ensures consistent accuracy in lab reports, homework, and beyond. MathBits Notebook: Sig Fig Practice
  7. Tiny Decimals & Negative Exponents - Move the decimal right and tag on a negative exponent to pack small numbers into compact form, like 0.00042 becoming 4.2×10−4. This trick keeps your work clean when dealing with microscopic scales. SparkNotes: Tiny Numbers, Big Fun
  8. Interpreting Exponent Signs - A positive exponent means a big number, a negative one means a small number - simple as that. Spotting the sign quickly helps you estimate magnitudes without doing grunt work. SparkNotes: Understanding Exponents
  9. Simplifying Complex Calculations - Use scientific notation to keep long multiplications and divisions neat, reducing typos and slip-ups. It's like a math shortcut that speeds you through enormous or minuscule puzzles. Carleton College: Advanced Practice
  10. Practice Builds Confidence - Tackle a variety of scientific notation problems daily to level up your skills and banish notation anxiety. With each drill, you'll cement your mastery and breeze through exams. MathBits Notebook: Daily Drills
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