21 64 as a decimal

Charlotte

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26-02-2025

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Converting Fractions to Decimals: A Step-by-Step Guide (Focusing on 21/64)

Many everyday situations require converting fractions to decimals. Whether you're working on a project, balancing your budget, or simply solving a math problem, understanding how to perform this conversion is crucial. This article will guide you through the process, using the fraction 21/64 as a practical example.

What is a Decimal?

A decimal is a way of writing a number that includes a decimal point, separating the whole number part from the fractional part. Decimals are based on powers of 10 (tenths, hundredths, thousandths, and so on).

Methods for Converting Fractions to Decimals

There are two main methods for converting a fraction like 21/64 to a decimal:

1. Long Division:

This is the most straightforward method. You divide the numerator (the top number, 21) by the denominator (the bottom number, 64).

• Step 1: Set up the long division problem: 21 ÷ 64
• Step 2: Since 21 is smaller than 64, add a decimal point to 21 and add a zero to make it 210.
• Step 3: Now, determine how many times 64 goes into 210. It goes in 3 times (3 x 64 = 192).
• Step 4: Subtract 192 from 210, which leaves 18.
• Step 5: Add another zero to the remainder (180).
• Step 6: Determine how many times 64 goes into 180. It goes in 2 times (2 x 64 = 128).
• Step 7: Subtract 128 from 180, leaving 52.
• Step 8: Continue this process, adding zeros as needed, until you reach the desired level of accuracy or a repeating pattern emerges.

Using long division, 21/64 is approximately 0.328125.

2. Using a Calculator:

The easiest method is simply to use a calculator. Divide 21 by 64, and the calculator will give you the decimal equivalent. This method bypasses the manual steps of long division. Again, the answer is 0.328125.

Understanding the Result

The decimal representation of 21/64 is 0.328125. This means that 21/64 represents 328,125 ten-millionths. Notice that this decimal terminates – it doesn't go on forever. This is because the denominator (64) is a power of 2 ($64 = 2^6$), and fractions with denominators that are powers of 2 or 5 (or both) always result in terminating decimals.

Practical Applications

Converting fractions to decimals is useful in various situations, including:

• Measurements: Converting inches to decimals for precise measurements.
• Financial calculations: Dealing with percentages, interest rates, or unit pricing.
• Data analysis: Working with datasets that require decimal representations.
• Scientific calculations: Expressing quantities in a standard decimal format.

Understanding how to convert fractions to decimals is a valuable skill for anyone working with numbers. While a calculator can quickly provide the answer, understanding the long division method offers a deeper understanding of the underlying mathematical principles. This, in turn, leads to a more confident and accurate approach to calculations involving fractions and decimals.