Please explain how I write this into a decimal and as a fraction in simplest form:
94.6%
Thanks!
For a decimal, move the decimal point two places to the left or divide by 100.
94.6% = 0.946
Reading the decimal in words we get --
nine hundred forty-six thousandths or
946/1000
Remember that "percent" means "per hundred". So 94.6% means 94.6 per hundred, which is the same as
94.6
-----
100
Either use a calculator or move the decimal point 2 places to the left in the numerator. Either way, you get 0.946.
Reading the decimal, we get 946 thousandths. Or
946
-----
1000
We have to reduce that. Both the numerator and the denominator are divisible by 2. Dividing both by 2 we get
473
---
500
Now the problem is trying to figure out whether or not 473 has any factors at all, let alone any in common with 500. Using the rules of divisibility, we can see that 473 is not divisible by 2, 3, 4, 5, 6, 8, 9, or 10. Trying other numbers shows that 473 is not divisible by 7, but it is divisible by 11: 473 / 11 = 43. However, the only factors of 473 (11 and 43) are both prime, and neither goes into 500, so 473/500 is reduced.
To write 94.6% as a decimal, you need to convert the percentage to its decimal form. To do this, you divide the percentage by 100.
In this case, you divide 94.6 by 100:
94.6 ÷ 100 = 0.946
Therefore, 94.6% can be written as the decimal 0.946.
To write 0.946 as a fraction in simplest form, you have to express the decimal as a fraction by putting the decimal part over the place value of the decimal.
Since the decimal is 0.946, the place value is in the thousandths place (3 decimal places after the decimal point). To convert this decimal to a fraction, you can write it as:
0.946 = 946/1000
However, fractions can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 946 and 1000 is 2.
Dividing both numerator and denominator by 2 yields:
946 ÷ 2 / 1000 ÷ 2 = 473/500
Therefore, 94.6% can be expressed as the decimal 0.946 or as the fraction 473/500 in simplest form.