Question
The standard form of a number 0.000035 is - \( \begin{array}{ll}\text { (a) } 3.5 \times 10^{-3} & \text { (b) } 3.5 \times 10^{-2} \\ \text { (c) } 3.5 \times 10^{-5} & \text { (d) } 3.5 \times 10^{-7}\end{array} \)
Ask by Page Harris. in India
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The standard form of 0.000035 is \(3.5 \times 10^{-5}\).
Solution
Step 1: Write \(0.000035\) by identifying the significant digits. We have \(3\) and \(5\), so the number can be written as \(3.5\).
Step 2: Count the number of decimal places we need to move to get from \(0.000035\) to \(3.5\). Moving the decimal point 5 places to the right gives:
\[
0.000035 \times 10^5 = 3.5
\]
Step 3: Since we moved the decimal point to the right, the exponent in the standard form is negative. Thus, the number in standard form is:
\[
3.5 \times 10^{-5}
\]
Answer: \(3.5 \times 10^{-5}\)
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To convert the number 0.000035 into standard form, you first need to express it as a number between 1 and 10 multiplied by a power of ten. Here, 0.000035 can be rewritten as 3.5 multiplied by \(10^{-5}\), since moving the decimal point five places to the right gives you the original number. So, the correct answer is (c) \(3.5 \times 10^{-5}\). When thinking about standard form, it's useful to remember it’s all about clarity. This notation isn’t just helpful in math class – it’s often used in science and engineering to handle very large or very small numbers easily, making it a vital skill in various fields such as physics, chemistry, and finance!
