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Quizzes > Mathematics > Basic Math & Arithmetic

Master Scientific Notation and Significant Figures Quiz

Think you can convert 101000 grams and nail scientific notation? Dive in!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art featuring rulers beakers numbers on coral background for quiz on scientific notation and significant figures

Ready to level up your math skills, students and science aficionados? Dive into our "Scientific Notation of 101000 Quiz - Convert & Ace It" and see if you can convert measurements like the scientific notation of 101000 or tackle "convert the following measurement to scientific notation: 101 000 grams" flawlessly. This free scientific notation quiz and significant figures quiz are your gateway to reinforcing your measurement conversion practice. Hone your precision now with our scientific notation practice or push further in the significant figures and scientific notation quiz . Take the challenge today and discover your score!

Convert 5000 to scientific notation.
50 x 10^2
500 x 10^1
5 x 10^3
0.5 x 10^4
In scientific notation, the coefficient must be between 1 and 10 and multiplied by a power of ten. 5000 equals 5 times 10 raised to the third power, which is 5 x 10^3. Coefficients like 0.5 or multiples outside 1 to 10 violate the normalized form. Wikipedia: Scientific notation
Express 0.0052 in scientific notation.
5.2 x 10^-3
5.2 x 10^3
52 x 10^-4
0.52 x 10^-2
To convert a small decimal to scientific notation, move the decimal point right until one non-zero digit remains to the left. Moving it three places gives 5.2 x 10^-3. Incorrect options have wrong exponents or improperly placed decimals. Wikipedia: Scientific notation
Write 120000000 in scientific notation.
1.2 x 10^8
120 x 10^6
12 x 10^7
0.12 x 10^9
120,000,000 has eight zeros after the 1, so it is 1.2 x 10^8 in normalized form. Coefficients must be between 1 and 10. Other options either violate normalization or use incorrect exponents. Wikipedia: Scientific notation
Convert 3.75 x 10^4 to standard notation.
375,000
37,500
0.000375
3,750
Multiplying 3.75 by 10^4 shifts the decimal four places to the right, giving 37,500. Other options either shift the decimal incorrectly or misplace digits. Wikipedia: Scientific notation
Express 0.00089 in scientific notation.
89 x 10^-6
8.9 x 10^-4
0.89 x 10^-3
8.9 x 10^4
Moving the decimal point four places right converts 0.00089 to 8.9, and the exponent is -4. Other answers misplace the decimal or use incorrect exponent signs. Wikipedia: Scientific notation
Convert 7 x 10^2 to standard form.
70
700
0.7
7000
Multiplying 7 by 10^2 shifts the decimal two places right, yielding 700. Other options either shift incorrectly or misinterpret the exponent. Wikipedia: Scientific notation
How many significant figures are in 0.00450?
1
2
3
4
Leading zeros are not significant. The digits 4, 5, and trailing zero are significant, giving three significant figures. Wikipedia: Significant figures
How many significant figures are in 1200?
2
3
4
1
Without a decimal point, trailing zeros in 1200 are not considered significant. Only digits 1 and 2 count, giving two significant figures. Wikipedia: Significant figures
Convert 0.1 to scientific notation.
1 x 10^1
0.1 x 10^0
1 x 10^-1
10 x 10^-2
0.1 equals 1 times 10 to the power of -1, since the decimal moves one place to the right. Other options misplace the decimal or use incorrect exponents. Wikipedia: Scientific notation
Which of the following is the correct scientific notation for 9600?
96 x 10^2
9.6 x 10^3
960 x 10^1
0.96 x 10^4
Moving the decimal three places left normalizes 9600 to 9.6, so the exponent is 3. Other options misalign the decimal or use coefficients outside 1-10. Wikipedia: Scientific notation
Convert 4.2 x 10^-3 to standard notation.
0.0042
4.2
0.00042
0.042
A negative exponent moves the decimal point left. With an exponent of -3, 4.2 becomes 0.0042. Other options move the decimal the wrong number of places. Wikipedia: Scientific notation
How many significant figures are in 6.070?
2
1
3
4
All non-zero digits and any zeros between or after decimal digits are significant. In 6.070, digits 6,0,7,0 all count, giving four significant figures. Wikipedia: Significant figures
