Place values in decimal numbers

Learning Objectives Identify the place value of each digit in a decimal number up to the thousandths place. Read and write decimal numbers correctly using place value terminology. Express decimal numbers in expanded form and convert expanded form back to standard form. Compare and order decimal numbers by analyzing their place values. Explain the relationship between adjacent place values in a decimal number (multiplying or dividing by 10). Represent decimal numbers using a place value chart. Ever wondered how stores calculate prices like $3.99 or how Olympic scores are so precise, like 9.85? 💰 It all comes down to understanding decimal numbers! In this lesson, you'll discover that every digit in a decimal number has a special 'job' or value based on its pos...

TermDefinitionExample Decimal NumberA number that includes a whole number part and a fractional part, separated by a decimal point.3.14, 0.75, 12.005 Decimal PointThe dot that separates the whole number part from the fractional part in a decimal number.In 5.23, the '.' is the decimal point. Place ValueThe value of a digit based on its position within a number. For decimals, positions to the right of the decimal point represent fractions.In 0.45, the '4' is in the tenths place, and the '5' is in the hundredths place. Tenths PlaceThe first digit to the right of the decimal point, representing fractions of 1/10.In 7.82, the '8' is in the tenths place, meaning 8/10. Hundredths PlaceThe second digit to the right of the decimal point, representing fractio...

Value of a Digit $ \text{Value of Digit} = \text{Digit} \times \text{Place Value} $ To find the actual value a digit represents, multiply the digit itself by the value of its position (e.g., 0.1 for tenths, 0.01 for hundredths). Relationship Between Adjacent Place Values $ \text{Moving one place left} = \times 10 \quad \text{Moving one place right} = \div 10 $ Each place value to the left is 10 times greater than the one to its right. Each place value to the right is 1/10 (or divided by 10) of the one to its left. This applies across the decimal point too! Decimal Expanded Form $ \text{Decimal Number} = (\text{Digit}_1 \times 10^n) + ... + (\text{Digit}_0 \times 1) + (\text{Digit}_{-1} \times \frac{1}{10}) + (\text{Digit}_{-2} \times \frac{1}{100}) + ... $ To write a...