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Chapter 1: Problem 57

Convert the number to standard form. Six thousand, five

Short Answer

Expert verified
6.005 脳 10^3

Step by step solution

01

Understand the Problem

The task is to convert the number written in words, 'six thousand, five', into its numerical form and then express that number in standard form.
02

Convert Words to Numerical Form

First, convert 'six thousand, five' into a numerical form. 'Six thousand' corresponds to 6000 and 'five' is 5. Combining these, we get 6000 + 5 = 6005.
03

Express in Standard Form

To express 6005 in standard form, place the decimal after the first non-zero digit and count the number of places the decimal has 'moved' to get to that position. For 6005, this is 6.005. Since the decimal point moved 3 places to the left, multiply by \(10^3\). Hence, the standard form is \(6.005 脳 10^3\).

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Key Concepts

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

Numerical Form
Numerical form is the way we express numbers using digits. In this exercise, we started with the words 'six thousand, five'.
To convert it to numerical form, we break it down into parts:
'Six thousand' translates to 6000 and 'five' is simply 5.
By adding these two parts together, we get 6000 + 5 = 6005.
This step is crucial because it translates the written number into a form that is easier to work with mathematically.
Now that we've got 6005, we can move on to converting this numerical form into standard form.
Decimal Placement
Decimal placement is an important concept in mathematics, especially when converting numbers to standard form. When we talk about placing the decimal, we mean identifying where the decimal point goes in a number.
In our example, the number 6005 doesn't explicitly show a decimal point, so it's understood to be at the end: 6005.0.
To convert this to standard form, we place the decimal right after the first non-zero digit. This results in 6.005.
By recognizing this key step of placing the decimal, we help simplify and prepare the number for scientific notation.
Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a concise and standardized format. This is particularly useful in science and engineering.
For our number 6005, after placing the decimal point, we get 6.005.
Next, count the number of places the decimal has moved from its original position to get to 6.005. In this case, it has moved 3 places to the left.
The resulting standard form becomes 6.005 脳 10^3.
Here, 10^3 represents the power of ten that fits the original decimal shift.
Using scientific notation not only makes numbers more manageable but also simplifies operations like multiplication and division.

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