The image provided is a
Place Value Chart that illustrates the concept of place value for a given number. Let's break down the problem and explain the solution step by step.
---
Given Information:
The number in question is
222,222,222.222.
####
Components of the Place Value Chart:
1.
Standard Form: The number written as it appears:
222,222,222.222.
2.
Expanded Form: The number broken down into its place values.
3.
Word Form: The number written out in words.
---
Step-by-Step Solution:
####
1. Standard Form:
The standard form of the number is already given as:
\[
222,222,222.222
\]
####
2. Expanded Form:
To write the number in expanded form, we break it down into the sum of its place values. Each digit is multiplied by its corresponding place value.
-
Billions (Hundreds): \(2 \times 100,000,000,000 = 200,000,000,000\)
-
Billions (Tens): \(2 \times 10,000,000,000 = 20,000,000,000\)
-
Billions (Ones): \(2 \times 1,000,000,000 = 2,000,000,000\)
-
Millions (Hundreds): \(2 \times 100,000,000 = 20,000,000\)
-
Millions (Tens): \(2 \times 10,000,000 = 2,000,000\)
-
Millions (Ones): \(2 \times 1,000,000 = 200,000\)
-
Thousands (Hundreds): \(2 \times 100,000 = 20,000\)
-
Thousands (Tens): \(2 \times 10,000 = 2,000\)
-
Thousands (Ones): \(2 \times 1,000 = 200\)
-
Ones (Hundreds): \(2 \times 100 = 200\)
-
Ones (Tens): \(2 \times 10 = 20\)
-
Ones (Ones): \(2 \times 1 = 2\)
-
Decimals (Tenths): \(2 \times 0.1 = 0.2\)
-
Decimals (Hundredths): \(2 \times 0.01 = 0.02\)
-
Decimals (Thousandths): \(2 \times 0.001 = 0.002\)
Adding these together gives the expanded form:
\[
200,000,000,000 + 20,000,000,000 + 2,000,000,000 + 20,000,000 + 2,000,000 + 200,000 + 20,000 + 2,000 + 200 + 20 + 2 + 0.2 + 0.02 + 0.002
\]
####
3. Word Form:
To write the number in word form, we describe each group of digits according to their place values:
-
Billions: Two hundred twenty-two billion
-
Millions: Two hundred twenty-two million
-
Thousands: Two hundred twenty-two thousand
-
Ones: Two hundred twenty-two
-
Decimals: Two hundred twenty-two thousandths
Putting it all together:
\[
\text{Two hundred twenty-two billion, two hundred twenty-two million, two hundred twenty-two thousand, two hundred twenty-two AND two hundred twenty-two thousandths}
\]
---
Final Answer:
\[
\boxed{222,222,222.222}
\]
This is the standard form of the number, which matches the given information. The expanded form and word form are also correctly derived from the place value chart.
Parent Tip: Review the logic above to help your child master the concept of place value 5th grade math.