Rounding whole numbers (nearest 10, 100, 1,000)

Key idea

To round a whole number, choose a rounding place (like the nearest ten, hundred, or thousand), then look at the digit one place to the right.

• If the digit to the right is \(0,1,2,3,4\), round down (keep the rounding digit the same).
• If the digit to the right is \(5,6,7,8,9\), round up (increase the rounding digit by 1).

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Summary

• Choose the rounding place (ten, hundred, thousand).
• Look one digit to the right to decide up or down.

Rounding decimals (decimal places)

Key idea

Decimal places are positions to the right of the decimal point: tenths, hundredths, thousandths, and so on. Rounding decimals uses the same rule as whole numbers: look at the digit one place to the right.

Worked example

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Summary

• Find the target decimal place (tenth, hundredth, etc.).
• Look one place to the right to decide up or down.

Rounding to significant figures (fast estimation)

Key idea

The first significant figure is the first non-zero digit from the left. When you round to one significant figure, you keep that first digit and use the next digit to decide up or down. For whole numbers, digits after the first significant digit become zeros.

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Summary

• Significant figures create fast, easy-to-calculate estimates.
• One significant figure is a common choice for quick mental math.

Estimating sums and differences

Key idea

To estimate a sum or difference, round each number to a friendly place value, then add or subtract. A good rule is to round both numbers to the same place (for example, both to the nearest ten).

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Summary

• Round to a place that makes the math easy (nearest ten or nearest hundred).
• Use the estimate to check whether your exact answer makes sense.

Estimating products and quotients

Key idea

For multiplication, round factors to friendly numbers (often nearest ten or one significant figure). For division, choose numbers that divide easily (called compatible numbers).

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Summary

• Multiply: round factors to friendly numbers and multiply.
• Divide: use compatible numbers to get an easy quotient.

Estimation to check reasonableness

Key idea

Estimation is a powerful “sanity check.” Before trusting a result, compare it to a quick estimate. If your exact answer is far from the estimate, recheck your work (place value errors are common).

Overestimate vs underestimate

Rounding can push an estimate up or down. If you round both numbers up in a sum, the estimate becomes an overestimate. If you round both numbers down, it becomes an underestimate. Rounding to the nearest gives a balanced estimate for “closest” thinking.

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Summary

• Use estimation to catch place value mistakes quickly.
• Know when rounding creates an overestimate or an underestimate.

Why rounding and estimation matter

Where you use rounding and estimation

• Money: estimate totals, tips, and change.
• Measurement: lengths, weights, time, and temperature are often rounded.
• Mental math: quick decisions without a calculator.
• Checking work: a fast estimate can spot errors immediately.

Worked example (everyday estimation)

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Final recap

• Rounding depends on place value: look one digit to the right.
• Decimals round the same way: tenths, hundredths, thousandths.
• One significant figure is great for quick, friendly estimates.
• Use estimation to check reasonableness in addition, subtraction, multiplication, and division.