Question

Write each number in scientific notation. 0.000423

Short answer

4.23 \times 10^{-4}

Step-by-step solution

Identify the Significant Figures

Determine the significant figures in the number 0.000423. These are the non-zero digits: 4, 2, and 3.

Rewrite the Number with Only Significant Figures

Rewrite 0.000423 using only the significant figures, placing the decimal point after the first significant figure: 4.23.

Determine the Exponent

Count the number of decimal places the decimal point has moved to the right to place it after the first significant figure. Here, it moved 4 places to the right.

Write in Scientific Notation

Combine the result of step 2 with the exponent from step 3. The exponent will be negative since the original number is less than 1. Therefore, the scientific notation is: \[ 0.000423 = 4.23 \times 10^{-4} \]

Key concepts

Significant Figures

When dealing with scientific notation, identifying significant figures is crucial. Significant figures are the meaningful digits in a number.

The number 0.000423 has three significant figures: 4, 2, and 3. These are the digits that provide precision to the number.

Key points to remember about significant figures include:

• Non-zero digits are always significant.
• Any zeros between significant digits are also significant.
• Leading zeros, which appear before all non-zero digits, are not significant.
• Trailing zeros in a decimal number are significant.

Understanding significant figures helps maintain accuracy and consistency when performing mathematical transformations, such as converting a number to scientific notation.

Decimal Places

Decimal places are a way to express the precision of a number. They represent the positions of numbers to the right of the decimal point.

In 0.000423, the decimal places indicate the number's value in relation to one. Counting the decimal places helps in identifying how much the decimal point must move to rewrite a number in scientific notation.

Remember these important aspects about decimal places:

• Each shift of the decimal point by one place changes the power of ten by one exponent.
• Moving the decimal to the right indicates a negative exponent when the original number is less than one.
• When rewriting a number, count how many places you move the decimal to correctly determine the exponent.

Proper handling of decimal places ensures accurate representation in scientific notation.

Exponents

Exponents in scientific notation represent how many times a number is multiplied by ten.

For the number 0.000423, we need to move the decimal point 4 places to the right to place it after the first significant figure (4.23). This movement means the exponent in the scientific notation will be -4.

Key points to understand about exponents:

• Positive exponents indicate the number is greater than 1.
• Negative exponents indicate the number is less than 1.
• The exponent shows how many times the decimal point has been moved.
• Exponents make it easier to work with extremely large or small numbers.

Using exponents effectively allows for a clear and concise representation of numbers in scientific notation.