Definition:

Estimation: Estimation is finding an approximate value or solution to a problem. It is useful when an exact answer is not required or quickly checks a calculation's reasonableness.

Rounding: Rounding is a method of simplifying numbers to a specified place value (such as nearest tens, hundreds, or thousands) to make them easier to work with in estimation.

Estimation Using Rounding:

Example 1: 

Sarah went shopping and spent $48 on clothes, $32 on shoes, and $19 on accessories. Estimate the total amount she spent by rounding each value to the nearest ten.

Solution:

1. Round each value to the nearest ten:
   • $48 rounds to $50.
   • $32 rounds to $30.
   • $19 rounds to $20.
2. Add the rounded values:
   $50+30+20=100$.

Answer: Sarah spent approximately $100.

Example 2:

A factory produces 2,587 toys in January, 3,432 toys in February, and 2,764 toys in March. Estimate the total number of toys produced in three months by rounding each number to the nearest thousand.

Solution:

1. Round each value to the nearest thousand:
   • 2,587 rounds to 3,000.
   • 3,432 rounds to 3,000.
   • 2,764 rounds to 3,000.
2. Add the rounded values:
   $3,000+3,000+3,000=9,000$.

Answer: The factory produced approximately 9,000 toys in three months.

Example 3:

A family drives 284 miles to visit relatives, then another 367 miles to a vacation spot. Estimate the total distance they traveled by rounding to the nearest hundred.

Solution:

1. Round each value to the nearest hundred:
   • 284 rounds to 300.
   • 367 rounds to 400.
2. Add the rounded values:
   $300+400=700$.

Answer: The family traveled approximately 700 miles.

Example 4: 

John has $675 in his bank account. He plans to buy a new laptop for $489. After rounding both amounts to the nearest hundred, will he have enough money?

Solution:

1. Round each value to the nearest hundred:
   • $675 rounds to $700.
   • $489 rounds to $500.
2. Compare the amounts:
   $700-500=200$.

Answer: John can afford the laptop because, after estimation, he will have about $200 left over.

Let's practice solving place values, and stay tuned with us for more content.