Lesson 4: Model mixed numbers with units of hundreds, tens, ones, tenths, and hundredths in expanded form and on the place value chart.

Property

Numbers with decimals can be visually represented on a place value chart using disks. Each column on the chart corresponds to a place value (e.g., hundreds, tens, ones, tenths, hundredths), and the number of disks in a column represents the digit in that place.

Examples

• To model the number $243.58$, you would place 2 disks in the hundreds column, 4 disks in the tens column, 3 disks in the ones column, 5 disks in the tenths column, and 8 disks in the hundredths column.
• To model the number $107.09$, you would place 1 disk in the hundreds column, 0 disks in the tens column, 7 disks in the ones column, 0 disks in the tenths column, and 9 disks in the hundredths column.

Explanation

A place value chart is a tool used to visualize the value of each digit in a number. By placing disks in the appropriate columns, you create a concrete model of the number, including its whole number and decimal parts. This visual representation helps in understanding concepts like unit form and expanded form. The decimal point separates the whole number places (ones, tens, hundreds) from the fractional places (tenths, hundredths).

Property

A decimal number can be written in expanded form by showing the sum of the value of each digit. The decimal part can be expressed using either fraction notation or decimal notation.

Fraction Expanded Form: $378.73 = (3 \times 100) + (7 \times 10) + (8 \times 1) + (7 \times \frac{1}{10}) + (3 \times \frac{1}{100})$

Property

A mixed number with a fractional part whose denominator is a power of 10 (such as 10 or 100) is equivalent to a decimal number. The whole number is written to the left of the decimal point, and the numerator of the fraction is written to the right, with its last digit's place value determined by the denominator.

Examples