Question
upstudy study bank question image url

\( \begin{array}{lll} & & 3,458.9 \div \square \\ \text { A. } 10^{1} \\ \text { B. } 10^{2} \\ \text { C. } 10^{3} \\ \text { D. } 10^{4}\end{array} \)

Ask by Beck Jimenez. in the United States
Mar 18,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The correct choice is \(10^3\).

Solution

\[ \text{Step 1: Identify the problem.} \] We have the number \(3,458.9\) and we want to choose a power of 10 from the options \(10^1,\,10^2,\,10^3,\,10^4\) such that dividing \(3,458.9\) by that power of 10 gives a result in the range from 1 (inclusive) to 10 (exclusive). This format is characteristic of scientific notation. \[ \text{Step 2: Write } 3,458.9 \text{ in scientific notation.} \] To do that, we want to express \(3,458.9\) as \(a \times 10^n\) where \(1 \leq a < 10\). Observe that: \[ 3,458.9 = 3.4589 \times 10^3. \] \[ \text{Step 3: Interpret the division.} \] Since \[ \frac{3,458.9}{10^3} = 3.4589, \] dividing by \(10^3\) converts the original number into its scientific notation form (with the coefficient \(a = 3.4589\) in the proper range). \[ \text{Step 4: Choose the correct option.} \] Among the given options, the power of 10 that works is \(10^3\). Thus, the answer is: \[ \boxed{10^3} \]

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Extra Insights

To solve \(3,458.9 \div \square\), we need to find out which power of ten would result in a quotient that is close to 1, as that will help us determine the correct option. Dividing \(3,458.9\) by \(10^3\) (or \(1,000\)) gives us approximately \(3.4589\). Dividing by \(10^2\) (or \(100\)) gives \(34.589\), which is too high, and dividing by \(10^4\) (or \(10,000\)) yields \(0.34589\), which is too low. Therefore, the only option that keeps the quotient above 1 but reasonably close to it is \(10^3\). So, the answer is \( \text{C. } 10^{3} \).

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy