Which comparison is correct? A. 0.298 < 0.289 B. 0.420 > 0.42 C. 1.32 < 1.319 D. 3.544 > 3.455
The correct answer and explanation is:
The correct comparison is D. 3.544 > 3.455.
Explanation:
Let’s analyze each option carefully by comparing the numbers digit by digit:
A. 0.298 < 0.289
- Look at the digits after the decimal point:
- 0.298 has digits 2, 9, 8.
- 0.289 has digits 2, 8, 9.
- Compare digit by digit:
- The first digit after decimal is 2 in both.
- The second digit: 9 (in 0.298) vs. 8 (in 0.289). Since 9 > 8, 0.298 > 0.289.
- Therefore, 0.298 < 0.289 is false.
B. 0.420 > 0.42
- 0.420 and 0.42 are actually the same number because trailing zeros after the decimal point do not change the value.
- So, 0.420 = 0.42.
- Therefore, 0.420 > 0.42 is false because they are equal.
C. 1.32 < 1.319
- Compare digit by digit:
- First digit: 1 = 1.
- Decimal part: 3 = 3.
- Next digit: 2 (in 1.32) vs. 1 (in 1.319). Since 2 > 1, 1.32 > 1.319.
- Therefore, 1.32 < 1.319 is false.
D. 3.544 > 3.455
- Compare digit by digit:
- First digit: 3 = 3.
- Decimal part first digit: 5 = 4 (5 > 4), so 3.544 > 3.455.
- Therefore, 3.544 > 3.455 is true.
Summary:
The only true statement is D. 3.544 > 3.455.
Additional Notes:
When comparing decimals:
- Start comparing from the left-most digit (whole number part).
- If whole number parts are equal, move digit by digit to the right after the decimal point.
- Trailing zeros after the decimal do not affect the value (e.g., 0.42 = 0.420).
- Always compare digits in the same place value.
Understanding this method helps avoid common mistakes when comparing decimal numbers.