Express 250000 as scientific notation with two significant figures.
2.5 x 10^5
25 x 10^4
2.50 x 10^5
0.25 x 10^6
With two significant figures, 250000 becomes 2.5 x 10^5. The option 2.50 x 10^5 has three significant figures due to the extra zero. Wikipedia: Significant figures
Convert 8.03 x 10^1 to standard notation.
8.03
80.3
803
0.803
Multiplying by 10^1 shifts the decimal one place right, turning 8.03 into 80.3. Other answers shift incorrectly or miscount digits. Wikipedia: Scientific notation
Express 0.00032 with one significant figure in scientific notation.
3 x 10^-4
0.3 x 10^-3
3.2 x 10^-4
32 x 10^-6
One significant figure means only the leading digit is kept. Moving the decimal four places right gives 3 x 10^-4. Other options either include extra digits or misplace the decimal. Wikipedia: Scientific notation
How many significant figures are in 120.30?
2
5
3
4
All digits except leading zeros count. In 120.30, digits 1,2,0,3,0 all count, giving five significant figures. Wikipedia: Significant figures
Convert 0.00000678 to scientific notation.
6.78 x 10^-6
67.8 x 10^-8
0.678 x 10^-5
6.78 x 10^-5
To express a small number in scientific notation, move the decimal six places right to get 6.78, giving an exponent of -6. Other options misplace the decimal or use incorrect exponents. The coefficient must remain between 1 and 10. Wikipedia: Scientific notation
Round 5.6721 x 10^3 to three significant figures in scientific notation.
5.672 x 10^3
5.67 x 10^4
5.67 x 10^3
5.7 x 10^3
For three significant figures, keep the first three digits (5, 6, 7) and round based on the fourth digit (2), which does not change the third digit. Therefore, the result is 5.67 x 10^3. Other options either include too many or too few significant figures. Wikipedia: Significant figures
Express 98765 in scientific notation.
98.765 x 10^3
9.8765 x 10^5
9.8765 x 10^4
0.98765 x 10^5
Moving the decimal four places left normalizes 98765 to 9.8765 and sets the exponent to 4. Other answers either use incorrect exponents or coefficients outside the required 1 - 10 range. Wikipedia: Scientific notation
How many significant figures are in 0.02000?
2
5
3
4
Leading zeros are not significant, but all zeros after the first non-zero digit in a decimal number are significant. Thus 0.02000 has four significant figures (2, 0, 0, 0). Wikipedia: Significant figures
Express 1.2345e-6 in normalized scientific notation.
0.12345 x 10^-5
1.2345 x 10^-6
12.345 x 10^-7
1.2345 x 10^6
The notation 1.2345e-6 is already in normalized form with a coefficient between 1 and 10. Incorrect options either shift the decimal wrong or invert the exponent sign. Wikipedia: Scientific notation
Convert 7.89 x 10^-2 to standard notation.
0.0789
0.00789
0.789
7.89
A negative exponent of 2 shifts the decimal two places left, producing 0.0789. Other answers move the decimal an incorrect number of places. Wikipedia: Scientific notation
Write 654000 in scientific notation with three significant figures.
6.54 x 10^5
0.654 x 10^6
65.4 x 10^4
6.540 x 10^5
To get three significant figures, use digits 6, 5, and 4, so the coefficient is 6.54 and the exponent is 5. The option 6.540 x 10^5 has four significant figures. Wikipedia: Significant figures
Round 2.999 x 10^2 to two significant figures in scientific notation.
3.0 x 10^2
2.9 x 10^2
3.0 x 10^1
2.99 x 10^2
For two significant figures, take the first two digits (2 and 9) and look at the third digit (9) to round up, turning 2.999 into 3.0. The exponent remains 2. Other options miscount digits or use the wrong exponent. Wikipedia: Significant figures
Convert 0.0003456 to scientific notation.
34.56 x 10^-6
3.456 x 10^-3
3.456 x 10^-4
0.3456 x 10^-3
Moving the decimal four places right gives 3.456 and an exponent of -4. Other answers either use wrong exponents or incorrect coefficients. Wikipedia: Scientific notation
How many significant figures are in 4500.0?
2
3
4
5
All non-zero digits and zeros between or after the decimal point count. In 4500.0, digits 4, 5, 0, 0, and the trailing 0 after the decimal make five significant figures. Wikipedia: Significant figures
Express 5.06 x 10^7 in standard notation.
