To solve the problem of eliminating decimals in the given equation [tex]\(-m + 0.02 + 2.1m = -1.45 - 4.81m\)[/tex], we need to determine which number we can multiply each term by to convert all the decimal numbers into whole numbers.
Let's analyze the decimals we have in the equation:
- [tex]\(0.02\)[/tex] (two decimal places)
- [tex]\(2.1\)[/tex] (one decimal place)
- [tex]\(-1.45\)[/tex] (two decimal places)
- [tex]\(-4.81\)[/tex] (two decimal places)
To eliminate the decimal places, we should choose a number that will transform all these decimal coefficients into integers. Looking at the largest number of decimal places (which is 2), we multiply all terms by [tex]\(100\)[/tex]. This is because [tex]\(100 = 10^2\)[/tex] and moving the decimal place two positions to the right will convert each term to a whole number.
Here’s how each term transforms when multiplied by [tex]\(100\)[/tex]:
[tex]\[
-100m + 100 \cdot 0.02 + 100 \cdot 2.1m = 100 \cdot (-1.45) + 100 \cdot (-4.81m)
\][/tex]
Simplifying this, we get:
[tex]\[
-100m + 2 + 210m = -145 - 481m
\][/tex]
Thus, by multiplying each term by [tex]\(100\)[/tex], we have successfully removed the decimals from the equation. The equation now contains only whole numbers.
Hence, the correct number to multiply each term of the given equation by to eliminate the decimals is:
100
