Rounding to the Nearest Ten

Round $67$ to the nearest ten.

Find the tens place: In $67$, the tens digit is $6$ = Tens place = $6$

Look at the digit to the right (ones place): The ones digit is $7$ = Check digit = $7$

Apply the rounding rule: Since $7 \geq 5$, we round UP = Round up

Round up to the next ten: $6$ tens becomes $7$ tens, ones become $0$ = $67 \rightarrow 70$

Answer: $67$ rounded to the nearest ten is $70$.

Rounding to the Nearest Hundred

Round $438$ to the nearest hundred.

Find the hundreds place: In $438$, the hundreds digit is $4$ = Hundreds place = $4$

Look at the digit to the right (tens place): The tens digit is $3$ = Check digit = $3$

Apply the rounding rule: Since $3 < 5$, we round DOWN = Round down

Round down to the current hundred: Keep $4$ hundreds, make tens and ones $0$ = $438 \rightarrow 400$

Answer: $438$ rounded to the nearest hundred is $400$.

Rounding to the Nearest Thousand

Round $6,749$ to the nearest thousand.

Find the thousands place: In $6,749$, the thousands digit is $6$ = Thousands place = $6$

Look at the digit to the right (hundreds place): The hundreds digit is $7$ = Check digit = $7$

Apply the rounding rule: Since $7 \geq 5$, we round UP = Round up

Round up to the next thousand: $6$ thousands becomes $7$ thousands = $6,749 \rightarrow 7,000$

Answer: $6,749$ rounded to the nearest thousand is $7,000$.

Rounding When the Digit is Exactly 5

Round $85$ to the nearest ten.

Find the tens place: In $85$, the tens digit is $8$ = Tens place = $8$

Look at the digit to the right (ones place): The ones digit is $5$ = Check digit = $5$

Apply the rounding rule: Since $5 \geq 5$, we round UP = Round up

Round up to the next ten: $8$ tens becomes $9$ tens = $85 \rightarrow 90$

Answer: $85$ rounded to the nearest ten is $90$. When the digit is exactly $5$, we always round up.

Mistake: Looking at the wrong digit when rounding

Why: Students sometimes look at the digit IN the rounding place instead of the digit to its RIGHT.

Correct: Always look at the digit ONE PLACE TO THE RIGHT of where you're rounding. For rounding to tens, look at the ones digit.

Mistake: Forgetting to change digits to the right to zeros

Why: When rounding $438$ to hundreds, some write $430$ instead of $400$.

Correct: After rounding, ALL digits to the right of the rounding place become zeros.

Mistake: Rounding down when the digit is exactly 5

Why: Some students think 5 is 'in the middle' so it could go either way.

Correct: The rule is '5 or more, round up.' The digit 5 ALWAYS means round up.

Estimating Shopping Totals

Round prices to quickly estimate if you have enough money.

Items cost 23 dollars, 47 dollars, and 31 dollars. Round each: 20 + 50 + 30 = about 100 dollars total.

Reporting Large Numbers

News and statistics often use rounded numbers for clarity.

A concert had 23,847 attendees. The news reports 'about 24,000 people attended.'

Q: Why do we round up when the digit is exactly 5?

A: This is a mathematical convention that ensures consistency. Since 5 is exactly in the middle, mathematicians agreed to always round up in this case. This is called 'round half up' and is the most common rounding rule.

Q: Can I round to any place value?

A: Yes! You can round to tens, hundreds, thousands, ten-thousands, or any place value. The same rule applies: look at the digit to the right and decide whether to round up or down.

Q: Is the rounded number bigger or smaller than the original?

A: It depends! When you round up, the rounded number is larger. When you round down, it's smaller. For example, 67 rounded to 70 is larger, but 43 rounded to 40 is smaller.