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Chapter 7: Problem 304

In the following exercises, write as the ratio of two integers. $$ 2.9 $$

Short Answer

Expert verified
The ratio is \( \frac{29}{10} \).

Step by step solution

01

- Understanding the Problem

The task is to express the decimal number 2.9 as the ratio of two integers.
02

- Identify Decimal Form

Identify the decimal number 2.9 and recognize that it can be expressed as a fraction.
03

- Write as a Fraction

Considering 2.9, we can write it as \( \frac{29}{10} \). This is because 2.9 means 29 tenths.
04

- Simplify the Fraction

The fraction \( \frac{29}{10} \) is already in its simplest form because 29 and 10 have no common divisors other than 1.

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Key Concepts

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

decimal to fraction conversion
When you encounter a decimal number like 2.9, you can convert it to a fraction. The process is straightforward, and understanding it can help greatly in your math studies. The first step is to recognize the decimal and understand its place value. Here, 2.9 translates to 2 whole units and 9 tenths. To write it as a fraction, think of the decimal as being over a power of ten. Since the number 9 is in the tenths place, you can write 2.9 as \( \frac{29}{10} \). This is the process of converting a decimal to a fraction.
ratios
A ratio is a way to compare two numbers by expressing one as a fraction of the other. In this example, you expressed 2.9 as the ratio \( \frac{29}{10} \). This means for every 10 units, there are 29 corresponding units, clearly showing the relationship between the two numbers. Understanding ratios is valuable in many areas of mathematics and daily life, such as calculating proportions in recipes or determining scale in models. When you see a decimal, always remember it can potentially be converted into a ratio of two integers, enabling easier comparisons and applications.
simplifying fractions
After converting a decimal to a fraction, the final step is to simplify the fraction, if possible. Simplifying involves reducing the fraction to its lowest terms. This means you find the greatest common divisor (GCD) of the numerator and denominator and divide both by that number. In the exercise, \( \frac{29}{10} \) is already in its simplest form because 29 and 10 have no common divisors other than 1. Simplifying fractions makes them easier to work with and understand. Always check if the numerator and denominator can be divided by a common factor to achieve the simplest form.

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Most popular questions from this chapter

In the following exercises, solve using the appropriate unversions. Larry had 5 phone customer phone calls yesterday. The calls lasted \(28,44,9,75,\) and 55 minutes. How much time, in hours and minutes, did Larry spend on the(1 hour \(=60\) minutes)

In the following exercises, solve and write your answer in mixed units. Judy bought 1 pound 6 ounces of almonds, 2 pounds 3 ounces of walnuts, and 8 ounces of cashews. What was the total weight of the nuts?

Cooking time Helen bought a 24-pound turkey for her family鈥檚 Thanksgiving dinner and wants to know what time to put the turkey in the oven. She wants to allow 20 minutes per pound cooking time. a. Calculate the length of time needed to roast the turkey by multiplying 24\(\cdot 20\) to find the number of minutes and then multiplying the product by \(\frac{1}{60}\) to convert minutes into hours. b. Multiply 24\(\left(20 \cdot \frac{1}{60}\right)\) c. Which of the Properties of Real Numbers allows you to multiply 24\(\left(20 \cdot \frac{1}{60}\right)\) instead of \((24 \cdot 20) \frac{1}{60} ?\)

In the following exercises, ldentify whether each given number is rational or irrational. $$ (a)\sqrt{72} $$ $$ (b)\sqrt{64} $$

In the following exercises, identify whether each example is using the identity of addition or multiplication. $$ 29+0=29 $$
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