Which decimal is the best estimate of a fraction 29/40
The Correct Answer and Explanation is:
The best decimal estimate of the fraction 29/40 is 0.725.
Explanation
To estimate a fraction as a decimal, we divide the numerator (top number) by the denominator (bottom number). For 29/40, this means: 29÷40=0.72529 \div 40 = 0.725
So, the decimal equivalent of the fraction 29/40 is exactly 0.725.
Why is this the best estimate?
Estimating a fraction as a decimal helps us compare it with other numbers and understand its size on the number line. In real-life situations—such as money, measurements, or percentages—decimals are often easier to interpret than fractions. For example, if someone eats 29 slices out of a 40-slice pizza, knowing they ate 72.5% (or 0.725) helps quickly understand how much was consumed.
Step-by-step breakdown:
- Understanding the fraction:
The fraction 29/40 is a proper fraction because the numerator (29) is less than the denominator (40), so the value is less than 1. - Using long division:
Dividing 29 by 40 gives:- 40 goes into 290 seven times (40 × 7 = 280),
- leaving a remainder of 10,
- then 40 goes into 100 two times (40 × 2 = 80),
- remainder 20,
- and 40 goes into 200 five times (40 × 5 = 200), remainder 0.
- No need to round:
Since 0.725 terminates and doesn’t repeat, this is the exact decimal—not an approximation—so it is the best estimate. - Verifying:
You can check it by multiplying: 0.725×40=290.725 \times 40 = 29
Thus, 0.725 is both the most accurate and the most useful decimal estimate for the fraction 29/40.
