➕ Algebra 1 · Exponents and Polynomials
Scientific Notation practice questions
Questions start easy and step up. Before you answer, rate how sure you are. It trains you to know what you really know.
Want more questions?
These 10 samples are free for everyone. A free account adds 50 more questions and 2 hours of practice time every month, and HighSchoolQ Plus unlocks the full question bank, mixed review, progress tracking and printable packs.
See plansAnswer key with explanations
Write 86,000,000 in scientific notation.
Answer: 8.6 × 107. Slide the point left until one nonzero digit is to its left: 8.6. The point slides 7 places, and the number is big, so the exponent is +7: 8.6 × 107. The choice with exponent 6 counts the zeros instead of the slides, the choice with 8 counts the digits, and a negative exponent is for numbers between 0 and 1.
Write 5.3 × 10−4 in ordinary form.
Answer: 0.00053. The exponent is −4, so slide the point 4 places left: 5.3 → 0.53 → 0.053 → 0.0053 → 0.00053. Check: 5.3 ÷ 10,000 = 0.00053. Sliding 3 places gives 0.0053, sliding 5 places gives 0.000053, and sliding right (the wrong direction) gives 53,000.
Write 0.000306 in scientific notation.
Answer: 3.06 × 10−4. Slide the point right until one nonzero digit is to its left: 3.06. The point passes 0, 0, 0 and 3, so that is 4 slides, and the number is between 0 and 1, so the exponent is −4. The zero inside stays in the front number (3.06, not 3.6). Check: 3.06 ÷ 10,000 = 0.000306.
Which of these numbers is the greatest?
Answer: 1.1 × 10−2. Compare the exponents first. The greatest exponent is −2, which belongs only to 1.1 × 10−2 (0.011). The others are 0.0096, 0.0005 and 0.000087. A bigger front number does not win when the exponent is smaller: 9.6 is bigger than 1.1, but 9.6 × 10−3 is smaller. Remember that −2 is greater than −3, −4 and −5.
Multiply (6 × 104)(7 × 103). Write the answer in scientific notation.
Answer: 4.2 × 108. Multiply the front numbers: 6 × 7 = 42. Add the exponents: 4 + 3 = 7. That gives 42 × 107, but 42 is not between 1 and 10. Slide the point one place left (42 → 4.2) and add 1 to the exponent: 4.2 × 108. Check: 60,000 × 7,000 = 420,000,000. Forgetting to fix the front number gives exponent 7, multiplying the exponents (4 × 3) gives 12, and adding the front numbers gives 13, which becomes 1.3.
Divide (1.2 × 106) ÷ (3 × 109). Write the answer in scientific notation.
Answer: 4 × 10−4. Divide the front numbers: 1.2 ÷ 3 = 0.4. Subtract the exponents: 6 − 9 = −3. That gives 0.4 × 10−3, but 0.4 is less than 1. Slide the point one place right (0.4 → 4) and subtract 1 from the exponent: 4 × 10−4. Check: 1,200,000 ÷ 3,000,000,000 = 0.0004. The choice with −3 forgot to fix the front number, the choice with 14 added the exponents (and then fixed the front number), and the choice with 2 subtracted in the wrong order (9 − 6 = 3, giving 0.4 × 103 = 4 × 102).
Add 5.4 × 106 + 3.1 × 105. Write the answer in scientific notation.
Answer: 5.71 × 106. The powers differ, so match them first: 3.1 × 105 = 0.31 × 106. Then add the front numbers: 5.4 + 0.31 = 5.71, and keep the power: 5.71 × 106. Check: 5,400,000 + 310,000 = 5,710,000. The choice 8.5 × 106 added 5.4 + 3.1 without matching the powers. The choice 8.5 × 1011 also added the exponents. The choice 3.64 × 107 slid the point the wrong way when matching (31 × 106, so 5.4 + 31 = 36.4).
Subtract 7.2 × 10−2 − 5 × 10−3. Write the answer in scientific notation.
Answer: 6.7 × 10−2. Match the powers: 5 × 10−3 = 0.5 × 10−2 (slide the point one place left and add 1 to the exponent). Subtract the front numbers: 7.2 − 0.5 = 6.7, and keep the power: 6.7 × 10−2. Check: 0.072 − 0.005 = 0.067. The choice 2.2 × 10−2 subtracted 7.2 − 5 without matching the powers. The choice 6.7 × 10−3 kept the exponent of the wrong number. The choice 2.2 × 101 also subtracted the exponents (−2 − (−3) = 1).
Light travels about 3.0 × 108 meters in one second, and a year has about 3.15 × 107 seconds. Using these values, about how far does light travel in one year?
Answer: About 9.45 × 1015 meters. Distance = speed × time, so multiply: (3.0 × 108)(3.15 × 107). Front numbers: 3.0 × 3.15 = 9.45. Exponents: 8 + 7 = 15. The front number 9.45 is already between 1 and 10, so the distance is about 9.45 × 1015 meters. The choice with 56 multiplied the exponents (8 × 7), the choice with 1 subtracted them (8 − 7), and the choice with 6.15 added the front numbers (3.0 + 3.15).
Jon added 3 × 104 + 5 × 103 and got 8 × 107. What did he do wrong, and what is the correct sum?
Answer: He added the exponents as well as the front numbers. After matching the powers, 3 × 104 + 0.5 × 104 = 3.5 × 104.. Jon added 3 + 5 = 8 and also 4 + 3 = 7. When adding, do not add the exponents. The powers differ, so match them first: 5 × 103 = 0.5 × 104. Then add the front numbers (3 + 0.5 = 3.5) and keep the power: 3.5 × 104. Check: 30,000 + 5,000 = 35,000. Keeping the larger exponent without rewriting the 5 gives 8 × 104 = 80,000, which treats 5,000 as 50,000. Multiplying would answer a different question.