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Chapter 4: Problem 44

Round the mixed number to the nearest whole number. $$6 \frac{3}{7}$$

Short Answer

Expert verified
6

Step by step solution

01

Understand the Mixed Number

The given mixed number is \(6 \frac{3}{7}\), which consists of a whole part (6) and a fractional part (\(\frac{3}{7}\)).
02

Convert the Fraction to Decimal

Divide the numerator of the fraction (3) by the denominator (7) to get a decimal. \(\frac{3}{7} \approx 0.4286\).
03

Add the Decimal to the Whole Number

Add the decimal value (0.4286) to the whole number (6) to get the decimal equivalent of the mixed number. \(6 + 0.4286 = 6.4286\).
04

Round to the Nearest Whole Number

Look at the decimal part (0.4286). Since it is less than 0.5, round down. Therefore, 6.4286 rounds down to 6.

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Key Concepts

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

Mixed Numbers
A mixed number combines a whole number and a fraction. In this exercise, the given mixed number is \(6 \frac{3}{7}\). Here:
  • 6 is the whole number part
  • \(\frac{3}{7}\) is the fractional part.
A mixed number is useful for representing numbers that aren't whole but also not just fractions.
It makes understanding the size of the number easier. For example, \(6 \frac{3}{7}\) tells you there are 6 whole units and a bit more.
Fraction to Decimal Conversion
To convert a fraction to a decimal, you divide the numerator by the denominator. In our exercise, we have \(\frac{3}{7}\). So, we divide 3 by 7.
This gives us a decimal of approximately 0.4286.
Here鈥檚 a quick recap:
  • The numerator (3) goes inside the division.
  • The denominator (7) goes outside.
  • Perform the division: 3 梅 7 鈮� 0.4286.
Now we have converted the fractional part of our mixed number to a decimal.
Rounding to the Nearest Whole Number
Rounding makes numbers easier to work with by keeping them close to their original values but simpler. In this exercise, we are given a decimal number 6.4286 and we need to round it to the nearest whole number.
Here's how you do it:
Look at the first decimal place:
  • If it鈥檚 5 or higher, round up.
  • If it鈥檚 less than 5, round down.
For 6.4286, the first decimal place is 4, which is less than 5. Therefore, we round down.
So, 6.4286 rounded to the nearest whole number is 6.

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Most popular questions from this chapter

Add or subtract the mixed numbers. Write the answer as a mixed number. $$3 \frac{1}{2}-\left(-2 \frac{1}{4}\right)$$

Write the fraction as an equivalent fraction with the indicated denominator. $$\frac{3}{4 x}=\frac{ }{12 x^{2}}$$

Simplify. $$7 \frac{1}{8} \div\left(-1 \frac{1}{3}\right) \div\left(-2 \frac{1}{4}\right)$$

Solve the equations. Write the answers as fractions or whole numbers. $$\frac{a}{4}=12$$

For Exercises 65鈥�76, convert the improper fraction to a mixed number. $$\frac{37}{8}$$
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