Question

How would the number 17,060 be written in scientific notation? A. \(1706 \times 10^{1}\) B. \(1.706 \times 10^{4}\) C. \(1.7060 \times 10^{4}\) D. \(0.17060 \times 10^{5}\)

Short answer

B. \(1.706 \times 10^{4}\)

Step-by-step solution

Identify the Number

Understand that the number to convert is 17,060.

Move the Decimal Point

Move the decimal point in 17,060 to create a number between 1 and 10. The number becomes 1.706.

Count the Decimal Places Moved

Count how many places you moved the decimal point. For 17,060, you move the decimal point 4 places to the left.

Write in Scientific Notation

Combine the number from Step 2 with the exponent from Step 3. The number 17,060 in scientific notation is written as \(1.706 \times 10^{4}\).

Match with Given Choices

Compare the final scientific notation form with the given options. The correct choice is B. \(1.706 \times 10^{4}\).

Key concepts

Decimal Point

Let's start with the concept of the decimal point. The decimal point is a dot used in numerical writing to separate the whole number part of a value from its fractional part. For instance, in the number 17.060, the decimal point separates 17 (the whole number) from .060 (the fractional part). When converting a number to scientific notation, moving the decimal point is a crucial step. You need to shift the decimal point so that you get a number between 1 and 10. In our exercise, we have 17,060. Moving the decimal point four places to the left, we get 1.706. This makes it easier to represent the number in a compact form while preserving its original value.

Exponent

Next, we need to understand what an exponent is. In scientific notation, an exponent indicates how many places the decimal point has moved from its original position. In simpler terms, it tells you the power of 10 by which you need to multiply the base number to get back to the original value. When writing in scientific notation, the exponent is represented as a power of 10. For example, in the step-by-step solution of our exercise, the decimal point in 17,060 moved four places to the left to become 1.706. Here, the exponent will be 4, indicating that 1.706 must be multiplied by 10 raised to the power of 4, i.e., \(10^{4}\). So, the number 17,060 can be expressed as \(1.706 \times 10^{4}\).

Standard Form

Finally, we should talk about the standard form. The standard form or scientific notation is a way to write very large or very small numbers concisely. It makes mathematical calculations more manageable. It usually consists of three parts:

• A coefficient (a number between 1 and 10)
• A base of 10
• An exponent that tells how many places the decimal point has moved

For the number 17,060, by moving the decimal point four places to the left, we get 1.706. Then we use the exponent 4. Therefore, in standard form, 17,060 is written as \(1.706 \times 10^{4}\). This notation makes even complex calculations simpler and more straightforward.