- Ordering Rounding and Order of Operations
- Home
- Introduction to Inequalities
- Comparing a Numerical Expression With a Number
- Ordering Large Numbers
- Rounding to Tens or Hundreds
- Rounding to Hundreds or Thousands
- Rounding to Thousands, Ten Thousand, or Hundred Thousand
- Estimating a Sum of Whole Numbers
- Estimating a Difference of Whole Numbers
- Estimating a Product of Whole Numbers
- Estimating a Quotient of Whole Numbers
- Writing Expressions Using Exponents
- Introduction to Exponents
- Power of 10: Positive Exponent
- Power of 10: Negative Exponent
- Introduction to Parentheses
- Comparing Numerical Expressions With Parentheses
- Introduction to Order of Operations
- Order of Operations With Whole Numbers
- Order of Operations With Whole Numbers and Grouping Symbols
- Order of Operations With Whole Numbers and Exponents: Basic

The whole numbers are first rounded as specified, i.e., rounded to the nearest ten, hundred and so on. Then the quotient of the rounded whole numbers is found to **estimate** the quotient of whole numbers.

Estimate the quotient 5873 ÷ 346 by first rounding each number so that it has only one non-zero digit.

**Step 1:**

Rounding 5873 such that it has only one non-zero digit means rounding it to nearest thousand. Since the hundreds digit, 8 > 5; 587󠄀3 rounds up to 6,000.

**Step 2:**

Rounding 346 such that it has only one non-zero digit means rounding it to nearest hundred. Since the tens digit, 4 < 5 346 rounds down to 300.

**Step 3:**

So the estimate of the quotient after rounding

= 6,000 ÷ 300 = 20

Estimate the quotient 2162 × 176 by first rounding each number nearest ten.

**Step 1:**

**2162**: Here the digit in ones place, 2 < 5. So 2162 rounds down to nearest ten as 2160.

**Step 2:**

**176**: Here the digit in ones place, 6 > 5. So 176 rounds up to nearest ten as 180.

**Step 3:**

So the estimate of the quotient after rounding

= 2160 ÷ 180 = 12

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