8.75 as a Decimal: Understanding Decimals and How to Convert Them
If you’ve ever been confused about how to convert decimals, you’re not alone. Understanding how decimals work and how to convert them can be a challenging task. In this article, we’ll be discussing the decimal number 8.75 and how to convert it into different formats. We’ll also be looking at the history of decimals and how they’ve evolved over time.
Table of Contents
What is a Decimal?
Decimals are a system of numbers that use the base 10, which means that there are 10 possible digits (0-9) that can be used in each place value. The decimal point separates the whole number from the fractional part of the number.
History of Decimals
The concept of decimals has been around since ancient times. The Babylonians and the Mayans both used a base 20 system, which included fractions. The decimal system as we know it today was developed in India around 500 AD. This system was brought to Europe by the Arabs in the 12th century and quickly became widely adopted.
Understanding Decimal Places
The decimal point separates the whole number from the fractional part of the number. Each digit to the right of the decimal point represents a specific decimal place. For example, in the number 8.75, the 7 represents the tenths place, and the 5 represents the hundredths place.
Converting 8.75 into Different Formats
Converting to a Fraction
To convert 8.75 to a fraction, we first need to count the number of decimal places. Since there are two decimal places, we’ll place 8.75 over 100.
8.75/100 = 875/1000
We can simplify this fraction by dividing both the numerator and denominator by 125:
875/1000 = 7/8
Therefore, 8.75 as a fraction is 7/8.
Converting to a Percentage
To convert 8.75 to a percentage, we multiply by 100:
8.75 x 100 = 875%
Therefore, 8.75 as a percentage is 875%.
Converting to Scientific Notation
To convert 8.75 to scientific notation, we first need to move the decimal point so that there is only one digit to the left of the decimal point. In this case, we can simply move the decimal point one place to the left:
8.75 = 8.75 x 10^0
Therefore, 8.75 in scientific notation is 8.75 x 10^0.
Converting to Binary
To convert 8.75 to binary, we first need to convert the whole number part and the fractional part separately.
Whole Number Part
To convert the whole number part (8) to binary, we use the repeated division-by-2 method:
8 / 2 = 4 remainder 0
4 / 2 = 2 remainder 0
2 / 2 = 1 remainder 0
1 / 2 = 0 remainder 1
Therefore, 8 in binary is 1000.
Fractional Part
To convert the fractional part (.75) to binary, we use the repeated multiplication-by-2 method:
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0.75 x 2 = 1.5 -> 1
0.5 x 2 = 1.0 -> 1
