- 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

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# Estimating a Quotient of Whole Numbers

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.

### Solution

**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.

### Solution

**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