Which decimal is the best estimate of a fraction 29/40

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:

  1. 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.
  2. 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.
    So, the full decimal is 0.725.
  3. 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.
  4. 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.

Scroll to Top