طرح‌ها

ماشین‌حساب گرد کردن: رقم اعشار و رقم معنادار

این ماشین‌حساب عدد را به تعداد رقم اعشار یا رقم معنادار دلخواه، یا به نزدیک‌ترین ده، صد، هزار و غیره گرد می‌کند. نشان می‌دهد کدام رقم تعیین‌کننده است و چرا عدد بالا می‌رود یا همان می‌ماند.

نتیجه

مقادیر را وارد کنید و برای دیدن نتیجه «محاسبه» را بزنید.

فرمول

next digit≥5⇒round up;<5⇒keep\text{next digit} \geq 5 \Rightarrow \text{round up}; \quad < 5 \Rightarrow \text{keep}

Look at the digit just after the last one you keep. Halves round away from zero, so 2.5 → 3 and −2.5 → −3.

نحوه استفاده از این ماشین‌حساب

  1. Enter the number. Decimals, negative numbers and fractions such as 2/3 all work.
  2. Choose decimal places, significant figures or a place value, and how many.
  3. Press Calculate to see the rounded number and the digit that decided it.

مثال‌های حل‌شده

Round 3.14159 to 2 decimal places

Keep two digits after the point: 3.14. The next digit is 1.

1 is less than 5, so the 4 stays the same: 3.14.

Round 0.0045678 to 3 significant figures

Leading zeros are not significant, so the first significant figure is 4. Keep 4, 5 and 6.

The next digit is 7, which is 5 or more, so round up: 0.00457.

Round 1,234,567 to the nearest thousand

The thousands digit is 4 and the next digit (hundreds) is 5.

5 rounds up, so the answer is 1,235,000.

Round 2.5 to the nearest whole number

The digit after the point is 5, so round up to 3.

Round 9.996 to 3 significant figures

Keep 9, 9 and 9; the next digit is 6, so round up. 9.99 becomes 10.0.

The zero after the point is kept: it is the third significant figure.

اشتباه‌های رایج

  • Rounding in several stages (2.445 → 2.45 → 2.5). Always round the original number once.
  • Counting leading zeros as significant figures: 0.0045 has 2 significant figures.
  • Dropping zeros that matter: 2.50 to 3 significant figures keeps the final 0.

پرسش‌های متداول

How do you round to 2 decimal places?

Look at the third digit after the point. If it is 5 or more, add 1 to the second digit; otherwise leave it. 3.14159 → 3.14 and 2.678 → 2.68.

What are significant figures?

The digits that carry meaning, starting from the first non-zero digit. 0.04560 has 4 significant figures: 4, 5, 6 and the final 0.

Does 5 round up or down?

At school, 5 rounds up (away from zero), so 2.5 → 3 and 7.45 to one decimal place → 7.5. Some software uses “round half to even” instead.