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Chapter 5: Problem 16

Write each number as a fraction or a mixed number. Do not reduce your answers. $$2.00106$$

Short Answer

Expert verified
The number is \( 2 \frac{106}{100000} \) as a mixed number.

Step by step solution

01

Identifying the Whole and Decimal Parts

Observe carefully that the number given is 2.00106. Here, the whole number part is 2 and the decimal part is 0.00106.
02

Expressing the Decimal Part as a Fraction

To express 0.00106 as a fraction, count the number of decimal places. There are 5 decimal places, which means 0.00106 is equivalent to \( \frac{106}{100000} \).
03

Combining to Form a Mixed Number

Combine the whole part from Step 1 with the fraction from Step 2. Therefore, the mixed number form is \( 2 \frac{106}{100000} \).

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Key Concepts

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

Decimal to Fraction Conversion
Converting a decimal to a fraction involves expressing the decimal in terms of a numerator (on top) and a denominator (on the bottom). It's simpler than it sounds! The key is knowing how many decimal places your number has, because this determines the denominator.
  • First, count the decimal places. For instance, in the decimal 0.00106, there are 5 places because the decimal ends at the digit 6 with four zeros ahead of it.
  • Next, write the decimal as a fraction. Each decimal place represents a power of ten. So, 0.00106 becomes a fraction where the numerator is 106 (the digits after the decimal), and the denominator is 100,000 (10 to the power of 5).
  • This forms the fraction \( \frac{106}{100000} \).

Turning decimals into fractions is all about placing your decimal in the context of base 10 mathematics. Practice with different decimals will solidify your understanding of this process.
Mixed Numbers
Mixed numbers combine a whole number portion with a fraction. This kind of representation is commonly used in scenarios where you have a total that overflows into more than just a fraction but isn't a whole number either.
  • The first part is the whole number. In our exercise, the number 2 is the whole part.
  • The second part is our fraction, \( \frac{106}{100000} \), which came from turning the decimal into a fraction.

Together, these two parts make up a mixed number, written as \( 2 \frac{106}{100000} \). Mixed numbers are handy because they express values in a way that instantly shows how much you have past the nearest whole number. Using them correctly can make dealing with numbers in real-world contexts a lot easier.
Whole Numbers in Fractions
When placing a whole number into a fraction, remember that any whole number can be expressed over the number 1. This is useful when you want to include a whole number in arithmetic that involves fractions, such as addition or subtraction.
  • A whole number like 2 can be represented as \( \frac{2}{1} \).
  • This way, the whole number can easily be combined with fractions.

In problems requiring the combination of whole numbers and fractions, writing the whole number as a fraction simplifies the process. For instance, combining the fraction from decimal conversion with the whole number 2 as in \( \frac{2}{1} \), makes forming mixed numbers or doing further operations straightforward.

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Most popular questions from this chapter

A surveying team wants to calculate the length of a straight tunnel through a mountain. They form a right angle by connecting lines from each end of the proposed tunnel. One of the connecting lines is 6 miles, and the other is 8 miles. What is the length of the proposed tunnel?

Indicate whether each of the statements is True or False. $$\sqrt{100}-\sqrt{36}=\sqrt{100-36}$$

Use the rule for order of operations to simplify each expression. $$12+18 \div 2-1$$

Add and subtract as indicated. $$8.3-(1.2+3.4)$$

Perform the following operations according to the rule for order of operations. $$4.09+0.5(6+0.02)$$
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