Problem 47
Question
For exercises \(47-58\), rewrite the percent as a decimal number. $$ 2 \% $$
Step-by-Step Solution
Verified Answer
0.02
1Step 1: Understand what a percent means
A percent means 'per hundred'. For example, 2% means 2 out of 100, or 2 per 100.
2Step 2: Convert the percent to a fraction
Write 2% as a fraction. This is written as \(\frac{2}{100}\).
3Step 3: Simplify the fraction
Simplify the fraction \(\frac{2}{100}\). This fraction is already in its simplest form.
4Step 4: Convert the fraction to a decimal
Convert \(\frac{2}{100}\) to a decimal by dividing the numerator (2) by the denominator (100). \(\frac{2}{100} = 0.02\)
Key Concepts
percentfractionsdecimal conversionsimplifying fractions
percent
Percent is a term we use very often in mathematics and daily life.
It simply means 'out of a hundred.' So, when we say 2%, it means 2 parts out of 100 parts.
Another way to look at it is to consider percentages as a way to measure proportions.
For instance, if you score 80% on a test, you got 80 out of 100 questions correct.
This also means that you can express any percentage as a fraction or a decimal.
Understanding this basic concept helps us with various calculations, especially when converting between different forms like fractions and decimals.
It simply means 'out of a hundred.' So, when we say 2%, it means 2 parts out of 100 parts.
Another way to look at it is to consider percentages as a way to measure proportions.
For instance, if you score 80% on a test, you got 80 out of 100 questions correct.
This also means that you can express any percentage as a fraction or a decimal.
Understanding this basic concept helps us with various calculations, especially when converting between different forms like fractions and decimals.
fractions
Fractions are a way of representing parts of a whole.
In our exercise, we started with 2%, which can be written as a fraction: \(\frac{2}{100}\).
The top number here (the numerator) shows how many parts we have, and the bottom number (the denominator) shows into how many parts the whole is divided.
Knowing how to handle fractions is crucial for converting percentages and simplifying expressions.
Whenever you see a percent, try writing it first as a fraction to make it easier to work with.
This is often the first logical step before any further conversions.
In our exercise, we started with 2%, which can be written as a fraction: \(\frac{2}{100}\).
The top number here (the numerator) shows how many parts we have, and the bottom number (the denominator) shows into how many parts the whole is divided.
Knowing how to handle fractions is crucial for converting percentages and simplifying expressions.
Whenever you see a percent, try writing it first as a fraction to make it easier to work with.
This is often the first logical step before any further conversions.
decimal conversion
Decimal conversion is the process of transforming fractions or percentages into decimal form.
To convert a percentage to a decimal, you divide the percentage by 100.
For instance, converting 2% involves moving the decimal point two places to the left, giving us 0.02.
Mathematically, \(\frac{2}{100} = 0.02\).
This is because division by 100 shifts the decimal point two places.
Decimal is a simpler form for many calculations and helps in quick arithmetic operations.
Getting comfortable with converting between different forms can make solving more complex problems much simpler.
To convert a percentage to a decimal, you divide the percentage by 100.
For instance, converting 2% involves moving the decimal point two places to the left, giving us 0.02.
Mathematically, \(\frac{2}{100} = 0.02\).
This is because division by 100 shifts the decimal point two places.
Decimal is a simpler form for many calculations and helps in quick arithmetic operations.
Getting comfortable with converting between different forms can make solving more complex problems much simpler.
simplifying fractions
Simplifying fractions means making the fraction as simple as possible.
This involves dividing both the numerator and the denominator by their greatest common divisor (GCD).
In our example, \(\frac{2}{100}\), both 2 and 100 can be divided by 2. However, in this specific case, the fraction \(\frac{2}{100}\) is already in its simplest form.
Simplifying fractions helps to make numbers easier to work with.
It also helps in identifying equivalent fractions, making addition and subtraction of fractions easier and helping to understand relationships between different fractional representations.
Mastering this skill is essential for solving many types of mathematical problems efficiently.
This involves dividing both the numerator and the denominator by their greatest common divisor (GCD).
In our example, \(\frac{2}{100}\), both 2 and 100 can be divided by 2. However, in this specific case, the fraction \(\frac{2}{100}\) is already in its simplest form.
Simplifying fractions helps to make numbers easier to work with.
It also helps in identifying equivalent fractions, making addition and subtraction of fractions easier and helping to understand relationships between different fractional representations.
Mastering this skill is essential for solving many types of mathematical problems efficiently.
Other exercises in this chapter
Problem 46
For exercises 39-46, rewrite the percent as a fraction. Simplify the fraction into lowest terms. $$ 117 \% $$
View solution Problem 46
For exercises 1-80, evaluate. $$ (50-24) \cdot 3 \div 2 $$
View solution Problem 47
For exercises \(23-74\), evaluate. $$ \frac{2}{3} \div \frac{4}{27} $$
View solution Problem 47
For exercises 1-80, evaluate. $$ 12 \div 3 \cdot 2 \cdot 4-9 $$
View solution