Written as fractions, the decimal numbers 0.3 and 0.11 are 3/10 and 11/100, respectively. Can you see a pattern? Use this knowledge to convert 0.0625 into a fraction.Then find its simplest form.
Yes, the pattern is that the number of decimal places determines the denominator of the fraction.
For example, 0.3 has one decimal place, so the denominator is 10. 0.11 has two decimal places, so the denominator is 100.
To convert 0.0625 into a fraction, we count the number of decimal places (four) and use that as the denominator:
0.0625 = 625/10000
To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 625:
625/10000 ÷ 625/625 = 1/16
Therefore, 0.0625 can be written as the fraction 1/16 in simplest form.
Yes, there is a pattern in converting decimals to fractions.
To convert a decimal to a fraction, we can compare the decimal number to its place value.
For example:
- In the decimal 0.3, the 3 is in the tenths place. So, it can be written as 3/10.
- In the decimal 0.11, the 11 is in the hundredths place. So, it can be written as 11/100.
Now, let's convert the decimal 0.0625 into a fraction.
The decimal 0.0625 can be written as 625/10000 because the 625 is in the ten-thousandths place, and there are four decimal places in the number.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 625 in this case.
Calculating the GCD of 625 and 10000, we find that the GCD is 625.
Dividing both 625 and 10000 by 625, we get:
625 ÷ 625 = 1
10000 ÷ 625 = 16
Therefore, the simplified fraction for 0.0625 is 1/16.