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Chapter 5: Problem 13

Write each number in scientific notation. $$ 5,876,000,000 $$

Short Answer

Expert verified
5.876 \times 10^9

Step by step solution

01

Identify the significant digits

The number is 5,876,000,000. The significant digits in this number are 5.876.
02

Count the number of places to move the decimal point

To convert 5,876,000,000 to scientific notation, move the decimal point to just after the first non-zero digit. In this case, move the decimal point 9 places to the left, turning 5,876,000,000 into 5.876.
03

Write in scientific notation

Combine the significant digits with the appropriate power of 10. Since we moved the decimal point 9 places to the left, the power of 10 is 9. Therefore, the number in scientific notation is written as: \( 5.876 \times 10^9 \)

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Key Concepts

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

Significant Digits
In scientific notation, **significant digits** (or significant figures) are the numbers that carry meaningful information about the precision of the original figure. They include all non-zero digits, any zeros between significant digits, and any trailing zeros in the decimal part.

For the number 5,876,000,000, the significant digits are 5, 8, 7, and 6, forming the number 5.876.

It's essential to identify the significant digits accurately when converting any number to scientific notation. They determine the precision of the reported value.
Decimal Point
A **decimal point** is a symbol used to separate the integer part of a number from its fractional part. When converting a number to scientific notation, the decimal point placement is crucial.

For our number 5,876,000,000, we need to position the decimal point just after the first non-zero digit to simplify the number. This means moving the decimal point so that only the leading significant digits are to its left.

Thus, by shifting the decimal point 9 places to the left, we transform 5,876,000,000 into 5.876.
Power of 10
The **power of 10** is a key component in scientific notation. It tells us how many places the decimal point has been moved.

Positive powers (like 9 in our example) mean the decimal has been moved left, while negative powers indicate a right shift.
  • Moving the decimal 9 places to the left converts 5,876,000,000 into 5.876, which we write as: \ \ \( 5.876 \times 10^9 \).

    This notation helps simplify and standardize the representation of very large or very small numbers, making them easier to read and compare.

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Most popular questions from this chapter

Perform each division using the "long division" process. $$ \frac{6 p^{4}-16 p^{3}+15 p^{2}-5 p+10}{3 p+1} $$

Use scientific notation to calculate the answer to each problem. Pollux, one of the brightest stars in the night sky, is 33.7 light-years from Earth. If one light-year is about \(6,000,000,000,000 \mathrm{mi},\) about how many miles is Pollux from Earth?

Match each expression in Column I with the equivalent expression in Column II. Choices in Column II may be used once, more than once, or not at all. An Exercise \(17, x \neq 0 .\). I (a) \(x^{0}\) (b) \(-x^{0}\) (c) \(7 x^{0}\) (d) \((7 x)^{0}\) (e) \(-7 x^{0}\) (f) \((-7 x)^{0}\) II A. 0 B. 1 C. -1 D. 7 E. -7 F. \(\frac{1}{7}\)

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Use scientific notation to calculate the answer to each problem. In \(2007,9.63 \times 10^{9}\) dollars were spent to attend motion pictures in the United States. Domestic admissions (the total number of tickets sold) for that year totaled 1.4 billion. What was the average ticket price?
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