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)
left parenthesis 2 times 10 right parenthesis plus left parenthesis 3 times 1 right parenthesis plus left parenthesis 7 times Start Fraction 1 over 10 superscript 1 baseline End Fraction right parenthesis plus left parenthesis 5 times Start Fraction 1 over 10 squared End Fraction right parenthesis
(2×10)+(3×1)+(7×110)+(5×1100)
left parenthesis 2 times 10 right parenthesis plus left parenthesis 3 times 1 right parenthesis plus left parenthesis 7 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 5 times Start Fraction 1 over 100 End Fraction right parenthesis
(2×10)+(3×1)+(5×110)+(7×1100)
left parenthesis 2 times 10 right parenthesis plus left parenthesis 3 times 1 right parenthesis plus left parenthesis 5 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 7 times Start Fraction 1 over 100 End Fraction right parenthesis
(5×10)+(7×1)+(3×110)+(2×1100)
left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 3 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 2 times Start Fraction 1 over 100 End Fraction right parenthesis
Oh, I love decimal expansions! They're like number piñatas, you never know what's gonna come out. So, let's take a look at the options:
Option 1: (2×10)+(3×1)+(7×1101)+(5×1102)
Wow, that looks like an equation from a complicated alien math textbook. We're in decimals, not outer space!
Option 2: (2×10)+(3×1)+(7×110)+(5×1100)
Ah, now we're getting warmer! They've got the right idea, but let's double-check the powers of 10.
Option 3: (2×10)+(3×1)+(5×110)+(7×1100)
Bingo! We have a winner! This is the correct expanded form of 23.75. Those other options were just trying to confuse us like a tricky jigsaw puzzle.
So, the answer is Option 3: (2×10)+(3×1)+(5×110)+(7×1100). Good job, brainiac!
The expanded form of 23.75 can be expressed as (2×10)+(3×1)+(7×1/10)+(5×1/100).
To find the expanded form of 23.75, we need to break down each digit in the given number and multiply it by the corresponding place value.
In 23.75, the digit 2 is in the tens place, the digit 3 is in the ones place, the digit 7 is in the tenths place, and the digit 5 is in the hundredths place.
So, the expanded form is:
(2 × 10) + (3 × 1) + (7 × 1/10) + (5 × 1/100)
This can be simplified as:
(20) + (3) + (0.7) + (0.05)
Therefore, the correct expanded form of 23.75 is:
(2 × 10) + (3 × 1) + (7 × 1/10) + (5 × 1/100) or simply 20 + 3 + 0.7 + 0.05.