1. Scientific (Exponential) Notation Practice (9)
Which of the following numbers in scientific notation has the greatest value? a. 2.53 × 10^4 b. 6.32 × 10^−2 c. 8.9453 × 10^2 d. 3.33 × 10^−5
The correct answer is A: 2.53 × 10^4 Explanation: The number that has the larger exponent is the larger number. If the exponents are the same, the magnitude of the first part will determine the size of the number. In normal form 2.53 × 104 is equal to 25,300.
Which choice shows the correct value, in scientific notation, for the answer to the expression cuberoot(27*10^6) to the correct number of significant figures? a. 3,000 b. 3.0 × 10^2 c. 30.00 × 10^2 d. 300 e. None of the above
The correct answer is B: 3.0 × 10^2 Explanation: This is the correct answer, since 3.0 × 10^2 is the cube root of 27 × 10^6. It is also written in standard scientific notation, with the correct number of significant figures (two), which is determined by the number 27. It is calculated as 27^(1/3) × 10^(6/3).
What is the correct sum for the expression 2.78 × 10^2 + 3.5 × 10^3, written in scientific notation using the correct number of significant figures? a. 3.778 × 10^3 b. 3.8 × 10^3 c. 38 × 10^2 d. 3,778
The correct answer is B: 3.8 × 103 Explanation: The sum of 2.78 × 10^2+ 3.5 × 10^3 is 3,778. Written in standard form, the sum is 3.8 × 10^3 (which accounts, amongst other things, for significant figures).
Calculate the following and express the answer in scientific notation with the proper number of significant figures. (5907) × (10000) a. 5.9 × 10^7 b. 5.907 × 10^7 c. 59,070,000 d. 5.9070 × 10^7
The correct answer is B: 5.907 × 10^7 Explanation: The answer must have 4 significant figures.
Which of these numbers is properly written in scientific notation and has the least value? a. 2.34 × 10^4 b. 6.833 × 10^−2 c. 884.29 × 10^−9 d. 6.253 × 10^7
The correct answer is B: 6.833 × 10^−2 Explanation: Although its value is not the least of the four answer choices (Answer C has a lesser value), this expression is the correct answer. It has the least value of those answers correctly written in standard scientific notation (with a single digit to the left of the decimal).
What is the value of sqrt(64*10^-4), written in scientific notation to the correct number of significant figures? a. 8 × 10^−4 b. 8.0 × 10^−2 c. 0.08 d. 8 × 10^2
The correct answer is B: 8.0 × 10^−2 Explanation: This is the correct answer because it has the correct numerical value and is written in standard form with respect to both significant figures (two) and the use of an exponential.
Which of the following shows 10,000 in scientific notation with three significant figures? a. 1.0 × 10^4 b. 1 × 10^4 c. 1.00 × 10^4 d. 1.000 × 10^4
The correct answer is C: 1.00 × 10^4 Explanation: 1.00 × 10^4 has three significant figures. This is because the two zeros after the decimal further define the value (and do not just occupy a place).
Which of the following choices shows the number 0.00504 written in scientific notation? a. 5.4 × 10^−3 b. 5.04 × 10^3 c. 50.4 × 10^−4 d. 5.04 × 10^−3
The correct answer is D: 5.04 × 10^−3 Explanation: This is written in standard form with respect to the number of significant figures (three). (In the question, the value is given as 0.00504, which has three significant figures, 5, 0, and 4.) It also has a numerical part that is ≥ 1 and < 10.
Select the choice that correctly shows the product of (1*10^a) * (2*10^b). a. (1*2) * 10 ^(a-b) b. (1*2) * 10 ^(a*b) c. (1*2) * 10 ^(a/b) d. (1*2) * 10 ^(a+b)
The correct answer is D: (1*2) * 10^(a+b) Explanation: The rule for multiplying two numbers written in exponential form is to multiply the numerical part of the numbers (in this case, (1 • 2) and add the values of the exponents (a + b).
How many significant figures are in the number 53,630,208? a. 4 b. 5 c. 6 d. 8
The correct answer is D: 8 Explanation: This is the correct choice because, all non-zero digits are significant and all embedded zeros are significant.
