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Considering the defintion of area of a rectangle and multiplication in scientific notation, you obtain:
- the rectangular piece of land with an area of 2.6×10⁵ m² is 2×10³ m long.
- the width of the rectangular piece is 1.3×10² m.
Scientific notation
Scientific notation is a quick way to represent a number using powers of base 10.
The numbers are written as a product:
a×10ⁿ
where:
- a is a real number greater than or equal to 1 and less than 10, to which a decimal point is added after the first digit if it is a non-integer number.
- n is a whole number, which is called an exponent or an order of magnitude. Represents the number of times the point decimal is shifted. It is always an integer, positive if it is shifted to the left, negative if it is shifted to the right.
Area of a rectangle
A rectangle is a flat geometric figure with four sides, of which two sides that are opposite parallel to each other have the same length and the remaining two have another length.
The area of a rectangle is calculated from the two different sides (a and b). It is the product of the two contiguous sides of the rectangle:
Area of a rectangle= a×b
where a and b are the measures of the two sides.
Area and length in scientific notation
A rectangular piece of land with an area of 260,000 m² is 2,000 m long.
To write the area and length in scientific notation, the following steps are performed:
- The decimal point is moved to the left as many spaces until it reaches the right of the first digit. This number will be the value of a in the previous expression. Then: area= 2.60000= 2.6 and length= 2.000= 2.
- The base 10 is written with the exponent equal to the number of spaces that the decimal point moves. This is a positive number because the decimal point is shifted to the left, and it will have a value of: in the value of area: n=5 and in the value of length: n= 3.
So, the rectangular piece of land with an area of 2.6×10⁵ m² is 2×10³ m long.
Width of the rectangular piece
In this case, you know that a rectangular piece has:
- an area of 2.6×10⁵ m².
- a length of 2×10³ m.
Replacing in the definition of a rectangle:
2.6×10⁵ m²= width× 2×10³ m
2.6×10⁵ m²÷ 2×10³ m= width
To divide two numbers in scientific notation, you must divide the numbers that are not powers of 10 (what was previously called the "a" number). To divide the powers of ten, you must subtract the exponents. In this case:
Width= (2.6÷ 2)×10⁵⁻³ m
Width= 1.3×10² m
Finally, the width of the rectangular piece is 1.3×10² m.
Summary
In summary, you obtain:
- the rectangular piece of land with an area of 2.6×10⁵ m² is 2×10³ m long.
- the width of the rectangular piece is 1.3×10² m.
Learn more about
area of a rectangle:
brainly.com/question/7690330
scientific notation:
brainly.com/question/18073768
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