To express the multiplication of 357.25 in expanded form, we first break down the number into its place value components. The expanded form represents a number as the sum of its parts according to their place value.
Expanded Form of 357.25
- Hundreds: \(3 \times 100 = 300\)
- Fifties: \(5 \times 10 = 50\)
- Sevenths: \(7 \times 1 = 7\)
- Tenths: \(2 \times 0.1 = 0.2\)
- Hundredths: \(5 \times 0.01 = 0.05\)
Now, we can write the expanded form of 357.25 as:
\[ 357.25 = 3 \times 100 + 5 \times 10 + 7 \times 1 + 2 \times 0.1 + 5 \times 0.01 \]
Example with Multiplication and Fractions
If you're looking for an example of how to multiply fractions involving 357.25, here's a simple illustration:
Let's say we want to multiply \(357.25\) by the fraction \(\frac{1}{2}\).
-
Convert the decimal to a fraction: \[ 357.25 = \frac{35725}{100} \]
-
Multiply by \(\frac{1}{2}\): \[ \frac{35725}{100} \times \frac{1}{2} = \frac{35725 \times 1}{100 \times 2} = \frac{35725}{200} \]
-
If needed, convert back to a decimal: Dividing \(35725\) by \(200\) gives \(178.625\).
Summary
- The expanded form of \(357.25\) is: \[ 357.25 = 300 + 50 + 7 + 0.2 + 0.05 \]
- When multiplying it by \(\frac{1}{2}\), we get: \[ 357.25 \times \frac{1}{2} = 178.625 \]
2 answers