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Chapter 7: Problem 2

Write the ratio 195 to 100 as a percent.

Short Answer

Expert verified
195%

Step by step solution

01

Understand the Ratio

A ratio compares two numbers. In this exercise, the ratio is 195 to 100. We need to convert this into a percentage.
02

Convert the Ratio to a Fraction

Since percentages are based on the number 100, we can express the ratio as a fraction: \( \frac{195}{100} \).
03

Write as a Decimal

Divide 195 by 100 to get a decimal. Do the division: 195 梅 100 = 1.95.
04

Convert the Decimal to a Percentage

To convert a decimal to a percentage, multiply the decimal by 100. So, 1.95 脳 100 = 195%.

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Key Concepts

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

Ratios
A ratio is a way to compare two numbers or quantities. Think of it as a relationship between two values, like comparing the number of apples to oranges in a fruit basket. It helps you understand how much of one thing there is compared to another. You express it as two numbers separated by a colon, for example, 195:100. In our exercise, we have the ratio 195 to 100.
Ratios can be simplified like fractions, but in this case, we are interested in converting it into a percentage. This is because percentages are another common way of expressing the relative size of two quantities, and they are based on 100 parts of a whole.
Fractions
A fraction is another method of expressing numbers in relation to each other. It consists of two parts: the numerator and the denominator. In the ratio 195 to 100, we can express this as the fraction \( \frac{195}{100} \).
  • The numerator (195) is the top number, which tells us how many parts of the whole we have.
  • The denominator (100) is the bottom number, which tells us into how many parts the whole is divided.
When we convert ratios into fractions, it often makes it easier to perform math operations, such as division and multiplication, which are necessary for further conversions like finding percentages or decimals.
Decimals
Decimals are another form of fractions; however, they are based on powers of 10, making them very useful for calculations and conversions. To convert the fraction \( \frac{195}{100} \) into a decimal, we divide the numerator by the denominator. This means we calculate 195 divided by 100, which equals 1.95.
Decimals represent portions of a whole in terms of tenths, hundredths, thousandths, and so on. In our case, 1.95 indicates 1 whole part plus 95 hundredths. Understanding this decimal representation is crucial, as it constitutes an essential step towards converting it into a percentage.
Percentage Conversion
Converting a decimal into a percentage is straightforward. Once you have your decimal, the next step is to bring it into a percentage form, which is widely used to express proportions in everyday situations.
  • Start by taking the decimal number, which in our exercise is 1.95.
  • To convert it to a percentage, you multiply the decimal by 100. This action essentially moves the decimal point two places to the right.
  • So, multiplying 1.95 by 100 gives us 195%.
Percentages express how many parts out of 100 a particular number represents. Thus, saying our original ratio 195:100 as a percentage identifies 195 as 195% when represented in percentage terms, indicating a full value and half again more.

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Most popular questions from this chapter

Write the percent \(362 \%\) as a ratio in fractional form.

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