506,000,000
50,600,000
5,060,000
500,600,000
Multiplying by 10^7 shifts the decimal seven places to the right, resulting in 50,600,000. Other answers shift incorrectly or misplace digits. Wikipedia: Scientific notation
Round 4.5678 x 10^-3 to three significant figures and express in scientific notation.
4.57 x 10^-3
4.568 x 10^-3
0.00457
4.6 x 10^-3
For three significant figures, digits 4, 5, and 6 are kept and rounded based on the fourth digit (7), raising 6 to 7. The coefficient remains between 1 and 10 with exponent -3. Other options misround or misformat. Wikipedia: Significant figures
Which of the following is not in normalized scientific notation?
3.2 x 10^0
0.5 x 10^2
5 x 10^1
1.23 x 10^-3
A normalized scientific notation requires the coefficient to be ?1 and <10. The coefficient 0.5 is less than 1, making 0.5 x 10^2 invalid. Other choices meet normalization. Wikipedia: Scientific notation
Express 123.45 x 10^2 in normalized scientific notation.
1234.5 x 10^2
1.2345 x 10^3
1.2345 x 10^4
12.345 x 10^3
Move the decimal two places left to normalize the coefficient to 1.2345 and increase the exponent from 2 to 4. Incorrect options either misplace the decimal or use the wrong exponent. Wikipedia: Scientific notation
Convert 9.81 x 10^4 to standard notation.
981,000
9,810
98,100
9.81
Multiplying 9.81 by 10^4 shifts the decimal four places to the right, resulting in 98,100. Other options misplace the decimal or misinterpret the exponent. Wikipedia: Scientific notation
How many significant figures are in 0.006040?
2
5
4
3
Leading zeros are not significant, but all zeros after the first non-zero digit are. The digits 6, 0, 4, 0 count, giving four significant figures. Wikipedia: Significant figures
Add 2.5 x 10^3 and 3.75 x 10^2 and express the result in scientific notation.
2.875 x 10^3
2.0875 x 10^3
2.75 x 10^3
2.875 x 10^2
First convert both terms to standard form or adjust exponents: 2.5 x10^3 is 2500 and 3.75 x10^2 is 375, summing to 2875. Normalizing this gives 2.875 x10^3. Other options miscalculate the sum or misplace the decimal. Wikipedia: Scientific notation
Multiply (3.2 x 10^2) by (4.5 x 10^3) and express in normalized scientific notation.
14.4 x 10^6
1.44 x 10^6
14.4 x 10^5
1.44 x 10^5
Multiply coefficients (3.2×4.5=14.4) and add exponents (2+3=5), giving 14.4 x10^5. Normalizing shifts the decimal one place left to 1.44 and increments exponent to 6. Wikipedia: Scientific notation
A lab report lists a length as 0.0005678 m. Express this value to three significant figures in scientific notation.
0.0005678 m
5.68 x 10^-4 m
5.677 x 10^-4 m
5.68 x 10^-3 m
0.0005678 becomes 5.678 x10^-4; rounding to three significant figures gives 5.68 x10^-4. Including units clarifies the measurement. Other answers misround or misplace the exponent. Wikipedia: Scientific notation
Express 314.159 in scientific notation, rounding to four significant figures.
3.1416 x 10^1
31.42 x 10^1
3.142 x 10^2
3.1416 x 10^2
Moving the decimal two places gives 3.14159 x10^2. Rounding to four significant figures looks at the fifth digit (9), raising the fourth digit (5) to 6, resulting in 3.1416 x10^2. Wikipedia: Scientific notation
Convert 1.23 x 10^-4 to standard notation and report with two significant figures.
0.0012
0.00012
0.000123
0.0001
1.23 x10^-4 equals 0.000123. Reporting two significant figures rounds to 0.00012. Other options either misround or misplace the decimal. Wikipedia: Significant figures
Express 0.000000789 in scientific notation.
78.9 x 10^-9
7.89 x 10^-6
7.89 x 10^-7
0.789 x 10^-6
Moving the decimal seven places right gives 7.89, with exponent -7 for a small number. Other options use incorrect exponents or coefficients. Wikipedia: Scientific notation
Round 9.999 x 10^5 to three significant figures in scientific notation.
1.00 x 10^6
10.0 x 10^5
1.0 x 10^6
9.99 x 10^5
9.999 x10^5 equals 999900. Rounding to three significant figures yields 1.00 x10^6 as the digits roll over. The coefficient must stay normalized between 1 and 10. Wikipedia: Scientific notation
Express 98000 with one significant figure in scientific notation.
10 x 10^4
1 x 10^4
9 x 10^4
1 x 10^5
