The image shows a
place value chart and the
expanded form of a decimal number. Let's break it down step by step to understand and verify the solution.
---
🔢 Step 1: Understand the Number from the Chart
The chart displays the digits in their respective place values:
| THOUSANDS | HUNDREDS | TENS | ONES | DECIMAL | TENTHS | HUNDREDTHS | THOUSANDTHS |
|-----------|----------|------|------|--------|--------|------------|-------------|
| |
3 |
1|
7|
. |
2 |
9 | |
So, the number is:
317.29
---
🧮 Step 2: Expanded Form Breakdown
Now, let’s write each digit in its expanded form based on its place value:
-
3 is in the
hundreds place → $ 3 \times 100 = 300 $
-
1 is in the
tens place → $ 1 \times 10 = 10 $
-
7 is in the
ones place → $ 7 \times 1 = 7 $
-
2 is in the
tenths place → $ 2 \times 0.1 = 0.2 $
-
9 is in the
hundredths place → $ 9 \times 0.01 = 0.09 $
---
✔ Step 3: Add Them Up (Expanded Form)
$$
300 + 10 + 7 + 0.2 + 0.09
$$
Now add them:
- $ 300 + 10 = 310 $
- $ 310 + 7 = 317 $
- $ 317 + 0.2 = 317.2 $
- $ 317.2 + 0.09 = 317.29 $
✔ This matches the original number:
317.29
---
✔ Final Answer:
The expanded form of
317.29 is:
$$
\boxed{300 + 10 + 7 + 0.2 + 0.09}
$$
This correctly represents the number using place values, including decimals. ✔️
Parent Tip: Review the logic above to help your child master the concept of math expanded form.
