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Chapter 3: Problem 49

Estimate each of the following as \(0, \frac{1}{2},\) or 1 . $$ \frac{7}{100} $$

Short Answer

Expert verified
The best estimate for \(\frac{7}{100}\) is 0.

Step by step solution

01

Understand the Problem

You need to determine whether the fraction \(\frac{7}{100}\) is closest to \(\frac{0}{1}\), \(\frac{1}{2}\), or \(\frac{1}{1}\).
02

Compare to 0

Compare \(\frac{7}{100}\) to 0. Since \(\frac{7}{100} = 0.07\), it is slightly greater than 0.
03

Compare to \(\frac{1}{2}\)

Next, compare \(\frac{7}{100}\) to \(\frac{1}{2}\). Get a common denominator by rewriting \(\frac{1}{2}\) as \(\frac{50}{100}\). Since \(\frac{7}{100} \) is much smaller than \(\frac{50}{100}\), it is closer to 0 than to \(\frac{1}{2}\).
04

Compare to 1

Finally, compare \(\frac{7}{100}\) to 1. Rewrite 1 as \(\frac{100}{100}\). \(\frac{7}{100}\) is much smaller than \(\frac{100}{100}\), so it is closer to 0.
05

Conclusion

Since \(\frac{7}{100}\) is closer to 0 and not close to \(\frac{1}{2}\) or 1, the best estimate for \(\frac{7}{100}\) is 0.

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Key Concepts

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

Comparing Fractions
Understanding how to compare fractions is essential when working with them. When comparing fractions, one way is to convert them to a common denominator. This allows you to see which fraction is larger or smaller.
For example, to compare \(\frac{7}{100}\) and \(\frac{1}{2}\), you can rewrite \(\frac{1}{2}\) as \(\frac{50}{100}\). Since 7 is much less than 50, \(\frac{7}{100}\) is smaller than \(\frac{1}{2}\).
Another method is to convert fractions to decimals, which we'll explore in another section. Practicing these methods will improve your ability to quickly and accurately compare fractions.
Estimating Fractions
Estimating fractions helps simplify problems. It is useful when you need a rough comparison or a quick answer.
In the exercise, we estimated whether \(\frac{7}{100}\) was close to 0, \(\frac{1}{2}\), or 1. To make this estimation, we compared \(\frac{7}{100}\) with these benchmark values. Since \(\frac{7}{100}\) is much less than \(\frac{50}{100}\) and \(\frac{100}{100}\), it is closer to 0.
Estimation is particularly helpful in real-life scenarios where exact values are not necessary.
Fraction to Decimal Conversion
Converting fractions to decimals can make comparing them easier. To convert a fraction to a decimal, you simply divide the numerator by the denominator.
For instance, \(\frac{7}{100}\) converts to 0.07 by dividing 7 by 100. This conversion shows that \(\frac{7}{100}\) is a small number and very close to 0.
Using decimal conversions often simplifies understanding and can aid in making faster comparisons and estimations.

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Most popular questions from this chapter

Janine took \(\frac{1}{5} \mathrm{~g}\) of ibuprofen before lunch and \(\frac{1}{2} \mathrm{~g}\) after lunch. How much did she take altogether?

Estimate each of the following by estimating each mixed numeral as a whole number or as a mixed numeral where the fraction part is \(\frac{1}{2}\) and by estimating each fraction as \(0, \frac{1}{2},\) or 1 . $$ 24 \div 7 \frac{8}{9} $$

Add and simplify. $$ \frac{1}{2}+\frac{3}{8}+\frac{1}{4} $$

Add and simplify. $$ \frac{8}{10}+\frac{7}{100}+\frac{4}{1000} $$

Simplify. $$ \frac{3}{4} \div \frac{1}{2} \cdot\left(\frac{8}{9}-\frac{2}{3}\right) $$
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