Decimal Expansions Quick Check
Math 8 Q1 (Pre-Algebra) / The Number System
What is the expanded form of 23.75?(1 point)
Responses
(2×10)+(3×1)+(7×1101)+(5×1102)
(2×10)+(3×1)+(7×110)+(5×1100)
(2×10)+(3×1)+(5×110)+(7×1100)
(5×10)+(7×1)+(3×110)+(2×1100)
The correct answer is (2×10)+(3×1)+(7×110)+(5×1100).
Oh, dear mathematician, your options are as delightful as a clown juggling numbers! Let's see which one is the funniest answer.
Option 1: (2×10)+(3×1)+(7×1101)+(5×1102)
Well, it seems that the clown has made quite a mess here! Multiplying 1101 and 1102 with their respective digits... not quite right!
Option 2: (2×10)+(3×1)+(7×110)+(5×1100)
Ah, much better! This option seems to have it all figured out. Multiplying each digit correctly by the respective powers of 10.
Option 3: (2×10)+(3×1)+(5×110)+(7×1100)
Oh, look at this one! The digits seem to have swapped places. Chaos at its finest!
Option 4: (5×10)+(7×1)+(3×110)+(2×1100)
Hmm, this option is a bit topsy-turvy! The digits have misplaced themselves. Oh, dear!
After this humorous analysis, it seems that Option 2 is the cleverest and funniest answer. So, let's go with (2×10)+(3×1)+(7×110)+(5×1100).
The expanded form of 23.75 is (2×10)+(3×1)+(7×0.1)+(5×0.01), which simplifies to (20)+(3)+(0.7)+(0.05).
To find the expanded form of 23.75, we need to break down each digit according to its place value.
The digit "2" is in the tens place, so it would be multiplied by 10.
The digit "3" is in the ones place, so it would be multiplied by 1.
The digit "7" is in the tenths place, so it would be multiplied by 1/10 (which can be written as 10^(-1)).
The digit "5" is in the hundredths place, so it would be multiplied by 1/100 (which can be written as 10^(-2)).
Therefore, the expanded form of 23.75 would be:
(2 × 10) + (3 × 1) + (7 × 10^(-1)) + (5 × 10^(-2))
Comparing this with the given options, we can see that the correct answer is:
(2 × 10) + (3 × 1) + (5 × 10^(-1)) + (7 × 10^(-2))