Decimals and Measurement Basics

Study Notes

Decimals represent numbers with fractional parts, written using a decimal point.
They are a way to express numbers that are not whole numbers.
A decimal number has a whole number part and a fractional part separated by a decimal point.
Examples: 2.5, 0.75, 10.03
Place value in decimals is based on powers of ten. The first digit to the right of the decimal point represents tenths, the second represents hundredths, the third represents thousandths, and so on.
Comparing decimals requires considering place values from left to right and determining which digits are greater or smaller in each place value.
Rounding decimals involves approximating the value to a specified place value. Rules for rounding involve looking at the digit to the right of the place value to be rounded.

Measurement involves assigning numerical values to physical attributes such as length, weight, volume, and time.
Units of measurement are standardized values used to express quantities.
Common units of measurement include:
- Length: meters (m), centimeters (cm), millimeters (mm), kilometers (km)
- Weight/Mass: grams (g), kilograms (kg), milligrams (mg), tonnes (t)
- Volume: liters (l), milliliters (ml)
- Time: seconds (s), minutes (min), hours (hr), days, weeks, months, years
Converting between units of measurement involves multiplying or dividing by appropriate conversion factors. For example, 1 meter = 100 centimeters.
Understanding the relationships between different units is crucial in problem-solving and practical applications.

Area is the measure of the surface of a two-dimensional shape.
Volume is the measure of the space occupied by a three-dimensional object.
Area calculations depend on the shape:
- Rectangle: Area = length × width
- Triangle: Area = ½ × base × height
- Circle: Area = π × radius² (π is a mathematical constant approximately equal to 3.14)
Volume calculations also vary depending on the shape:
- Cube: Volume = length³
- Rectangular Prism: Volume = length × width × height
- Cylinder: Volume = π × radius² × height
Area calculations are crucial for determining surface measurements, while volume is necessary for calculating the space a solid object occupies.

Money is a medium of exchange that facilitates transactions between individuals and businesses.
Common currency units include dollars, pounds, euros, and yen.
Decimals are essential for working with money, as amounts are often expressed in cents (or other subdivisions of the currency).
Calculations with money involve addition, subtraction, multiplication, and division.
Fractions can also be used for representing or calculating money.
Budgeting and tracking income and expenses often use monetary calculations.
Understanding exchange rates (the value of one currency in relation to another) is critical in international transactions.
Bank accounts and transactions require the use of money and decimal operations.