Question

What is the value of 442+325+287, rounded to the nearest hundred? A. 700 B. 800 C. 900 D. 1,000 E. 1,100

Short answer

Answer: 1,100

Step-by-step solution

Adding the numbers together

To find the sum, we need to add the given numbers together: 442 + 325 + 287 First, add 442 and 325: 442 + 325 = 767 Next, add 767 and 287: 767 + 287 = 1054 So, the sum of the numbers is 1054.

Rounding to the nearest hundred

To round the sum to the nearest hundred, we need to determine which hundred is closest to 1054. We can do this by finding the hundreds place of the number and then checking whether the tens place is 5 or greater. In 1054, the hundreds place is 1 (representing 1000) and the tens place is 5. Since the tens place is 5 or greater, we round up to the next hundred, which is 1100.

Compare the rounded result to the given options

We found that the rounded sum is 1100. Now, let's compare this to the given options: A. 700 B. 800 C. 900 D. 1,000 E. 1,100 Our rounded sum, 1100, matches option E. Therefore, the correct answer is 1,100 (option E).

Key concepts

Rounding Numbers

Understanding how to round numbers is a fundamental skill in math that simplifies figures to make them more manageable. When rounding to the nearest hundred, the process involves looking at the digit in the tens place. If that digit is 5 or greater, you increase the digit in the hundreds place by one and replace all subsequent digits with zeros. Alternatively, if the tens place digit is less than 5, you keep the digit in the hundreds place the same and still replace all subsequent digits with zeros. For example, when rounding the number 1054:

• The digit in the hundreds place is 1 (representing 1000).
• The digit in the tens place is 5.
• Because the tens digit is 5 or more, we round up to give a rounded figure of 1100.

Rounding numbers can make calculations easier and quicker to perform, especially in mental math, and it is a skill that can save a lot of time during tests or in practical situations where an approximate number is sufficient.

Basic Arithmetic

Basic arithmetic is inclusive of addition, subtraction, multiplication, and division. These operations form the foundation for more complex mathematical concepts. In our example, we focus on addition, which involves combining numbers to find a total sum. It's performed sequentially, starting with the rightmost digits and moving left. Careful alignment of digits is crucial, especially when dealing with large numbers or carrying over values. In adding 442, 325, and 287, we first combine 442 and 325, followed by adding the sum 767 to 287, resulting in 1054. It's essential to understand the significance of each digit according to its place value to arrive at an accurate result. As arithmetic forms the basis of more advanced math problems, mastering it is necessary for academic success and in everyday activities that involve calculations, like budgeting or cooking.

Test Preparation

Preparing for standardized tests like the ACT requires practice and familiarity with various types of math problems. This includes strengthening skills like rounding numbers and basic arithmetic. To optimize test preparation, here are some proven strategies:

• Understand the format of the test and types of questions you'll face.
• Review basic mathematical operations until they can be performed quickly and accurately.
• Practice with past test questions to become efficient in recognizing patterns and common traps.
• Learn time management to ensure that each question gets an appropriate amount of focus.
• Work on developing mental math skills for efficiency, as this frees up time for more challenging problems.

Consistent practice is key to success. Each study session should include a variety of problems, and always examine errors closely to understand where improvements can be made. As with our rounding numbers example, knowing how to swiftly execute basic arithmetic is crucial as it enables you to allocate more time to complex questions that may appear later in the test.