# Write Scientific Notation From Standard Form Worksheet

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Writing scientific notation from standard form involves converting a number expressed in its full decimal form into a product of a coefficient and a power of ten (e.g., converting 35,000 to 3.5*10^4). This process includes identifying the significant digits, placing the decimal point after the first significant digit, and determining the exponent by counting the number of places the decimal point has moved. The coefficient is then multiplied by 10 raised to the appropriate power.

Algebra 1
Scientific Notation

## How Will This Worksheet on "Write Scientific Notation from Standard Form" Benefit Your Student's Learning?

• Worksheets help in enhancing understanding of converting large or small numbers.
• Building confidence in working with scientific notation.
• Improving accuracy in identifying significant figures and applying powers of ten.
• Preparing students for real-world applications in science and math.
• Reinforcing concepts through consistent practice.
• Encouraging critical thinking and problem-solving skills.

## How to Write Scientific Notation from Standard Form?

• Firstly Identify the first non-zero digit in the number.
• Then count the number of places the decimal point needs to be moved so that only one non-zero digit is to the left of the decimal point.
• If the decimal is moved to the right, the exponent is positive. If moved to the left, the exponent is negative.
• Write the first non-zero digit and any other digits to the right of it as the coefficient.
• Multiply the coefficient by 10 raised to the exponent.

## Solved Example

Q. How do you write $603,000$ in scientific notation?$\newline$$\_\_\_\_\_\_ \times 10^{\_\_\_\_\_\_}$
Solution:
1. Find Coefficient: What will be the coefficient when $603,000$ is written in scientific notation? Move the decimal to the left until the number is greater than or equal to $1$ and less than $10$. Coefficient: $6.03$
2. Sign of Exponent: Would $603,000$ have a positive or negative exponent when written in scientific notation? $603,000$ is a number greater than $10$. It can be represented by a positive exponent.
3. Determine Exponent: We know:
The coefficient is $6.03$.
The exponent will be positive.
What is the exponent when $603,000$ is written in scientific notation?
We moved the decimal to the left $5$ times to make the coefficient $6.03$.
$603,000 = 6.03\times 10^5$
Exponent: $5$
4. Write in Scientific Notation: We know the coefficient is $6.03$ and the exponent is $5$. Fill in the values to write $603,000$ in scientific notation. Substitute $6.03$ for $a$ and $5$ for $b$ in $a \times 10^b$. Scientific notation: $6.03 \times 10^5$

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