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Chapter 10: Problem 387

In the following exercises, write each number in scientific notation. $$1,290,000$$

Short Answer

Expert verified
1.29 \( \times 10^6 \)

Step by step solution

01

Identify the significant figures

The significant figures in the number 1,290,000 are 129. Remove all the trailing zeroes after the non-zero digits.
02

Determine the decimal point position

For scientific notation, the decimal point should be placed after the first significant digit. So, place the decimal after the 1, making it 1.29.
03

Count the powers of ten

Count how many places the decimal point has moved from its original position to the new position. Starting from the end of the number 1,290,000, the decimal point moves 6 places to the left.
04

Write the number in scientific notation

Combine the significant figures with the powers of ten. So, 1,290,000 in scientific notation is written as \( 1.29 \times 10^6 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

significant figures
Significant figures are essential in scientific notation. They indicate the precision of a number. For example, in the number 1,290,000, the significant figures are 1, 2, and 9. All the trailing zeros (those after the last non-zero digit) are not considered significant in this context. Always identify and retain these significant digits when converting a large number into scientific notation.
decimal point
The decimal point plays a crucial role in scientific notation. You must place it properly for accurate conversion. In scientific notation, the decimal point is placed directly after the first significant digit. For instance, in the number 1,290,000, the decimal point should be placed after the 1, resulting in 1.29.
powers of ten
Powers of ten help in scaling the number to its scientific notation form. To find the power, count the number of places the decimal point moves. For the number 1,290,000, the decimal point moves 6 places to the left, hence the power of ten is 6. So, a large number like 1,290,000 can be expressed in scientific notation as a smaller value multiplied by 10 raised to the power representing this shift: \[ 1.29 \times 10^6 \].
scientific notation conversion
Converting a number to scientific notation involves combining the significant figures, decimal point placement, and powers of ten. Here's the step-by-step process:

  • Identify the significant figures. For 1,290,000, they are 1, 2, and 9.
  • Place the decimal point after the first significant digit, giving 1.29.
  • Count how many places the decimal moves from its original position. Here, it moves 6 places to the left.
  • Combine them into the final scientific notation form: \[ 1.29 \times 10^6 \].

This concise method ensures that every number can be easily converted to its scientific notation, making large or small numbers more manageable.

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