How to Convert Decimals Expansions

How to Convert Decimal Expansions – Introduction

In mathematics, the ability to convert decimal expansions into fractions, percentages, and even different number systems like binary or hexadecimal, is essential. These skills are not only useful in practical situations, such as calculating sales discounts or analyzing data, but also form the basis for more complex concepts encountered in high school and beyond.

Understanding Decimal Conversions – Explanation

Converting decimal expansions involves changing a decimal number into other forms, such as fractions, percentages, or different bases (binary, hexadecimal, octal), depending on the requirement.

The process may differ slightly depending on the target form, but generally includes multiplying, dividing, or applying specific rules to achieve the desired conversion.

Conversion Type Step Example Result
Decimal to Fraction Write the decimal over 1 and simplify. $0.75 \to \frac{0.75}{1}$ $\frac{3}{4}$
Multiply to eliminate the decimal point and simplify. Multiply $0.75$ by $100$ to get $\frac{75}{100}$. $\frac{3}{4}$ (after simplifying)
Decimal to Percent Multiply the decimal by 100 and add the percent symbol. $0.75 \times 100$ $75\%$

Converting Decimals to Fractions

Convert $0.5$ to a fraction.

• Write the decimal over 1: $\frac{0.5}{1}$
• Multiply to remove decimal: Multiply by $10$ to get $\frac{5}{10}$
• Simplify: Divide both by their greatest common divisor ($5$), resulting in $\frac{1}{2}$
Convert $0.25$ into a fraction.
What is $0.125$ expressed as a simplified fraction?
How would you write $0.75$ as a fraction in simplest form?

Converting Repeating Decimals to Fractions

Express $0.333...$ as a fraction.

• Let $x = 0.333...$
• Multiply by $10$ to get $10x = 3.333...$
• Subtract $x$ from $10x$ to find $9x = 3$
• Divide both sides to find $x = \frac{1}{3}$
Convert $0.777...$ into a fraction.
What is the fraction form of $0.8181...$?
Express $0.2121...$ as a fraction.

Converting Decimals to Percentages

Express 0.5 as a percentage.

• Multiply by 100: $0.5 \times 100 = 50$%
• Attach the percent symbol: 50%
Convert 0.65 into a percentage.
What is 0.03 as a percentage?
Express 2.5 as a percentage.

Converting Decimals to Scientific Notation

Convert 0.00057 to scientific notation.

• Move the decimal: After the first non-zero digit to get 5.7.
• Count the places: Moved the decimal 4 places to the left.
• Write in scientific notation: $5.7 \times 10^{-4}$
Write 0.0073 in scientific notation.
Express 0.0000012 in scientific notation.
How would you express 0.09 in scientific notation?

Converting Decimals to Binary, Hexadecimal, and Octal

Convert the decimal number 5 to binary.

• Divide by 2: 5 ÷ 2 = 2 remainder 1 (LSB).
• Continue dividing: 2 ÷ 2 = 1 remainder 0.
• Until the quotient is 0: 1 ÷ 2 = 0 remainder 1 (MSB).
• Read remainders from bottom to top: 101.
Convert the decimal number 15 to binary.
Convert the decimal number 7 to hexadecimal.
What is the octal equivalent of the decimal number 10?

How to Convert Decimal Expansions – Summary

Key Learnings from this Text:

• To convert decimals to fractions, multiply by 10n where n is the number of decimal places and simplify the fraction.
• Repeating decimals can be converted to fractions by setting up algebraic equations.
• Multiplying a decimal by 100 converts it to a percentage.
• Scientific notation of decimals involves moving the decimal point to just after the first non-zero digit and indicating the number of moves as a power of 10.
• Decimals can be converted to binary, hexadecimal, or octal by dividing by the base and recording remainders.

Explore other content on our website platform for interactive practice problems, videos, and printable worksheets to further enhance your understanding of decimal conversions.

How to Convert Decimal Expansions – Frequently Asked Questions

How do you convert a decimal to a fraction?
Can repeating decimals be converted into fractions?
How do you convert a decimal to a percentage?
What are the steps to convert a decimal to scientific notation?
What is the process for converting decimals to binary?
Is there a difference between converting decimals to binary and to hexadecimal?
How can you convert a decimal to an octal number?
Can all decimals be converted into fractions?
What do you do with the decimal when converting to scientific notation?
Why do you multiply by 100 to convert a decimal to a percentage?
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