To express 1/16 as a decimal, we need to understand what a decimal is and how it relates to fractions. A decimal is a way of expressing numbers that uses a decimal point to separate the whole number part from the fractional part. Fractions, on the other hand, are a way of expressing a number as a ratio of two integers.
To convert a fraction to a decimal, we need to divide the numerator (top number) by the denominator (bottom number). Let’s take the example of 1/16:
1 ÷ 16 = 0.0625
Therefore, 1/16 as a decimal is 0.0625.
To understand why this works, we need to understand the concept of place value in decimals. In a decimal number, each digit to the right of the decimal point represents a decreasing power of 10. The first digit to the right of the decimal point represents tenths (10^-1), the second represents hundredths (10^-2), the third represents thousandths (10^-3), and so on.
In the case of 0.0625, the 6 represents six tenths, the 2 represents two hundredths, the 5 represents five thousandths, and the 0 to the right of the 5 represents ten thousandths (which we can ignore, as it has no effect on the value of the number).
We can also see that the value of the digits to the right of the decimal point is determined by their position relative to the decimal point. For example, the 6 in 0.6 represents six tenths, while the 6 in 0.06 represents six hundredths.
Another way to think about this is to use the concept of fractions with powers of 10 as the denominators. For example, we can rewrite 0.6 as 6/10 and 0.06 as 6/100. We can then simplify these fractions by dividing both the numerator and denominator by their greatest common factor (in this case, 2), giving us 3/5 and 3/50, respectively.
In the case of 0.0625, we can rewrite it as 625/10,000. We can then simplify this fraction by dividing both the numerator and denominator by their greatest common factor (in this case, 625), giving us 1/16.
Therefore, we can see that 0.0625 and 1/16 are equivalent representations of the same value.
It’s also worth noting that there are other ways to express 1/16 as a decimal. For example, we could use long division to divide 1 by 16, which would give us:
0.06
16|1.00
0
10 8
Copy code20
16
yamlCopy code 40
32
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80
80
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0
Therefore, we can see that 1/16 is equal to 0.0625 or 0.06 (rounded to two decimal places).
In conclusion, to express 1/16 as a decimal, we need to divide 1 by 16. This gives us 0.0625, which represents the value of one sixteenth in decimal form. We can also use the concept of place value in decimals or fractions with powers of 10 as denominators to understand why this works. Finally, we can use long division to find other decimal representations of 1/16, such as 0.06.