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Chapter 1: Problem 58

Estimate each quotient by first rounding to the nearest hundred. Show your work. $$ 3641 \div 571 $$

Short Answer

Expert verified
6

Step by step solution

01

Round 3641 to the nearest hundred

Examine the hundreds and tens place of the number 3641. The number in the hundreds place is 6, and the number in the tens place is 4. Since 4 is less than 5, round down. Therefore, 3641 rounded to the nearest hundred is 3600.
02

Round 571 to the nearest hundred

Examine the hundreds and tens place of the number 571. The number in the hundreds place is 5, and the number in the tens place is 7. Since 7 is greater than or equal to 5, round up. Therefore, 571 rounded to the nearest hundred is 600.
03

Divide the rounded numbers

Now, divide the rounded numbers obtained in steps 1 and 2. That is, calculate \[ 3600 \div 600 \]. Simplifying this, \[3600 \div 600 = 6\].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rounding Numbers
Rounding is a basic math skill that makes numbers simpler to work with. To round numbers, you look at the digit to the right of the place value you鈥檙e rounding to. For example, if you鈥檙e rounding to the nearest hundred, you look at the tens place.
If that digit is 5 or greater, you round up. If it is less than 5, you round down. In this exercise:
  • The number 3641 is rounded to 3600 because the tens place (4) is less than 5.
  • The number 571 is rounded to 600 because the tens place (7) is 5 or greater.
Rounding helps simplify the division process, especially when dealing with larger numbers.
Division
Division is one of the four fundamental operations in arithmetic, alongside addition, subtraction, and multiplication. It separates a number (the dividend) into a certain number of equal parts specified by another number (the divisor).
Estimating quotients by rounding first makes calculations easier and faster. In our exercise:
  • We rounded 3641 to 3600 and 571 to 600.
  • The simplified division problem becomes \[ 3600 \div 600 \].
By using rounding and basic division, you can quickly estimate the result to be 6.
Basic Arithmetic
Basic arithmetic refers to simple calculations like addition, subtraction, multiplication, and division. These skills are essential for all math problems. Here, knowing the basics makes understanding and solving more complex problems easier, even when rounding is used.
Let鈥檚 summarize our steps for estimating the quotient:
  • First, round each number to the nearest hundred.
  • Next, set up your division problem with the rounded numbers.
  • Finally, perform the division to estimate the quotient.
Practice these steps to get better at handling more complex arithmetic problems.

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Most popular questions from this chapter

Solve by trial. $$ 56 \div m=7 $$

Evaluate. $$ 3^{5} $$

Simplify. $$ 2^{2}+5^{2} $$

Simplify. $$ 17 \cdot 20-(17+20) $$

Solve. Be sure to check. $$ 15+t=22 $$
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