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Chapter 4: Problem 25

Write each number in standard notation. $$ 1.2 \times 10^{-5} $$

Short Answer

Expert verified
0.000012

Step by step solution

01

Understand Scientific Notation

Scientific notation is a way to express very large or very small numbers. It has the format: \( a \times 10^b \). Here, \( a \) is a number greater than or equal to 1 and less than 10, and \( b \) is an integer.
02

Identify the Components

In the expression \( 1.2 \times 10^{-5} \), \( a = 1.2 \) and \( b = -5 \).
03

Interpret the Exponent

Since the exponent \( b \) is -5, this tells us to move the decimal point 5 places to the left.
04

Move the Decimal Point

Starting with 1.2, move the decimal point 5 places to the left. This involves adding zeros where necessary.
05

Write the Standard Notation

When moved 5 places to the left, 1.2 becomes 0.000012.

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Key Concepts

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

standard notation
In everyday math, we often use standard notation to represent numbers in a familiar, straightforward way. When we talk about standard notation, we simply mean writing out the number in full, without using exponents.
For example, instead of writing a number like 1.2 脳 10^{-5}, we write out the full number as 0.000012.
This method helps us see the entire value at once, making it easier to understand, compare, and use in calculations.
decimal point movement
To convert a number from scientific notation to standard notation, we often need to move the decimal point. The direction and number of places we move it depend on the exponent.
When the exponent is negative, as in 10^{-5}, we move the decimal point to the left. The number of places we move it is equal to the value of the exponent.
For example, with 1.2 脳 10^{-5}, we start with 1.2. Moving the decimal point 5 places to the left gives us 0.000012.
negative exponent
A negative exponent tells us to divide by the base number, which is usually 10 in scientific notation. This means we are making the original number smaller.
For example, in the expression 10^{-5}, the -5 exponent means we divide by 10 five times. In simpler terms, we move the decimal point 5 places to the left.
So, in the case of 1.2 脳 10^{-5}, moving the decimal point 5 places to the left changes 1.2 into 0.000012.

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