Final answer:
To find the quotient of 0.4 divided by 0.05, convert both to the same place value as tenths, and then divide the number of tenths to get 8.
Step-by-step explanation:
Finding the Quotient of 0.4 and 0.05 Using Models
To find the quotient of 0.4 divided by 0.05, we can model the division as the number of times 0.05 fits into 0.4. Since both numbers are decimals, we can think of them in terms of place value. 0.4 is the same as 40 tenths, and 0.05 is the same as 5 hundredths, which is also 5 tenths when converted to the same place value (10 hundredths equal 1 tenth).
Now, we divide the larger quantity (40 tenths) by the smaller quantity (5 tenths) to find how many groups of 0.05 make up 0.4. Dividing tenths by tenths, 40 divided by 5 equals 8. So, 0.4 divided by 0.05 is 8, meaning 0.05 would fit into 0.4 a total of 8 times.
When drawing this out as equal groups, we would illustrate 8 groups, each representing 0.05, adding up to the total of 0.4. No complex models or exponential graphs are required for this division, as it can be solved by understanding place values and simple division.