2.2 Fractions and Decimals

Understanding Fractions

Fractions represent parts of a whole. They consist of two numbers: a numerator (the top number) and a denominator (the bottom number). The denominator indicates how many equal parts the whole is divided into, and the numerator shows how many of those parts are being considered.

Example: In the fraction 3/4, the denominator 4 indicates that the whole is divided into 4 equal parts, and the numerator 3 shows that 3 of those parts are being considered. Imagine a pizza cut into 4 slices; 3/4 means you have 3 out of those 4 slices.

Understanding Decimals

Decimals are another way to represent parts of a whole. They use a base-ten system, where each digit represents a power of ten. The decimal point separates the whole number part from the fractional part.

Example: The decimal 0.75 represents 75 parts out of 100. This can be visualized as 75 cents out of a dollar, where each cent is a hundredth part of the dollar.

Converting Between Fractions and Decimals

Converting fractions to decimals involves dividing the numerator by the denominator. Conversely, converting decimals to fractions requires expressing the decimal as a fraction with a power of ten in the denominator and then simplifying if possible.

Example: To convert 3/4 to a decimal, divide 3 by 4, which gives 0.75. To convert 0.75 to a fraction, express it as 75/100, then simplify to 3/4.

Applications in Machining

In machining, fractions and decimals are used to specify precise measurements. For instance, a machinist might need to cut a piece of metal to a length of 3/8 inch or 0.375 inch. Understanding how to convert between these forms ensures accuracy in measurements and avoids costly errors.

Example: If a blueprint specifies a hole diameter of 0.625 inches, the machinist must know that this is equivalent to 5/8 inch to set the correct drill bit size.