How to convert 90 inches in feet

Converting 90 Inches to Feet

To convert inches to feet, you need to use the conversion factor that 1 foot is equal to 12 inches.

Starting with 90 inches, the conversion can be shown in the following steps:

So, 90 inches is equal to 7.5 feet.

This simple division represents the fractional relationship between inches and feet, providing an easy way to handle various conversions between these units.

Understanding the Conversion Factor

A conversion factor is a numerical value used to convert a quantity expressed in one set of units to another set of units. It is essential in various scientific and engineering calculations to ensure that results are consistent and accurate.

Basic Concept

To convert from one unit to another, you multiply the original measurement by the conversion factor corresponding to the units involved. Conversion factors are derived from the relationships between different units.

Example

For example, if you need to convert inches to centimeters, the conversion factor is:

General Formula

To apply a conversion factor, you can use the following formula:

Detailed Example

Suppose you have 10 inches, and you want to convert it to centimeters:

Performing the calculation:

Multiplicative Identity

Note that the conversion factor can also be understood as a fraction that equals 1 because the quantity in the numerator and the denominator are equivalent:

Importance in Science and Engineering

Using the correct conversion factor is crucial in fields like physics, chemistry, and engineering where precision is key. Conversion factors enable scientists and engineers to communicate measurements accurately and standardize results across different units and systems.

By understanding and applying them correctly, you can ensure that all your measurements and calculations are consistent and reliable.

Introduction to Division

Division is a fundamental mathematical operation that involves splitting a quantity or a number into equal parts. It is one of the four basic arithmetic operations, the others being addition, subtraction, and multiplication.

Concept of Division

To understand division, let's look at a simple example:

Suppose you have 12 apples and you want to divide them equally among 4 friends. Each friend will get:

So, each friend receives 3 apples. Here, 12 is the dividend, 4 is the divisor, and 3 is the quotient.

Division Notation

There are several ways to denote division:

• Using the division symbol $\div$: $a \div b$
• Using a slash $/$: $a / b$
• Using fraction notation: $\frac{a}{b}$

Division as the Inverse of Multiplication

Division is considered the inverse operation of multiplication. If:

Then:

Properties of Division

Not Commutative: Unlike addition and multiplication, division is not commutative. This means:

Not Associative: Division is also not associative, which means:

Division by Zero

A very important rule in division is that division by zero is undefined. For any number $a$:

This is because no number multiplied by 0 will ever give a non-zero dividend.

Long Division

For larger numbers, we often use a method called long division. Here is a simplified version of the long division process:

1. Divide the first number of the dividend by the divisor.
2. Multiply the divisor by the quotient.
3. Subtract the result from the first number of the dividend.
4. Bring down the next number from the dividend and repeat the process.

Example of Long Division

Suppose you want to divide 987 by 32:

1. 32 goes into 98 two times (since $32 \times 2 = 64$).
2. Subtract 64 from 98 to get 34.
3. Bring down the next digit (7) to get 347.
4. 32 goes into 347 ten times (since $32 \times 10 = 320$).
5. Subtract 320 from 347 to get 27.

So, $987 \div 32 \approx 30$ with a remainder of 27.

Conclusion

Division is a critical arithmetic operation used in various fields of science, engineering, and daily life. Understanding the basic properties and rules of division helps in solving complex mathematical problems more efficiently.