/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 8 To convert an area measured in \... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 8

To convert an area measured in \(\mathrm{m}^{2}\) to one measured in \(\mathrm{cm}^{2}\), the area in \(\mathrm{m}^{2}\) is multiplied by \(10^{4}\). Convert the following areas to \(\mathrm{cm}^{2}\) : (a) \(5 \mathrm{~m}^{2}\), (b) \(0.33 \mathrm{~m}^{2}\), (c) \(6.2 \mathrm{~m}^{2}\)

Short Answer

Expert verified
(a) 50000 cm虏, (b) 3300 cm虏, (c) 62000 cm虏

Step by step solution

01

Understanding Area Conversion

To convert an area from square meters (\(\mathrm{m}^2\)) to square centimeters (\(\mathrm{cm}^2\)), multiply the given value by \(10^{4}\). This is because there are 100 cm in a meter, and when dealing with area, this factor is squared.
02

Conversion for 5 m虏

Multiply 5 by \(10^{4}\) to convert to \(\mathrm{cm}^2\): \[5 \times 10^{4} = 50000\]},
03

Conversion for 0.33 m虏

Multiply 0.33 by \(10^{4}\) to convert to \(\mathrm{cm}^2\): \[0.33 \times 10^{4} = 3300\]},
04

Conversion for 6.2 m虏

Multiply 6.2 by \(10^{4}\) to convert to \(\mathrm{cm}^2\): \[6.2 \times 10^{4} = 62000\]}],

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Key Concepts

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

Unit Conversion
Unit conversion is all about changing a measurement from one set of units to another. Understanding this is crucial in science, engineering, cooking, and more.
For example, you might need to convert kilometers to miles when traveling or cups to ounces when cooking.
  • Length Conversions: Think of converting inches to centimeters or feet to meters.
  • Volume Conversions: Like liters to gallons.
  • Area Conversions: Such as square meters to square centimeters.
Getting used to unit conversion involves understanding the relationship between different units and knowing how to correctly apply conversion factors. It鈥檚 like a puzzle where you have to place the right piece in the right spot.
Square Meters to Square Centimeters
When dealing with areas, converting square meters (m虏) to square centimeters (cm虏) is helpful, especially in detailed measurements.
This specific conversion is simple once you understand the rule:
  • 1 meter = 100 centimeters, so 1 square meter = 100 脳 100 square centimeters.
  • This gives us 1 m虏 = 10,000 cm虏.
Multiply the area in m虏 by 10,000 to convert it to cm虏. For instance, if you have 5 m虏: multiply 5 by 10,000 to get 50,000 cm虏.
It鈥檚 a straightforward multiplication task once the conversion factor is known.
Multiplying Powers of Ten
Multiplying powers of ten is a fundamental math concept and incredibly useful for making calculations quick and easy.
In our example, converting from m虏 to cm虏 involves multiplying by 10鈦�. When you multiply a number by 10鈦�, you move the decimal point four places to the right.
  • Example: For 0.33 m虏, multiplying by 10鈦� simply shifts the decimal point four places, making it 3300 cm虏.
  • Practice: Try multiplying 2.5 by 10鈦�. The result is 25,000.
Remember, multiplying by a power of ten helps in scaling numbers quickly, perfect for unit conversions or scientific calculations.

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Most popular questions from this chapter

Remove the brackets from each of the following expressions: (a) \(2(m n)\) (c) \(a(m n)\) (d) \(a(m+n)\) (e) \(a(m-n)\) (f) \((a m) n\) (g) \((a+m) n\) (h) \((a-m) n\) (i) \(5(p q)\) (j) \(5(p+q)\) (1) \(7(x y)\) \((\mathrm{m}) 7(x+y)\) (n) \(7(x-y)\) (o) \(8(2 p+q)\) (p) \(8(2 p q)\) (q) \(8(2 p-q)(\mathrm{r}) 5(p-3 q)\) (s) \(5(p+3 q)\) (t) \(5(3 p q)\)

Find the value of \(5(8+3)-2(-3-6)\)

Remove the brackets from each of the following expressions: (a) \(4(a+b)\) (b) \(2(m-n)\) (c) \(9(x-y)\)

Evaluate, without using a calculator: (a) \(0.2^{2}\) (b) \(15^{2}\)

State the reciprocal of (a) 8, (b) \(\frac{9}{13}\).
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