Convert 342 to scientific notation by adding the prefix and exponent values in the provided boxes..
[Fill in the blank]
x10^[Fill in the blank]

Question

Convert 342 to scientific notation by adding the prefix and exponent values in the provided boxes..
[Fill in the blank]
 x10^[Fill in the blank]

BlackTom AI · Accepted Answer

Scientific notation expresses a number as a single coefficient between 1 and 10 multiplied by 10 raised to an integer power.

1. Relevant knowledge points and concepts
- Normalized scientific notation requires the coefficient (mantissa) to be ≥1 and <10.
- Moving the decimal point to the left by n places multiplies the number by 10^n (or equivalently, divides the coefficient by 10^n and increases the exponent by n). For numbers greater than 10, the exponent is positive.

2. Step-by-step reasoning
Start with 342. Place the decimal point after the last digit: 342.0. To get a coefficient between 1 and 10, move the decimal left until the leading part is between 1 and 10.

3. Intermediate steps and calculations
- Move the decimal 1 place left: 34.2. This corresponds to 34.2 × 10^1 (since moving left one place increases the exponent by 1).
- Move the decimal a second place left: 3.42. This corresponds to 3.42 × 10^2.
Verify: 3.42 × 10^2 = 3.42 × 100 = 342.0, which equals the original number.

4. Why the correct answer is correct
3.42 is within the required range (1 ≤ coefficient < 10), and an exponent of 2 accounts for the two-place left shift of the decimal point. Multiplying 3.42 by 10^2 recovers 342 exactly, so 3.42 × 10^2 is the normalized scientific notation.

5. Why other forms are incorrect
- 342 × 10^0 equals 342 but is not normalized because the coefficient is not between 1 and 10.
- 34.2 × 10^1 is mathematically equal to 342 but still not normalized because the coefficient is ≥10.
- 0.342 × 10^3 equals 342 mathematically but 0.342 is less than 1, so it violates normalization.

6. Conclusion
The normalized scientific notation of 342 is 3.42 × 10^2. This confirms the provided answer: first blank = 3.42, exponent = 2.

Convert 342 to scientific notation by adding the prefix and exponent values in the provided boxes.. [Fill in the blank] x10^[Fill in the blank] Multiple fill-in-the-blank

Similar Questions

Convert 0.0342 to scientific notation by adding the prefix and exponent values in the provided boxes.. [Fill in the blank] x10^[Fill in the blank]

Convert 0.00342 to scientific notation by adding the prefix and exponent values in the provided boxes.. [Fill in the blank] x10^[Fill in the blank]

How 0.000387 can be expressed using scientific notation?

How 0.00387 can be expressed using scientific notation?

Preform the following operation. Choose the correct answer that is in scientific notation. 6.92 − (13.0 ÷ 5.863)

Part 1Write the following in standard notation.55 times ×10Superscript negative 9−9 Part 155 times ×10Superscript negative 9−9equals=[input]enter your response here (Simplify your answer. Type an integer or a decimal.)

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler