Express 9 ten thousandths in Scientific notation

Express 9 ten thousandths in Scientific notation

The correct answer and explanation is:

✅ Correct Answer:

9 ten-thousandths in scientific notation is: 9×10−49 \times 10^{-4}

📘 Explanation (300 words):

To express 9 ten-thousandths in scientific notation, we need to understand both the decimal place value and the structure of scientific notation.

🔹 Step 1: Understand “ten-thousandths”

A “ten-thousandth” is a place value in the decimal number system. Specifically: 1 ten-thousandth=0.00011 \text{ ten-thousandth} = 0.0001

So, 9 ten-thousandths=9×0.0001=0.00099 \text{ ten-thousandths} = 9 \times 0.0001 = 0.0009

🔹 Step 2: What is Scientific Notation?

Scientific notation is a way of writing numbers that are very large or very small using powers of 10. The format is: a×10na \times 10^n

Where:

• 1≤a<101 \leq a < 10 (a number with one non-zero digit before the decimal),
• nn is an integer that indicates how many places the decimal is moved.

🔹 Step 3: Convert 0.0009 to Scientific Notation

Start with the decimal: 0.00090.0009

We want to express this as a number between 1 and 10, multiplied by a power of 10. Move the decimal 4 places to the right to get: 9.09.0

Since we moved the decimal 4 places to the right, the exponent will be -4 (because the original number was less than 1).

So: 0.0009=9×10−40.0009 = 9 \times 10^{-4}

✅ Final Answer:

9×10−4\boxed{9 \times 10^{-4}}

This is the scientific notation for 9 ten-thousandths, a concise and standardized way to represent very small values in math and science.