Rounding 98000 to one significant figure gives 100000, which in scientific notation is 1 x10^5. Other options either misround or misplace the decimal. Wikipedia: Significant figures
Convert 4.56 x 10^3 grams to kilograms and express in scientific notation.
4560 x 10^-3 kg
0.456 x 10^1 kg
4.56 x 10^0 kg
4.56 x 10^-3 kg
1 kilogram equals 10^3 grams, so dividing 4.56 x10^3 g by 10^3 gives 4.56 kg or 4.56 x10^0 kg in scientific notation. Units must also be converted. Other choices misapply unit conversion or notation. Wikipedia: Scientific notation
A photon has a wavelength of 632.8 nm. Express this wavelength in meters using scientific notation.
6.328 x 10^-6 m
0.6328 x 10^-6 m
6.328 x 10^-7 m
63.28 x 10^-8 m
1 nm equals 10^-9 m, so 632.8 nm is 632.8 x10^-9 m. Normalizing gives 6.328 x10^-7 m. Other options shift decimals incorrectly or misinterpret the prefix. Wikipedia: Scientific notation
Express the product of (2 x 10^-3) and (5 x 10^4) in scientific notation.
1 x 10^2
10 x 10^1
1 x 10^3
10 x 10^3
Multiply coefficients (2×5=10) and add exponents (-3+4=1), giving 10 x10^1. Normalizing shifts the decimal one place to produce 1 x10^2. Wikipedia: Scientific notation
Convert 0.0456 to scientific notation and specify the exponent.
4.56 x 10^-2
45.6 x 10^-3
4.56 x 10^-3
0.456 x 10^-1
Moving the decimal two places right gives 4.56, so the exponent is -2. Other options shift the decimal wrong or misidentify the exponent. Wikipedia: Scientific notation
If a quantity is 7.020 x 10^-3, how many significant figures does it have?
3
2
4
5
In 7.020 x10^-3, all digits including the zero between non-zero digits and the trailing zero after the decimal are significant, giving four significant figures. Wikipedia: Significant figures
Express 0.0001234 to three significant figures in scientific notation.
1.234 x 10^-4
12.3 x 10^-5
1.23 x 10^-4
1.23 x 10^-3
Moving the decimal four places right yields 1.234, and rounding to three significant figures gives 1.23 x10^-4. Incorrect choices misplace the decimal or include extra digits. Wikipedia: Scientific notation
Round 6.022 x 10^23 to two significant figures in scientific notation.
6.0 x 10^23
6 x 10^23
6.0 x 10^22
6.02 x 10^23
For two significant figures, keep digits 6 and 0, rounding based on the third digit (2), which does not change the second digit. Thus, 6.0 x10^23 is correct. Wikipedia: Significant figures
A particle has mass 0.000000000000000000000123 kg. Express this mass in scientific notation to two significant figures.
1.20 x 10^-23 kg
1.23 x 10^-22 kg
1.2 x 10^-22 kg
12 x 10^-23 kg
The number moves the decimal 22 places right to get 1.23, and rounding to two significant figures gives 1.2. Thus the exponent is -22. Wikipedia: Scientific notation
Perform the subtraction (5.00 x 10^4) - (3.456 x 10^3) and express the result in scientific notation rounded to three significant figures.
4.654 x 10^4
4.65 x 10^4
4.65 x 10^5
4.65 x 10^3
Convert both to standard form: 50000 - 3456 = 46544. Rounding to three significant figures based on the fourth digit (4) gives 4.65 x10^4. Wikipedia: Scientific notation
A measurement is quoted as 6.0 x 10^-5 m and another as 4.55 x 10^-6 m. Divide the first by the second and express the result in scientific notation with three significant figures.
13.2 x 10^0
1.32 x 10^0
1.318 x 10^1
1.32 x 10^1
Divide coefficients (6.0/4.55?1.3187) and subtract exponents (-5 -(-6)=1). Rounding to three significant figures gives 1.32 x10^1. Wikipedia: Scientific notation
Express the square root of 9.8 x 10^7 in scientific notation to two significant figures.
9.9 x 10^2
3.14 x 10^4
9.9 x 10^3
3.1 x 10^3
sqrt(9.8×10^7)=sqrt(9.8)×10^(7/2)=3.13×10^3.5=3.13×?10×10^3?9.9×10^3. Rounding to two significant figures yields 9.9 x10^3. Wikipedia: Scientific notation
A chemical sample has a mass of 0.045600 g. Express this measurement in scientific notation with the correct number of significant figures.
4.560 x 10^-2 g
4.56 x 10^-2 g
4.56000 x 10^-2 g
4.5600 x 10^-2 g
The original measurement 0.045600 g has five significant figures (4, 5, 6, 0, 0). In scientific notation this is 4.5600 x10^-2 g. Other options either drop or add significant figures. Wikipedia: Significant figures
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Study Outcomes

