Questions and Answers
What is a decimal?
A decimal is a way to represent a number using base 10 to show part of a whole.
How do you convert a fraction to a decimal?
To convert a fraction to a decimal, divide the numerator by the denominator.
What is the result of converting 3/4 to a decimal?
The result is 0.75.
How would you convert the decimal 0.5 to a fraction?
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What is the difference between terminating and non-terminating decimals?
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What method can you use to compare decimals?
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Describe the process of adding decimals.
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What is the first step to add fractions?
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How can you multiply a fraction?
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What does it mean to divide fractions?
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Study Notes
Decimals
- A decimal is a way to represent a number using base 10
- Decimals are used to show part of a whole
- Decimals can be terminating (ending) or non-terminating (repeating)
- Terminating decimals have a finite number of digits, while non-terminating decimals have an infinite number of digits
Converting Fractions to Decimals
- To convert a fraction to a decimal, divide the numerator by the denominator
- For example, 3/4 = 0.75
- If the division does not result in a whole number, the decimal will be non-terminating
- For example, 1/3 = 0.333... (non-terminating)
Converting Decimals to Fractions
- To convert a decimal to a fraction, write the decimal as a fraction with the same denominator as the number of decimal places
- For example, 0.5 = 1/2
- If the decimal is non-terminating, the fraction will be a repeating decimal
- For example, 0.333... = 1/3
Comparing and Ordering Decimals and Fractions
- Decimals and fractions can be compared and ordered using the same rules as whole numbers
- Decimals can be compared by looking at the digits from left to right
- Fractions can be compared by converting them to decimals or by comparing the numerators and denominators
Adding and Subtracting Decimals and Fractions
- Decimals can be added and subtracted by lining up the decimal points
- Fractions can be added and subtracted by finding a common denominator
- When adding or subtracting decimals and fractions, convert the fraction to a decimal first
Multiplying and Dividing Decimals and Fractions
- Decimals can be multiplied by multiplying the numbers as usual
- Fractions can be multiplied by multiplying the numerators and denominators separately
- Decimals can be divided by dividing the numbers as usual
- Fractions can be divided by inverting and multiplying
Decimals
- Decimals represent numbers using base 10, illustrating parts of a whole.
- Two types of decimals: terminating (finite digits) and non-terminating (infinite digits).
Converting Fractions to Decimals
- To convert fractions to decimals, divide the numerator by the denominator.
- Example: 3/4 equals 0.75, a terminating decimal.
- Non-terminating decimals emerge when divisions don't result in whole numbers.
- Example: 1/3 equals 0.333..., which is non-terminating.
Converting Decimals to Fractions
- To convert a decimal to a fraction, use a denominator based on the number of decimal places.
- Example: 0.5 translates to 1/2.
- Non-terminating decimals result in repeating fractions.
- Example: 0.333... converts to 1/3.
Comparing and Ordering Decimals and Fractions
- Decimals and fractions can be ordered similarly to whole numbers.
- Compare decimals by examining digits from left to right.
- Comparisons of fractions can be made by converting to decimals or comparing numerators and denominators.
Adding and Subtracting Decimals and Fractions
- Adding and subtracting decimals requires aligning decimal points.
- Fractions need a common denominator for addition or subtraction.
- Convert fractions to decimals before mixing addition or subtraction with decimals.
Multiplying and Dividing Decimals and Fractions
- Multiply decimals normally by multiplying corresponding numbers.
- Multiply fractions by multiplying respective numerators and denominators.
- Decimal division occurs similarly to regular division.
- To divide fractions, invert the second fraction and multiply.
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Description
Learn about decimals, their types, and how to convert fractions to decimals through division of numerator by denominator. Understand the difference between terminating and non-terminating decimals.
