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Chapter 1: Problem 27

Write the following numbers in standard form. $$7.56 E 4$$

Short Answer

Expert verified
The standard form of 7.56 E 4 is 75600.

Step by step solution

01

Understand Scientific Notation

The expression "7.56 E 4" is a scientific notation. Here, "E 4" represents the power of 10.
02

Convert to Standard Form

To convert the number from scientific notation to standard form, multiply the number before "E" (7.56) by 10 raised to the power indicated after "E" (4).
03

Perform Multiplication

Calculate the result of multiplying 7.56 by 10^4. This means moving the decimal point in 7.56 four places to the right.
04

Write the Final Result

After moving the decimal point in 7.56 four places to the right, we get 75600.

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Key Concepts

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

Standard Form Conversion
Scientific notation is a convenient way to write very large or very small numbers. It helps simplify calculations and comparison. The number "7.56 E 4" is in scientific notation, where "E 4" signifies the power of ten.
To transform this into standard form, you multiply the decimal 7.56 by a power of ten. Here, the power is 4, meaning 7.56 should be multiplied by 10,000. By doing so, you're supposed to shift the decimal point four places to the right.
After conversion, 7.56 becomes 75600 in standard form. This is a useful skill for working with scientific data, where numbers often need to be manipulated quickly.
Powers of Ten
When numbers are expressed in scientific notation, the components include the base (the number before the 'E') and the exponent, which is the number after the 'E'. The power of ten in this context regulates how many times you move the decimal point.
For instance, in the notation 7.56 E 4, the exponent is 4, meaning 10^4 or 10,000. This tells us to multiply 7.56 by 10,000.
In general, a positive exponent moves the decimal point to the right, making the number larger, while a negative exponent moves it to the left, making the number smaller. This method offers a straightforward approach to adjust numbers' scales during calculations.
Multiplication and Decimals
Multiplication involving decimals is slightly different, as it involves shifting the placement of the decimal. Performing such an operation helps in converting scientific notation to standard form.
When you multiply 7.56 by 10^4, you're essentially moving the decimal four places to the right. Start by noting the original position of the decimal in 7.56, then shift it four places to enhance the value.
This results in 75600, which reflects the accuracy of multiplication by a power of ten. Understanding how to handle decimal placements helps in accurately managing different forms of numbers, a key skill in scientific and mathematical computations.

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