T1_LO1 · lo-yr9-place-values-and-decimals
A digit's value depends on its place. The same digit can mean very different amounts in different positions.
Steps
Look at the digit you care about.
Name its place: ones, tens, tenths, hundredths, and so on.
Write its value, not just the digit.
Compare left to right.
Place-value reminder
In $347$, the $4$ means $40$.
In $5.3$, the $3$ means $0.3$.
In $2.74$, the $7$ means $0.7$.
In $2.74$, the $4$ means $0.04$.
Saying the value is just the digit. In $862$, the digit is $6$, but its value is $60$. In $2.74$, the digit is $7$, but its value is $0.7$.
What is the value of the $4$ in $347$?
What is the value of the $5$ in $5.3$?
What is the value of the $4$ in $3.48$?
Example 1: value of a digit
Find the value of the $6$ in $862$.$$ 862 = 800 + 60 + 2 $$So the value of the $6$ is $60$.
Example 2: decimal place value
Find the value of the $7$ in $2.74$.$$ 2.74 = 2 + 0.7 + 0.04 $$So the value of the $7$ is $0.7$.
Find the value of the $9$ in $291$.
Find the value of the $6$ in $4.63$.
Find the value of the $2$ in $8.205$.
Comparing numbers
\small When two numbers have the same whole-number part, compare the decimal places next.\normalsize
Example 3: compare decimals
Which is greater: $0.8$ or $0.08$?$$ 0.8 = 8 tenths $$$$ 0.08 = 8 hundredths $$A tenth is bigger than a hundredth, so $0.8 > 0.08$.
Example 4: order numbers
Order $3.2, 2.9, 3.02$ from smallest to largest.$$ 2.9 < 3.02 < 3.2 $$So the order is $2.9, 3.02, 3.2$.
Thinking more digits means a bigger decimal. For example, $0.08$ is not bigger than $0.8$. It is smaller because 8 hundredths is less than 8 tenths.
Partitioning numbers
\small Split a number into place-value parts.\normalsize
Example 5: whole number
Partition $407$.$$ 407 = 400 + 0 + 7 $$Usually we write this as $407 = 400 + 7$.
Example 6: decimal number
Partition $3.48$.$$ 3.48 = 3 + 0.4 + 0.08 $$That is 3 ones, 4 tenths, and 8 hundredths.
Which is greater: $45$ or $54$?
Order from smallest to largest: $0.5, 0.05, 0.15$.
Partition $4.7$.