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Chapter 4: Problem 10

Write each number in scientific notation. $$ 1600 $$

Short Answer

Expert verified
1600 in scientific notation is \(1.6 \times 10^3\).

Step by step solution

01

Identify the coefficient

Scientific notation expresses a number as a product of a coefficient and a power of 10. Start by identifying the coefficient, which must be a number between 1 and 10. For 1600, shift the decimal point to the left until it is between the digits 1 and 6. This results in 1.6.
02

Determine the exponent

Count the number of positions the decimal point was moved to obtain the coefficient. For 1600, the decimal point moves three positions to the left (from 1600 to 1.6). Therefore, the exponent is 3.
03

Write in scientific notation

Combine the coefficient and the exponent to express the number in scientific notation. Using the coefficient 1.6 and the exponent 3, the scientific notation is written as \(1.6 \times 10^3\).

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Key Concepts

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

coefficient
In scientific notation, the coefficient is a number between 1 and 10 that helps simplify large or small numbers. For example, when converting 1600 into scientific notation:
- Shift the decimal point until the number is between 1 and 10.
- In this case, moving the decimal point three places to the left gives 1.6.
So, the coefficient for 1600 in scientific notation is 1.6.
exponent
The exponent in scientific notation indicates how many times the base (10) must be multiplied or divided to transform the coefficient back into the original number. After determining the coefficient as 1.6 for 1600, the next step is:
- Count the number of decimal places moved, which is 3.
- The exponent represents powers of 10.
Therefore, the exponent for 1600 in scientific notation is 3.
decimal point manipulation
Manipulating the decimal point is crucial when converting a number into scientific notation. The procedure involves:
- Moving the decimal point to create a coefficient between 1 and 10.
- For example, in 1600, shifting the decimal three places left converts it to 1.6.
Through decimal point manipulation, the coefficient and exponent are determined.
powers of 10
Powers of 10 are central to expressing numbers in scientific notation. They simplify the writing and calculation of very large or small numbers. Here, after finding the coefficient (1.6) for 1600:
- The number of moves of the decimal point (3) becomes the exponent.
- This gives us a power of 10 represented as 10^3.
Thus, 1600 in scientific notation is written as \(1.6 \times 10^3\).

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