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Chapter 1: Problem 17

Convert to scientific notation. 803,000,000,000

Short Answer

Expert verified
8.03 * 10^{11}

Step by step solution

01

Identify the Significant Figures

Locate the significant figures in the number. For 803,000,000,000, the significant figures are 8, 0, and 3.
02

Move the Decimal Point

Place a decimal point after the first significant figure to form a number between 1 and 10. Moving the decimal point 11 places to the left converts 803,000,000,000 to 8.03.
03

Determine the Exponent

Count the number of places the decimal point was moved. In this case, the decimal point moved 11 places to the left. Therefore, the exponent is 11.
04

Write in Scientific Notation

Combine the significant figures with the exponent to form the final answer. The number in scientific notation is written as 8.03 * 10^{11}.

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Key Concepts

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

significant figures
In every number, **significant figures** are the digits that carry meaning and contribute to its precision. They include all non-zero numbers, any zeros between significant numbers, and any trailing zeros in a decimal number. For the number 803,000,000,000, the significant figures are 8, 0, and 3. Identifying these is crucial because they are the core of your scientific notation.
decimal point
Moving the **decimal point** is a key step in converting a large number into scientific notation. You need to place it so that only one non-zero digit comes before it. This transforms the original number into a format where the new number is between 1 and 10. In our example, 803,000,000,000 becomes 8.03 by moving the decimal point left until it follows the first significant figure (8). This requires moving the point 11 places to the left.
exponent
The **exponent** in scientific notation tells us how many places the decimal point was moved to transform the original number into a value between 1 and 10. The number of places the decimal point shifts determines the exponent on the base 10. For our number 803,000,000,000, we moved the decimal point 11 places to the left, so the exponent is 11. The exponent signifies the magnitude of the original number.
convert numbers
To **convert numbers** to scientific notation, follow these simple steps:
  • Identify the significant figures in the number.
  • Move the decimal point after the first significant figure.
  • Count how many places you moved the decimal point; this number is your exponent.
  • Combine the significant figures with the exponent to write the number in scientific notation.
Using our example, we start with 803,000,000,000, retain the significant figures 8.03, move the decimal 11 places, and combine them to get the scientific notation: \(8.03 \times 10^{11}\).

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Most popular questions from this chapter

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ 19-\left(4+2 \cdot 3^{2}\right) $$

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ \mathrm{H} \subseteq R $$

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ \mathbb{Z} \nsubseteq N $$

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ 43-(-9+2)^{2}+18 \div 6 \cdot(-2) $$

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ \mathrm{W} \subseteq Z $$
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