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Chapter 2: Problem 74

Divide. Round to the nearest hundredth. $$31.792 \div 0.86$$

Short Answer

Expert verified
The result is 36.97.

Step by step solution

01

Division

First, divide 31.792 by 0.86 using a calculator. The result will be approximately 36.96976744186047.
02

Rounding to the nearest hundredth

Next, the result should be rounded off to the nearest hundredth. The third place after the decimal point is 9, which is greater than or equal to 5, so the second place after the decimal point, which is 6, should be rounded up by 1. The final answer is 36.97.

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Key Concepts

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

Long Division
Long division is a method used to divide larger numbers that may not easily be divided by simple mental math. In the context of decimals, it involves the same process as with whole numbers, but with an added step to manage the decimal points. To begin, the divisor and dividend are set up in the traditional long division format. Here's a brief overview:

  • Place the divisor (the number you are dividing by) outside the division box, and the dividend (the number you want to divide) inside the box.
  • If the divisor is a decimal, move the decimal point to the right until it is a whole number. You must move the decimal point in the dividend by the same number of places.
  • Proceed with the standard long division steps, bringing down each digit of the dividend one at a time.
  • The quotient, or answer, will also have a decimal point. It should be directly above the decimal point in the dividend within the division box.
For our example, dividing 31.792 by 0.86, you would first convert 0.86 to a whole number by moving the decimal point two places to the right, which also means moving the decimal in 31.792 two places to the right, resulting in 3179.2 梅 86. The long division process would follow from there.
Rounding Decimals
Rounding decimals is a fundamental concept in arithmetic, particularly when you need a number that's easier to work with or when a specific degree of precision is required. To round decimals to the nearest hundredth, you look at the third decimal place, which is the thousandths place. Here's a simple guide:

  • If the third decimal place is 5 or higher, you increase the second decimal place (the hundredths place) by 1.
  • If the third decimal place is 4 or lower, you leave the second decimal place as it is.
  • After rounding, you can discard any remaining digits after the hundredths place.
In the given exercise, rounding 36.96976744186047 to the nearest hundredth means observing the third decimal place (9). Since 9 is greater than 5, we increase the second decimal place (6) by one, leading to the rounded answer of 36.97.
Calculator Use
Using a calculator can be a powerful tool if you understand the steps you're performing. For division with decimals, calculators provide a quick and accurate result. Follow these quick steps:

  • Enter the dividend, 31.792, into the calculator.
  • Press the division key.
  • Enter the divisor, 0.86.
  • Press equals to see the quotient: 36.96976744186047.
From here, you can round off the result as needed, often the calculator will have a key that allows you to directly round to the nearest hundredth, simplifying this process even further. Remember, though, that it's important to understand the process of division before relying on a calculator so to strengthen your mental math skills and ensure you always know the logic behind your calculations.

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