Lesson 42: Rounding Numbers to Estimate

New Concept

To round a number to the nearest hundred, we choose the closest multiple of 100 (number ending in two zeros).

Why it matters

Mastering estimation allows you to instantly verify the reasonableness of complex algebraic solutions, a critical skill in competitive math. This is your first step towards developing the number sense required for advanced topics where orders of magnitude are more important than exact figures.

What’s next

Next, you'll apply this skill to round numbers and use those values to estimate the results of multiplication problems.

Property

When multiplying by multiples of 10 and 100, we focus our attention on the first digit of the multiple. Then, we write as many zeros in the product as there are in the multiple of 10 or 100.

Examples

• To solve $4 \times 300$, first calculate $4 \times 3 = 12$. Then, add the two zeros from 300 to get $1200$.
• To solve $7 \times 50$, first calculate $7 \times 5 = 35$. Then, add the zero from 50 to get $350$.
• To solve $8 \times 500$, first calculate $8 \times 5 = 40$. Then, add the two zeros from 500 to get $4000$.

Explanation

Become a math wizard! Multiply the front digits, then count all the zeros in the original problem and attach them to the end of your answer. It's a simple trick for solving huge problems in your head, making you look like a genius.

Property

To round to the nearest hundred, find the closest multiple of 100. Look at the digit in the tens place: if it is 5 or more, round up. If it is less than 5, round down.

Examples

• To round 681, the tens digit is 8, which is more than 5, so we round up to the next hundred: $700$.
• To round 3440, the tens digit is 4, which is less than 5, so we round down to the current hundred: $3400$.
• To round 950, the tens digit is 5, so we follow the rule to round up to the next hundred: $1000$.

Explanation

Think of hundreds as stepping stones. The tens digit tells you where to jump! If it’s 5 or more, you have enough power to leap forward to the next, bigger stone. If it's less than 5, you just hop back to the previous one.

Property

To find a reasonable estimate for a multiplication problem, round the numbers first to make the arithmetic easier to do in your head. The result will be an approximation, not an exact answer.

Examples

• To estimate $8 \times 58$, we can round the numbers to $10 \times 60$, which gives us a reasonable estimate of $600$.
• Estimate the cost of 4 shirts that cost 28 dollars each. Round to $4 \times 30$ dollars. The estimated cost is 120 dollars.
• Estimate the total musicians in 21 rows of 8. Round to $20 \times 10$. The estimate is about 200 musicians.

Explanation

Why struggle with messy numbers like $8 \times 58$? Be a clever strategist! Round them to friendly numbers like $10 \times 60$. The answer is a quick estimate that’s close enough to the real deal, and you solved it in seconds.