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Chapter 7: Problem 12

Convert each number into scientific notation. $$0.0001234$$

Short Answer

Expert verified
1.234 脳 10^{-4}

Step by step solution

01

- Identify Non-zero Digits

Locate the significant digits of the number. For 0.0001234, the non-zero digits are 1234.
02

- Place the Decimal Point

Place the decimal point after the first non-zero digit. This gives 1.234.
03

- Count the Decimal Places

Count the number of places the decimal point was moved. From 0.0001234 to 1.234, the decimal point was moved 4 places to the right. So the exponent is -4.
04

- Formulate the Scientific Notation

Combine the value 1.234 with the exponent -4 to write the scientific notation as \(1.234 \times 10^{-4}\).

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Key Concepts

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

decimal places
Decimal places are the positions to the right of the decimal point in a number. For example, in the number 0.0001234, there are 7 decimal places,
which include the digits 0, 0, 0, 0, 1, 2, and 3.
When converting a number into scientific notation, the decimal places help determine where the decimal should be placed.
In our example, moving the decimal point four places to the right changes the number to 1.234.
This adjustment is crucial because it aligns the number correctly for scientific notation.
Remember, always count the number of decimal places accurately
to ensure the correct placement and the right exponent value.
significant digits
Significant digits, also known as significant figures, are the non-zero digits in a number.
They denote the precision of a measurement or calculation.
For instance, in the number 0.0001234, the significant digits are 1, 2, 3, and 4.
When converting a number to scientific notation, you focus on these significant digits.
The scientific notation of 0.0001234 is 1.234 脳 10^-4. Here, 1.234 contains three significant digits, ensuring precise representation of the number.
It鈥檚 important to always include all the significant digits in your scientific notation to preserve the number鈥檚 accuracy.
exponents
In scientific notation, the exponent indicates how many times the base (10) is multiplied by itself.
It shows the number of places the decimal point was moved.
For 0.0001234, moving the decimal point four places to the right transforms it into 1.234.
This means the exponent in the scientific notation is -4, resulting in 1.234 脳 10^-4.
A positive exponent means the decimal point was moved to the left, making the number larger.
A negative exponent means the decimal point was moved to the right, making the number smaller.
Understanding the role of exponents is key to mastering scientific notation and handling large or small numbers efficiently.

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Most popular questions from this chapter

Multiply out each of the following. As you work out the problems, identify those exercises that are either a perfect square or the difference of two squares. $$(2 y+3)(y-5)$$

What can you say about the sign of the exponent of 10 of a number written in scientific notation if the number is bigger than \(1 ?\) If the number is smaller than \(1 ?\) Why?

Perform the indicated operations and simplify. $$\frac{a}{3}-\frac{a}{2}+\frac{a}{5}$$

Do your computation using scientific notation. $$\frac{(2400)(1500)}{(90,000)(4000)}$$

Multiply out each of the following. As you work out the problems, identify those exercises that are either a perfect square or the difference of two squares. $$(2 a-5)^{2}$$
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