Rounding Whole Numbers
Rounding whole numbers means replacing a number with an approximation by identifying the target place value, looking at the next digit to the right, and either keeping the digit the same (if that next digit is less than 5) or increasing it by one (if it is 5 or greater). To round 47,832 to the nearest thousand: the thousands digit is 7, the next digit is 8 (greater than or equal to 5), so round up to 48,000. This Grade 7 math skill from Saxon Math, Course 2 is essential for estimation, mental math, and interpreting statistical data where approximate values are more useful than exact numbers.
Key Concepts
Property 1. If the circled digit is 5 or more, we add 1 to the underlined digit. If the circled digit is less than 5, we leave the underlined digit unchanged. 2. We replace the circled digit and all digits to the right of the circled digit with zeros.
Examples Round 472 to the nearest hundred: $$\underline{4}\textcircled{7}2 \rightarrow 500$$ Round 283 to the nearest ten: $$2\underline{8}\textcircled{3} \rightarrow 280$$ Round 5280 to have one nonzero digit: $$\underline{5}\textcircled{2}80 \rightarrow 5000$$.
Explanation Find the digit you're rounding, then peek at its neighbor to the right. If that neighbor is 5 or more, your digit rounds up before its neighbors turn to zero. If it's 4 or less, it stays put! It’s a trick to find the closest 'tidy' number.
Common Questions
How do I round a whole number?
Identify the place value you are rounding to, look at the digit immediately to the right, and round up if that digit is 5 or more, or round down (keep the digit) if it is less than 5.
How do I round 47,832 to the nearest thousand?
The thousands digit is 7. Look at the hundreds digit (8): since 8 is 5 or more, increase the thousands digit to 8. Replace all digits to the right with zeros: 48,000.
What do all the zeros in a rounded number mean?
When you round, the digits after the rounded place become zeros (placeholder zeros). They maintain the correct place value but indicate the precision of the approximation.
When should I round up vs round down?
Round up if the digit to the right of your rounding place is 5, 6, 7, 8, or 9. Round down (keep the digit the same) if the digit to the right is 0, 1, 2, 3, or 4.
When do students learn to round whole numbers?
Rounding whole numbers is introduced in Grade 3-4 and reviewed in Grade 7. Saxon Math, Course 2 covers it in Chapter 7 for use in estimation and data analysis.
What are common mistakes when rounding whole numbers?
Students sometimes round the digit they are looking at rather than the target digit, or change digits in other place values unnecessarily. Only the target digit changes; all digits after it become zero.
How does rounding help with estimation?
Rounding makes mental arithmetic faster and simpler by replacing complex numbers with convenient approximations. Estimating 48 x 19 as 50 x 20 = 1,000 is quicker than exact calculation.