Certainly! To fill in the gap in the given equation, let's follow a detailed, step-by-step approach to find the missing term.
We are given:
[tex]\[ \left(7.21 \times 10^4\right) + (\text{missing term} \times 10) = 8.01 \times 10^5 \][/tex]
1. Express the given values in standard form:
- [tex]\( 7.21 \times 10^4 \)[/tex] (This is 72100 in decimal form)
- [tex]\( 8.01 \times 10^5 \)[/tex] (This is 801000 in decimal form)
2. Set up the equation:
[tex]\[ 72100 + (\text{missing term} \times 10) = 801000 \][/tex]
3. Isolate the missing term:
To find the missing term, we need to isolate it on one side of the equation. Start by subtracting [tex]\( 72100 \)[/tex] from both sides:
[tex]\[ \text{missing term} \times 10 = 801000 - 72100 \][/tex]
[tex]\[ \text{missing term} \times 10 = 728900 \][/tex]
4. Solve for the missing term:
Now, solve for the missing term by dividing both sides of the equation by 10:
[tex]\[ \text{missing term} = \frac{728900}{10} \][/tex]
[tex]\[ \text{missing term} = 72890 \][/tex]
So the correct term that fills in the gap is [tex]\( 72890 \)[/tex]. Therefore, the complete equation is:
[tex]\[ \left(7.21 \times 10^4\right) + (72890 \times 10) = 8.01 \times 10^5 \][/tex]