  1. Convert Numbers to Scientific Notation -

    Apply the method to transform measurements like 101 000 grams into correct scientific notation, ensuring the mantissa falls between 1 and 10 and the exponent accurately reflects magnitude.

  2. Apply Significant Figures Rules -

    Use the quiz to identify and apply significant figures conventions when expressing numbers in scientific notation, improving precision in measurement conversion practice.

  3. Demonstrate Measurement Conversion Skills -

    Convert various numerical values between standard form and scientific notation, reinforcing your ability to handle metric measurements in scientific contexts.

  4. Evaluate Precision and Accuracy -

    Analyze quiz questions to assess the precision of your conversions and understand how significant figures affect the accuracy of reported values.

  5. Interpret Large and Small Quantities -

    Develop the skill to quickly interpret and compare very large or small numbers using scientific notation, making complex data more manageable and comprehensible.

  6. Identify and Correct Conversion Errors -

    Recognize common mistakes in converting measurements to scientific notation and learn strategies to correct them, enhancing your overall numerical fluency.

Cheat Sheet

  1. Converting to Scientific Notation -

    Scientific notation expresses numbers as M × 10^n, where 1 ≤ M < 10. For example, converting 101 000 grams gives 1.01 × 10^5 grams by moving the decimal five places left. Mnemonic: "One Digit, One Dot" helps you remember to stop when M is between one and ten.

  2. Counting Significant Figures -

    Significant figures reflect measurement precision and include all nonzero digits, captive zeros, and trailing zeros if a decimal is shown. In 101 000, the zeros at the end are ambiguous without a decimal; using scientific notation (1.01000 × 10^5) clarifies the number of significant digits. According to NIST guidelines, this practice prevents misinterpretation in lab reporting.

  3. Clarifying Precision with Notation -

    Scientific notation lets you control and display exact precision: writing 1.01000 × 10^5 clearly indicates five significant figures. University chemistry courses often require this format to avoid losing data quality during calculations. Always match the number of digits in M to the measurement's precision.

  4. Measurement Conversion Practice -

    Dimensional analysis helps convert units before applying scientific notation: 101 000 grams = 101 000 g × (1 kg/1 000 g) = 101 kg, then in notation 1.01 × 10^2 kg. Consistent practice with convert the following measurement to scientific notation: 101 000 grams builds accuracy and speed. Many engineering syllabi (e.g., MIT OpenCourseWare) include similar drills.

  5. Avoiding Common Pitfalls -

    Watch your decimal shifts and exponent signs: shifting right adds negative exponents (e.g., 0.000101 = 1.01 × 10^ - 4). Use the "Left Left, Right Right" trick - moving left adds positive exponents, moving right adds negatives. This simple rule, endorsed by chemistry departments, ensures error-free scientific notation conversions.

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